TECHNICAL CORNER by Greg Sitek

Introducing the

Cat C-series Power Shift T

he new Caterpillar® Power Shift transmission increases productivity and operator comfort by providing a single lever to control both speed and direction. The best keeps getting better. The Cat backhoe loader continues to be the best in its class - now with optional Power Shift. Change gears and directions effortlessly, while maintaining continuous traction throughout the work cycle. You’ll work faster with greater operator comfort. One lever does it all. The conventional shifter has been replaced by a twist-grip on the forwardreverse shuttle. This improves operator comfort and productivity by allowing direction and speed changes to be made with a single lever. There’s no floor-mounted gear shift lever, so the operator has more cab floor space. A neutral start provision prevents starting while directional clutches are engaged.

22 • ON YOUR OWN

Five forward gears. An additional forward speed is provided between the normal working and hauling ranges. Softer steps between 2nd, 3rd, and 4th gears enhance shift quality and powertrain durability while reducing wheel slip. Reverse gear ratios have been improved to better match application needs and increase loading cycle performance. Auto-Shift. With 4th forward gear selected, the Power Shift control system automatically shifts between 4th and 5th gears to maintain road speed. However, when higher speeds are not needed, a manual 5th-gear lockout switch prevents automatic shifts - especially desirable during such applications as load and carry. Transmission Disconnect. The loader control does not change with the Power Shift option. A transmission disconnect button is provided to divert full engine power to the main hydraulic pump. Torque Converter. Single stage, 2.63:1 stall ratio. Travel Speeds. Travel speeds at a full throttle when equipped with 16.9 x 24 rear tires, 3.6 to 20 mph. Caterpillar Model Availability. The new Power Shift transmission is available as an option on the following C-Series backhoe loaders — 416C (80 hp), 426C and 436C. ■

A single lever controls both speed and direction.

THE CAT EQUIPMENT LINE Building Construction Products Division

Backhoe Loaders 416C • 426C • 436C • 446B

Telescopic Handlers TH62 • TH63 • TH82 • TH83 • TH103

Track-Type Tractors and Loaders D3C III • D4C III • D5C III • 933C • 939C

Integrated Toolcarriers IT14G • IT24F • IT28G

Wheel Loaders 914G • 924F • 928G

Hydraulic Excavators 307 • 311B • 312B • 315B • M318

POWER SHOVEL • To

excavate the earth and load it into the trucks or other hauling equipments.

• Suitable for all class of earth except solid rocks. TYPE: By

its mounting

• Crawler-mounted power shovel • Wheel-mounted power shovel SIZE: By

the size of dipper

3/8, ½, ¾, 1, 1.25, 1.5, 2, 2.5 m3 etc. PARTS: Cab,

Dipper, Boom, Hoist line, Dipper stick, Mounting- Crawler or Wheel

OPERATION: Release

hoist line à Position Shovel à Boom apply downward force

by dipper stick àPull by hoisting line à Empty the dipper by opening the door.

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DRAGLINE •

Excavate earth and load it into hauling equipments or deposit it to site.

• Boom is light and long. • Function same as Power shovel TYPE: By its mounting •

Crawler-mounted Dragline – 2 kmph

• Wheel-mounted Dragline – 50 kmph • Truck-mounted Dragline – 50 kmph SIZE: By the size of bucket

Advantages •

A Dragline does not have to go into the pit – useful in removing the earth from a ditch, canal or pit.

• When excavating earth is to be deposited on nearby banks. • Good for trenching PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com

Disadvantages Output in terms of excavating earth is 70 to 80 % of power shovel.

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CLAMSHELLS •

Consists of a bucket of two halves, which are hinged together at top.

• Buckets are attached to the shovel Crane units or at the boom of a Dragline. • Digging is done like a Dragline and once the bucket is filled, it works like a Crane. • Suitable for loose material. • Suitable for vertical lifting of materials. TYPE: Bucket •

is classified as

Light bucket – for handling loose materials

• Heavy bucket – used for digging purposes and has long and sharp teeth.

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HOE •

Excavating equipment of the power shovel group.

• Exert greater tooth pressure. • Generally used in quarries which have tough digging conditions. • Dig trenches, footings or basements. • Operate on close-range work and dump into trucks.

OPERATION: Place

boom at the desired angle à Dipper moves at desired position

à Release hoist Cable to lower down the boom à Pull Cable à Raise boom and swing to the dumping position.

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SCRAPERS •

Tractor-pulled Scrappers are Self-sufficient and self operating construction equipment designed to scrape the ground, load it simultaneously, transport it over the required distance, dump and spread..

• Used in a wide range of material types • Economical over a wide rage of haul lengths and haul conditions. • Best suited for haul distances greater than 500 ft but less than 3000 ft. PRODUCTION CYCLE:

(1) Loading (2) haul travel (3) dumping and spreading (4) turning (5) return travel, and (6) turning and positioning to pick up another load. NOTE: Since

Scrapers are a compromise between machines designed exclusively

for either loading or hauling, they are not superior to function-specific equipments in either hauling or loading.lease hoist PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com

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DOZERS • • • •

Effective and versatile earth moving m/c. Is a tractor-power unit that has a blade attached to the machine’s front. The blade is used to push, shear, cut and roll material ahead of dozer. Used for ¤ Moving earth or rock for short haul distances. ¤ Spreading earth or rock fills ¤ Back-filling trenches. ¤ Clearing land of trees and stumps including roots and of vegetation. ¤ Opening of temporary roads through rocky areas. ¤ Helping load tractor-pulled scrappers. ¤ Clearing the construction sites of debris and rubbish. ¤ Maintaining haul roads. ¤ Stripping of the top soil that is not usable etc.

Bulldozer : Blade is set perpendicular to the direction of travel. Angledozer : If set at an angle.

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Types of Dozers 1. Crawler type 2. Wheel type

Crawler Type • Can work on variety of soil – travel over very rough surfaces. • Good for short work distance. • Can handle light soils • Slow return speeds • Can push large blade load Wheel Type • Best for level and downhill work. • Good for long travel distances • Best in handling loose soil • Can only handle moderate blade loads • Travel on paved soil without damaging the surfaces. PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com

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Wheel Excavators

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Crawler Excavator

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HOE

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HOE

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DRAGLINE

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Scrapers: Reynolds International

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PULL-TYPE SCRAPERS Bell

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Clamshell Buckets

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CRAWLER DOZER

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DOZER Komatsu

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EXCAVATOR AND BULLDOZER Kobelco

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Pavers

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“LA NUEVA MEDIANA MINERIA” PALAS HIDRÁULICAS 12 DE AGOSTO DE 2008

INDICE • Modelos disponibles de palas hidráulicas

• Comparación Palas vs Cargador sobre ruedas • Operación • Capacidad de Carga • Especificaciones • Movilidad

• Match Pala – Camión • Pala Frontal y Retro (producción) • Caracteristicas Generales de Palas • Preguntas

Palas Hidráulicas Terex O&K RH RH 40-E 40-E 84-90 t 392 kW 7,0 m³ (SAE 1:1)

RH RH 90-C 90-C 180 t 730 kW 10.0 m³ (SAE 2:1)

RH RH 170B 170B 380 t 1516 kW 22.0 m³ (SAE 2:1)

RH RH 340B 340B 553 t 2240 kW 34.0 m³ (SAE 2:1)

RH RH 70 70 102-112 t 477 kW 8.0 m³ (SAE 2:1)

RH RH 120-E 120-E 282 t 1008 kW 16,5 m³ (SAE 2:1)

RH RH 200 200 525 t 1680-1880 kW 26.0 m³ (SAE 2:1)

RH RH 400 400 1000 t-class 3280 kW 50.0 m³ (SAE 2:1)

Comparasión Excavadora Hidráulica O&K RH 40 E vs.

Cargador sobre Ruedas

Operación General Cargador Frontal Suelto, material tronado Gran área de carga (25 m) Nivelado, estable, seco Aprox. 16 pies (5 m) Siempre de abajo hacia arriba Baja: 480 lbf/in (0.85 kN/cm) Aprox. 45 segundos Alta: 21.8 mph (35 km/h) 60 - 80 psi Descarga descontrolada Visibilidad Limitada No

O&K RH 40 E Rango de Material Area de Carga Condición de Piso Altura de Banco Selectividad Fuerza de Penetración Tiempo de Ciclo Velocidad de Traslado Presión sobre el suelo Carga de Camiones Carga de Camiones Equipos de Apoyo

Compacto, aún sin tronar Area de carga reducida Deformado, húmedo, suelto Aprox. 38 pies (12 m) Carga selectiva Alta: 960 lbf/in (1.7 kN/cm) Aprox. 30 segundos Baja: 1.56 mph (2.5 km/h) 15 - 30 psi Descarga Controlada Buena visibilidad Pala: No, Retro: Si

Operación Cargador Frontal

Pila

Optimo Optimo Ciclo Ciclo Total: Total: 177.5 177.5 ftft (54.08 (54.08 m) m) 4 ft 2m

Cat 773 D

39’ 1” (11.90 m)

39’ 1” (11.90 m)

50’ 6” each (15.14 m) Radio de Giro Cargador: 24’ 10” (7.57 m)

Operación Pala Hidráulica

Frente

4 ft 2m O&K RH 40 E

Máxima Capacidad de Carga Cargador sobre Ruedas: Capacidad del Balde:

6.0 m3

Tiempo de Ciclo (favorable):

36-39 segundos

Ciclos por hora:

92 - 100

Factor de llenado:

100%

Máxima Producción:

957 - 1,040 t/hr

Excavadora Hidráulica:

RH 40 E

Capacidad del Balde :

7.0 m3

Tiempo de Ciclo (favorable):

23-26 segundos

Ciclos por hora:

138 - 156

Factor de llenado:

95%

Máxima Producción:

1,468 - 1,660 t/hr

Producción de la excavadora es hasta un 60% mayor

Especificaciones de las Máquina O&K RH 40 E

101,000 lb (46.1 t) 300 hp (224 kW) 8.0 yd3 (6.0 m3) 5 ciclos 3.2 min. 18.8 1.040 t/hr

Peso de Operación Potencia Motor Capacidad del Balde para Densidad 1,8 t/m3 Ciclos de Carga para Cat 773D (52.3 t) Tiempo de carga de camión Número max. de camiones por hora Máxima Producción por hora

487 lb/in (0.855 kN/cm) 14.6 mph (35.1 km/hr) 16 pies (4.9 m) 4” (0.098 m) 20” (0.50 m)

Fuerza de desgarramiento Velocidad de Traslado Max. Altura Excavación Max. Profundidad Excavación Distancia al suelo

220,000 lb (100 t) 607 hp (453 kW) 9.2 yd3 (7.0 m3) 4 ciclos 1.67 min. 35.9 1,660 t/hr

1,042 lb/in (1.82 kN/cm) 1.56 mph (2.5 km/hr) 36 pies (10.9 m) 83” (2.10 m) 35” (0.90 m)

La única ventaja del cargador sobre ruedas es la velocidad de desplazamiento. Todas las otras comparaciones son desfavorables

Costos O&K RH 40 E


COSTO CAPITAL
COSTO OPERACION
Reparaciones
Neumáticos
Lubricantes
Filtros
Combustible

Costos O&K RH 40 E

Costo de propiedad y operación por hora Menor Costo Excavadora: 13.13 % Costo de propiedad y operación por tonelada Menor Costo Excavadora: 44.85 %

Verdad Simple CARGADOR SOBRE RUEDAS Baja Producción a un Alto Costo pero tiene Gran Versatilidad

EXCAVADORA HIDRÁULICA No es un auto de carrera pero tiene Alta Productividad a Bajos Costo

Definición de cual es la verdad Costo Tons

Excavadora Hidráulica Favorable

Cargador de Ruedas Favorable

Costo por ton Excavadora Hidráulica

Costo por ton Cargador de Ruedas

Producción (t/hr) Cargador de Ruedas Producción (t/hr) Excavadora Hidráulica

Distancia de Traslado

Producción A mayor distancia de traslado menor es la producción horaria. La productividad de las excavadoras hidráulicas depende mucho mas de las distancias de traslado comparada con los cargadores de ruedas. Costos El costo por tonelada aumentará si existen mayores distancia de traslado. Esto se refleja con mayor incidencia en una excavadora hidráulica que en un cargador sobre ruedas equivalente

Soluciones para Incrementar la Movilidad SLEIPNER • Dos estructuras separadas con dos ruedas cada una y frenos de parqueo • Menor desgaste en los componentes del rodado • Velocidad de traslado 20 km/hr, pendientes de 15° • Se requieren 3 minutos de preparación

Operación Llenado de Balde Cargador de Ruedas Excavadora Hidráulica Generación de fuerza de penetración

ataque dinámico por manejo a la pila

hidráulica por cilindros

Cinemática

restringida

avance (frentes altas)

Estabilidad (confort del operador)

bajo (peso operación y métodos de trabajo)

alto (peso operación)

Minería Selectiva

dificil

fácil debido a configuración con Tripower

Excavación

no hay opción

factible debido a las altas fuerzas de penetración y desprendimiento

Operación Descarga

Cargador de Ruedas

Excavadora Hidráulica

Max. Altura descarga

suficiente

app. 20 % mas alta

Visión del Operador

suficiente

excelente

Descarga segura y controlada

dificil, por cercanía al camión y descarga adelantando solamente el balde

controlling of bucket opening width via cylinders and higher safety distance

Carga a dos lados

necesita gran espacio proceso de carga normal peligroso como equipo rápido en movimiento

Condiciones de Piso

se requieren pisos suaves y planos

no es necesario pisos planos, recomendable para camiones

Operación Resumen

Cargador de Ruedas Excavadora Hidráulica

Objetivos Principales carga

excavación y carga

Aplicaciones

operaciones de carga y traslado excava en material suelto

Excava y suelta material consolidado carga rápida

Desgaste

tensión en la estructura y articulación

menor tensión, debido a movimientos constantes

Aplicación Recomendada

carga en material bien excavación y carga de tronado con frecuentes material consolidado cambios de fase

Match Pala Camión RH40 pases 771 D 45 ton / 41 t

773 E 60 ton / 55 t

775 E

777 D

70 ton / 63 t

100 ton / 91 t

RH 40-E 7.0 m³ / 9.2 yd³ SAE 1:1

RH 40-E 7.0 m³ / 9.2 yd³ SAE 2:1

Calculos basados en densidad suelta de 1.8 t/m³ y 100 % factor de llenado

Match Pala Camión RH 90-C CAT 775E 62 - 63 t 68 - 70 tc

Aplicación Estándar Densidad Suelta 1.8 t/m³

CAT 777D 91 - 96 t 100 - 106 tc

Match Pala Camión RH 120-E CAT 777D 91 - 96 t 100 - 106 tc 3 - 4 Ciclos

Aplicación Estándar Densidad suelta 1.8 t/m³

CAT 785 C 136 - 154 t 150 – 170 tc 5 - 6 Ciclos

RH 40-E Pala Frontal con TriPower 477 kW 640 HP

7.0 m³ (2:1)

500 kN

104 t 650 kN

11

Pala Frontal y Tripower

10

•

7.0 m³

•

Fuerza de Penetración: Max. 650 kN

•

Fuerza de desprendimiento Max. 500 kN

•

Productividad Max: 1400 t/h Promedio: 1000 t/h

9 8 7 6 5 4 3 2 1 0 -1 -2 -3 12 11

10

9

8

7

6

5

4

3

2

1

0 m

Producción RH 40-E (Pala Frontal) Bucket size

7,0 m³ Fill factor

100%

95%

90%

12,6 t 63,0 t

12,0 t 59,9 t

11,3 t 56,7 t

Cycle time Truck spotting 30 sec

83%

78%

73%

68%

63%

Material density: 1,8 t/m³

Load per bucket Load per truck Utilizatiion

Number of cycles: 5

0,50 min

21 sec

23 sec

25 sec

27 sec

21 sec

23 sec

25 sec

27 sec

21 sec

23 sec

25 sec

27 sec

0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 1621 t/h 1524 t/h 1412 t/h 1338 t/h 1540 t/h 1448 t/h 1341 t/h 1271 t/h 1459 t/h 1372 t/h 1271 t/h 1204 t/h

45 sec

0,75 min

1436 t/h 1359 t/h 1269 t/h 1209 t/h 1364 t/h 1291 t/h 1206 t/h 1149 t/h 1292 t/h 1223 t/h 1142 t/h 1088 t/h

60 sec

1,00 min

1288 t/h 1227 t/h 1153 t/h 1103 t/h 1224 t/h 1165 t/h 1095 t/h 1048 t/h 1160 t/h 1104 t/h 1037 t/h

992 t/h

75 sec

1,25 min

1168 t/h 1117 t/h 1056 t/h 1014 t/h 1110 t/h 1061 t/h 1003 t/h

912 t/h

963 t/h

1052 t/h 1006 t/h

950 t/h

30 sec

0,50 min

1524 t/h 1433 t/h 1327 t/h 1257 t/h 1448 t/h 1361 t/h 1261 t/h 1194 t/h 1371 t/h 1289 t/h 1194 t/h 1132 t/h

45 sec

0,75 min

1349 t/h 1277 t/h 1193 t/h 1136 t/h 1282 t/h 1214 t/h 1133 t/h 1079 t/h 1214 t/h 1150 t/h 1073 t/h 1023 t/h

60 sec

1,00 min

1211 t/h 1153 t/h 1083 t/h 1036 t/h 1150 t/h 1095 t/h 1029 t/h

985 t/h

1090 t/h 1037 t/h

975 t/h

933 t/h

905 t/h

988 t/h

893 t/h

857 t/h

75 sec

1,25 min

1098 t/h 1050 t/h

30 sec

0,50 min

1426 t/h 1341 t/h 1242 t/h 1177 t/h 1355 t/h 1274 t/h 1180 t/h 1118 t/h 1283 t/h 1207 t/h 1118 t/h 1059 t/h

45 sec

0,75 min

1263 t/h 1196 t/h 1116 t/h 1063 t/h 1200 t/h 1136 t/h 1060 t/h 1010 t/h 1137 t/h 1076 t/h 1005 t/h

957 t/h

992 t/h

953 t/h

1043 t/h

998 t/h

942 t/h

945 t/h

60 sec

1,00 min

1133 t/h 1079 t/h 1014 t/h

970 t/h

1077 t/h 1025 t/h

963 t/h

921 t/h

1020 t/h

971 t/h

912 t/h

873 t/h

75 sec

1,25 min

1028 t/h

892 t/h

976 t/h

882 t/h

847 t/h

925 t/h

884 t/h

836 t/h

802 t/h

30 sec

0,50 min

1328 t/h 1249 t/h 1157 t/h 1096 t/h 1262 t/h 1187 t/h 1099 t/h 1041 t/h 1196 t/h 1124 t/h 1041 t/h

45 sec

0,75 min

1176 t/h 1114 t/h 1040 t/h

991 t/h

1118 t/h 1058 t/h

988 t/h

941 t/h

1059 t/h 1002 t/h

936 t/h

891 t/h

60 sec

1,00 min

1056 t/h 1005 t/h

944 t/h

903 t/h

1003 t/h

955 t/h

897 t/h

858 t/h

950 t/h

904 t/h

850 t/h

813 t/h

75 sec

1,25 min

957 t/h

865 t/h

831 t/h

909 t/h

870 t/h

822 t/h

789 t/h

862 t/h

824 t/h

778 t/h

747 t/h

983 t/h

915 t/h

928 t/h

934 t/h

987 t/h

30 sec

0,50 min

1231 t/h 1157 t/h 1072 t/h 1016 t/h 1169 t/h 1099 t/h 1018 t/h

965 t/h

1108 t/h 1041 t/h

965 t/h

914 t/h

45 sec

0,75 min

1090 t/h 1032 t/h

963 t/h

918 t/h

1035 t/h

980 t/h

915 t/h

872 t/h

981 t/h

1002 t/h

936 t/h

826 t/h

60 sec

1,00 min

978 t/h

931 t/h

875 t/h

837 t/h

929 t/h

884 t/h

831 t/h

795 t/h

880 t/h

838 t/h

787 t/h

753 t/h

75 sec

1,25 min

887 t/h

848 t/h

801 t/h

769 t/h

843 t/h

806 t/h

761 t/h

731 t/h

798 t/h

763 t/h

721 t/h

692 t/h

RH 40-E Retro 477 kW 640 HP

7.0 m³ (1:1)

N k 380

400 kN

102 106 t

14 13

Pala Retro

12 11 10 9 8

•

7.0 m³

•

Fuerza Penetración Max. 400 kN

•

Fuerza desprendimiento Max. 380 kN

•

Productividad Max. 1400 t/h Promedio 1000 t/h

7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7

16 15 14 13 12 11 10 9

8

7

6

5

4

3

2

1

0 m

Producción RH 40-E (Retro) Bucket size

7,0 m³ Fill factor

100%

95%

90%

12,6 t 63,0 t

12,0 t 59,9 t

11,3 t 56,7 t

Cycle time Truck spotting 30 sec

83%

78%

73%

68%

63%

Material density: 1,8 t/m³

Load per bucket Load per truck Utilizatiion

Number of cycles: 5

0,50 min

21 sec

23 sec

25 sec

27 sec

21 sec

23 sec

25 sec

27 sec

21 sec

23 sec

25 sec

27 sec

0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 1621 t/h 1524 t/h 1412 t/h 1338 t/h 1540 t/h 1448 t/h 1341 t/h 1271 t/h 1459 t/h 1372 t/h 1271 t/h 1204 t/h

45 sec

0,75 min

1436 t/h 1359 t/h 1269 t/h 1209 t/h 1364 t/h 1291 t/h 1206 t/h 1149 t/h 1292 t/h 1223 t/h 1142 t/h 1088 t/h

60 sec

1,00 min

1288 t/h 1227 t/h 1153 t/h 1103 t/h 1224 t/h 1165 t/h 1095 t/h 1048 t/h 1160 t/h 1104 t/h 1037 t/h

992 t/h

75 sec

1,25 min

1168 t/h 1117 t/h 1056 t/h 1014 t/h 1110 t/h 1061 t/h 1003 t/h

912 t/h

963 t/h

1052 t/h 1006 t/h

950 t/h

30 sec

0,50 min

1524 t/h 1433 t/h 1327 t/h 1257 t/h 1448 t/h 1361 t/h 1261 t/h 1194 t/h 1371 t/h 1289 t/h 1194 t/h 1132 t/h

45 sec

0,75 min

1349 t/h 1277 t/h 1193 t/h 1136 t/h 1282 t/h 1214 t/h 1133 t/h 1079 t/h 1214 t/h 1150 t/h 1073 t/h 1023 t/h

60 sec

1,00 min

1211 t/h 1153 t/h 1083 t/h 1036 t/h 1150 t/h 1095 t/h 1029 t/h

985 t/h

1090 t/h 1037 t/h

975 t/h

933 t/h

75 sec

1,25 min

1098 t/h 1050 t/h

905 t/h

988 t/h

893 t/h

857 t/h

30 sec

0,50 min

1426 t/h 1341 t/h 1242 t/h 1177 t/h 1355 t/h 1274 t/h 1180 t/h 1118 t/h 1283 t/h 1207 t/h 1118 t/h 1059 t/h

45 sec

0,75 min

1263 t/h 1196 t/h 1116 t/h 1063 t/h 1200 t/h 1136 t/h 1060 t/h 1010 t/h 1137 t/h 1076 t/h 1005 t/h

957 t/h

60 sec

1,00 min

1133 t/h 1079 t/h 1014 t/h

970 t/h

1077 t/h 1025 t/h

963 t/h

921 t/h

1020 t/h

971 t/h

912 t/h

873 t/h

75 sec

1,25 min

1028 t/h

892 t/h

976 t/h

882 t/h

847 t/h

925 t/h

884 t/h

836 t/h

802 t/h

30 sec

0,50 min

1328 t/h 1249 t/h 1157 t/h 1096 t/h 1262 t/h 1187 t/h 1099 t/h 1041 t/h 1196 t/h 1124 t/h 1041 t/h

983 t/h

992 t/h

928 t/h

953 t/h

1043 t/h

998 t/h

934 t/h

942 t/h

945 t/h

987 t/h

45 sec

0,75 min

1176 t/h 1114 t/h 1040 t/h

991 t/h

1118 t/h 1058 t/h

988 t/h

941 t/h

1059 t/h 1002 t/h

936 t/h

891 t/h

60 sec

1,00 min

1056 t/h 1005 t/h

944 t/h

903 t/h

1003 t/h

955 t/h

897 t/h

858 t/h

950 t/h

904 t/h

850 t/h

813 t/h

75 sec

1,25 min

957 t/h

865 t/h

831 t/h

909 t/h

870 t/h

822 t/h

789 t/h

862 t/h

824 t/h

778 t/h

747 t/h

915 t/h

30 sec

0,50 min

1231 t/h 1157 t/h 1072 t/h 1016 t/h 1169 t/h 1099 t/h 1018 t/h

965 t/h

1108 t/h 1041 t/h

965 t/h

914 t/h

45 sec

0,75 min

1090 t/h 1032 t/h

963 t/h

918 t/h

1035 t/h

980 t/h

915 t/h

872 t/h

981 t/h

1002 t/h

936 t/h

826 t/h

60 sec

1,00 min

978 t/h

931 t/h

875 t/h

837 t/h

929 t/h

884 t/h

831 t/h

795 t/h

880 t/h

838 t/h

787 t/h

753 t/h

75 sec

1,25 min

887 t/h

848 t/h

801 t/h

769 t/h

843 t/h

806 t/h

761 t/h

731 t/h

798 t/h

763 t/h

721 t/h

692 t/h

Cabina de Operación

Cabina de Operación

– Excelente Visibilidad (nivel visual 7.6 m) – Asiento con suspensión neumática con interruptor de seguridad. – Asiento auxiliar para el instructor – Sistema de Control a Bordo - BCS

Sistema de Control BCS – Pantalla transflectiva en colores.  Fácil de leer incluso con luz directa del sol – Monitoreo de datos de operación  App. 30 sensores análogos  App. 50 sensores digitales – Comparación de los parámetros seteados y sus desviaciones. – Alarmas visuales y acústicas – Asistencia de detección de fallas. – Asistencia de servicio  Programa de mantención y sus intervalos.  Memoria de fallas – Carácterísticas ajustable del Joystick de acuerdo a las preferencia del operador. – Varios idiomas  Español, Francés, Inglés, Alemán, Ruso

Ventajas Concepto de dos Motores 





 

La excavadora es totalmente operable con un solo motor (en el caso de falla de uno de estos o en su defecto falla de alguna bomba, etc.): – Por medidas de seguridad, el equipo puede ser movido fuera de algúna área de alta peligrosidad (bancos altos, etc.). – El equipo puede ser movido para permitir tronadura. – El equipo puede ser colocado en mejor posición para su reparación. Un 60% de la capacidad nominal de equipo se puede lograr con un solo motor, debidoa que: – La máxima presión de trabajo se logra tambien con un solo motor. (las potencias de penetración y desprendimiento se mantienen intactas). – Bajada de pluma y mango por gravedad. – Circuito hidráulico cerrado de giro con recuperación de energía. Detección de falla en el módulo de potencia es mucho mas simple – Se puede determinar y detectar de manera fácil algúna falla o problema entre una unidad de potencia y la otra. Dos unidades de potencia menores son de menor costo que una sola de gran tamaño. Costo de inversión de componentes de respaldo es considerablemente mas bajo

PREGUNTAS

Loading on Truck_s Good Side Good side positioning occurs when the truck backs in for a load and the shovel or loader is on the same side of the truck as the operator_s cab. Full view of the shovel or loader is possible while backing. The key points are as follows: 1. Trucks advance clockwise. 2. If the loading area is not occupied and is clear of obstructions or spillage, the truck operator is to move directly into the loading area without being spotted, lining up the edge of the dump body with the banjo arm in the case of a shovel, or lining up the edge of the dump body with the bucket teeth in the case of a loader. (Refer to Figures 6.8.5.1 through 6.5.8.6.) Note: Bring the truck to a complete stop before moving the Transmission Selector control lever to the Reverse position. 3. If the loading area is occupied, the truck is to wait at Position B. Note: Occupied means that there is another haul truck, cleanup equipment, maintenance equipment, personnel, etc. in the area. The reason for waiting at Position B is to maintain total visibility of the loading area. 4. Maintain the distance between Position B and the loading area two truck-lengths apart. 5. When the truck in Position B does move, the truck must travel at least one truck-length forward before making a right turn into Position C. Note: The distance between the loading area and Position C should be one truck-length. The distance between Position A and Position B should be two truck-lengths apart. When the truck in Position A moves, the truck must travel at least one truck-length forward before making a right turn into Position B. 6. When pulling in under a shovel or loader, follow the signals of the spotter or the operator of the shovel or loader. (Refer to Spotting Procedures further on in this section.)

6.1. When the shovel or loader operator is waiting with the bucket loaded and spotted, back up by lining up the edge of the dump body with the banjo arm in the case of a shovel, or lining up the edge of the dump body with the bucket teeth in the case of a loader. (Refer to Figures 6.5.8.1 through 6.5.8.6.)

6.2. Continue backing slowly until the shovel or loader operator dumps the bucket or blows the horn to stop. Note: The shovel or loader operator should not dump the first load before the truck stops when the VIMS payload measurement system is being used. Dumping the first load before the truck has stopped and the transmission is in Neutral may affect the accuracy of the payload weight.

6.3. Stage the truck as close to the digging face as possible while: Keeping the truck square to the shovel or loader. Avoiding tire damage from backing onto the digging face or spillage from previously loaded trucks. Keeping the truck on flat level ground, reducing torsional strain on the truck suspension. CAUTION: Stop before the tires roll up on sloughing material at the digging face to avoid tire damage.

6.4. When spotting, maintain a minimum of 1 meter to 1½ meters between the edge of the dump body and the rear of the shovel (counterweight) or radiator of the loader. When spotting a truck for loading by a loader, the best angle is at about 45° to the working face rather than at a right angle to it. In this position, the loader can swing some loads from the bank onto the truck with a minimal backward movement, thus increasing loading speed. It is always the loader operator_s responsibility to stage the trucks. (Refer to Figure 6.5.8.6.) 7. Do not back into the loading area if the shovel or loader is facing into the bank. Wait for the shovel or loader operator to turn the bucket away from the bank before backing. Note: Prompt and correct positioning of the trucks for loading cuts down on the loading cycle times and increases productivity. 8. While your truck is being loaded, stay in the truck cab. Place the Transmission Selector control lever in Neutral and engage the parking brake. Leave the engine running. Note: Staying in the truck cab is necessary because of the constant danger of material falling out of the bucket and injuring the operator. The exception to this rule is when the truck is being loaded with boulders. (Refer to Section 6.5, Operator Tasks: Loading Boulders.) WARNING: If the operator must leave the cab during loading, place the Transmission Selector control lever in Neutral and engage the parking brake. Leave the cab upon receiving positive communication from the shovel or loader operator. Dismount using the steps, grab irons, and three points of contact. Remain a safe distance from the truck during the loading cycle. 9. Do not drive over unprotected power cables. 10. When approaching or leaving the loading area, watch out for other vehicles and for personnel working in the area.

COMBINACIÓN DE MODELOS DE RUTAS DE VEHÍCULOS Y SIMULACIÓN MICROSCÓPICA DE TRÁFICO PARA EL DISEÑO Y LA EVALUACIÓN DE APLICACIONES DE LOGÍSTICA URBANA (CITY LOGISTICS- GESTIÓN DE FLOTAS EN TIEMPO REAL) J. Barceló(1), H. Grzybowska(1) and S. Pardo(2) (1) Departament d’Estadística i Investigació Operativa Univesitat Politècnica de Catalunya [email protected], [email protected] (2)TSS-Transport Simulation Systems [email protected] (http://www.aimsun.com)

LOGÍSTICA Y LOGÍSTICA URBANA (I) • LOGISTICA (Según el “Council of Logistics Management”): “Aquella parte de la cadena de suministro que planea, implementa y controla el flujo y almacenamiento eficiente de bienes y servicios, y la información asociada, desde el punto de origen al de destino para satisfacer los requerimientos de los clientes”. 16/06/05

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ESQUEMA CONCEPTUAL DE LA CADENA DE SUMINISTRO (ORIGEN A HUB)

ORIGEN CARGA 1

ORIGEN CARGA 2

(ORIGEN A HUB) TRANSPORTE: MARITIMO, AEREO, FERROCARRIL, CARRETERA

Client 1

Problema de Localización

ZAL ALMACENAMIENTO CONSOLIDACIÓN MANIPULACIÓN

Logistic Centres Warehouses (ZAL A CENTROS DISTRIBUCION O ALMACENES) TRANSPORTE: MARITIMO, AEREO, FERROCARRIL, CARRETERA

Logistic Centres Warehouses Logistic Centres Warehouses Logistic Centres Warehouses

ORIGEN CARGA j

. . Logistic Centres Warehouses

Modelos de Rutas de Vehículos y de Gestión de Flotas 16/06/05

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Client 2

Client 3

Client 4

Client i

Client j

Client k

Client m

Client n

3

LOGÍSTICA Y LOGÍSTICA URBANA (II) • Las actividades logísticas en áreas urbanas tienen características que las diferencian de las actividades logísticas generales: – su contribución a los flujos de tráfico (en promedio del orden de un 10%), – las consecuencias que este tiene sobre ellas (congestión, demoras en el proceso de suministro…) y – el porcentaje que representan en la contribución a los costes de trasporte (hasta un 40%) 16/06/05

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CITY LOGISTICS (Taniguchi et al.)

• “Es el proceso de optimización total de las actividades de logística y transporte realizadas por medio de empresas privadas en áreas urbanas, teniendo en cuenta el ámbito en que se realizan, su interacción con el tráfico, la manera en que están afectadas por la congestión, su contribución a ella, las consumos energéticos y las contribuciones a la polución, todo ello en el marco de una economía de mercado”

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PLANIFICACIÓN, DISEÑO, EVALUACIÓN Y MODELOS • Las decisiones sobre planificación y diseño, y la evaluación de las aplicaciones logísticas ha de tener una base cuantitativa, por medio de modelos adecuados a los objetivos • Lo que implica disponer de un conjunto de modelos ad hoc para • La localización de los centros logísticos • La programación y determinación de las rutas de los vehículos de las flotas • La gestión dinámica de las flotas

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MODELOS DE RUTAS DE VEHÍCULOS •

Los modelos de Rutas de Vehículos (Vehicle Routing and Scheduling) proporcionan las técnicas para modelar las aplicaciones de “City Logistics”, dos casos de especial interés son: • Cuando los clientes especifican la ventanas temporales dentro de las cuales s han de realizar los servicios de entrega-recogida (pick-up and delivery) los vehículos de las flotas logísticas • Cuando la programación y determinación de las rutas de servicio ha de ser dinámica, basada en información en tiempo real.

•

•

Han de tener en cuenta que la información cambia mientras los vehículos prestan los servicios y debe procederse a una actualización secuencial de las rutas cuando se dispone de nueva información. Ejemplos de información en tiempo real son: • Sobre las condiciones de operación del sistema: Tiempos de viaje, Tiempos de servicio, de espera, etc(afectados por congestiones, incidentes, averías…),. • Sobre la demanda de los clientes: Localización, Ventanas temporales, cantidades, prioridades…., • Sobre el vehículo: Localización, Estado de la carga… 16/06/05

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UNA PROPUESTA METODOLÓGICA DESDE LA PERSPECTIVA DE LA INVESTIGACIÓN OPERATIVA • MODELOS PARA TOMAR DECISIONES, SIGNIFICA – Que los modelos sean accesibles a los responsables de la toma de decisiones – Asistiéndoles en • El proceso de construcción del modelo • La selección y aplicación de los algoritmos adecuados • El análisis e interpretación de los resultados • La evaluación de los resultados

• LO QUE IMPLICA QUE LOS MODELOS HAN DE SER COMPONENTES DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES 16/06/05

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IMPLEMENTACIÓN DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES PARA EL DISEÑO Y EVALUACIÓN DE APLICACIONES DE “CITY LOGISTICS” A PARTIR DE LA METODOLOGÍA DE TANIGUCHI PROBLEM DEFINITION

OBJECTIVES

CRITERIA

DATA COLLECTION

REVIEW

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MODELS

SENSITIVITY

RESOURCES

CONSTRAINTS

IMPLEMENTA TION

DECISIÓN SUPPORT SYSTEM FOR LOGISTIC ANALYSIS

ALTERNA TIVES

SELECTION

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EVALUATION

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ESQUEMA CONCEPTUAL DE LA ARQUITECTURA DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES CUANTITATIVAS (Sprage, Turban) SIG-T BASE DE MODELOS

BASE DE DATOS

ACTUALIZACION DE DATOS

SISTEMA DE GESTION DE LA BASE DE DATOS

SISTEMA DE GESTION DE LA BASE DE MODELOS

INTERFAZ GRAFICA DE USUARIO

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BASE DE MODELOS • LOCALIZACIÓN DE PLANTAS – Continuos – Discretos – En redes

• DE RUTAS DE VEHÍCULOS – – –

Rutas de Vehículos con Limitaciones de Capacidad Rutas de Vehículos con Ventanas Temporales Rutas de Vehículos para problemas de Recogida y Entrega (Pickup and Delivery) con Ventanas Temporales

• MODELOS DE TRÁFICO – Asignación de Tráfico (Equilibrio de Usuario) – Simulación Dinámica (p.e. Simulación Microscópica con AIMSUN NG) 16/06/05

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LA ARQUITECTURA DEL AIMSUN NG (Entorno integrado para el análisis de sistemas de transporte)

GUI

Edition, 2D and 3D animation

CAD

Transport planning

GIS

Demand analysis

GETRAM

Extensible object model

Logistic Applications AIMSUN Simulator

Traffic data Scenario analysis module Internet

Model DB

Data analysis

… Filters

Validation tools

Kernel

Traffic tools

AIMSUN NG Importing a .dwg

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AIMSUN NG Importing a Shape File

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Transport Planning: User Equlibrium Assignment

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Transport Planning: Shortest Path Analysis

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COMENTARIOS SOBRE LA AYUDA A LA CONSTRUCCIÓN DE MODELOS Y LAS PECULIARIDADES DE LOS MODELOS DE RUTAS DE VEHÍCULOS PARA APLICACIONES CITY LOGISTICS

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El modelo de la red viaria para las aplicaciones de Logística Urbana • • • • •

Modelada como un grafo G=(N,A) Traducción de la red viaria urbana definida por un mapa (digital) Cuyos nodos n∈N representan orígenes y destinos Con centros logísticos y clientes localizados en nodos o arcos Y arcos a∈A, que representan la infrastructura de transporte

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DEL MAPA DIGITAL DEL MODELO DE MICROSIMULACION A LA REPRESENTACIÓN NODOS-ARCOS (Detalle de la “traducción”: Inclusión explícita de los movimientos de giro)

2 7

1

5

4

8

6 3

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EL “COSTE DE USAR UN ARCO” EN UNA RED URBANA

• Depósito: cuadrado rojo • Clientes: cuadrados azules • Coste c0i: coste del camino (en verde) desde el depósito (nodo 0) al cliente i (nodo i) • Los Costes no son simétricos (c0i ≠ ci0) • El grafo no es euclídeo • La propiedad triangular no se satisface

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EJEMPLO DE LA ASIMETRÍA DE LOS COSTES DE VIAJE EN UNA RED VIARIA URBANA

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DOS CASOS DE ESPECIAL INTERÉS EN LA LOGÍSTICA URBANA: PROBLEMAS DE RUTAS DE VEHÍCULOS CON VENTANAS DE TIEMPO PROBLEMAS DE ENTREGA Y RECOGIDA (PICKUP AND DELIVERY) CON VENTANAS DE TIEMPO

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Problemas de Rutas de Vehículos

MAGATZEM CENTRAL

1. Assignment of clients to vehicles

2. Route sequencing 16/06/05

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PROBLEMAS DE RUTAS DE VEHICULOS CON VENTANAS DE TIEMPO (VRPTW) • •

• •

El Problema de Rutas de Vehículos con Ventanas de Tiempo (VRPTW) es una extensión del CVRP en la que: Cada cliente i está asociado a una demanda no negativa di, una duración del servicio si no negativa y una ventana temporal [ei, li] que representa respectivamente los instantes más temprano y más tardío, en que se puede prestar el servicio. El VRPTW consiste en asignar k rutas de vehículos en G tales que: – i. Toda ruta empieza y acaba en el depósito – ii. Todo cliente pertenece exactamente a una ruta – iii. La carga total y duración de una ruta k no excede Ek y Lk respectivamente – iv. El servicio al cliente i se realiza en el intervalo [ei, li], y todo vehículo sale del depósito y regresa a él en en intervalo [e0, l0]; y – Minimiza tiempo total de viaje (o el coste) de operación de la flota 16/06/05

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• • •

•

El VRPTW se define en un grafo G=(V,A) en el que el depósito está representado por los nodos 0, y n+1. Todas las rutas factibles corresponden a caminos en G que empiezan en el nodo 0 y terminan en el nodo n+1 Los nodos 0 y n+1 tienen asociada una ventana temporal [e0,l0]=[en+1,ln+1]=[E,L] que representa, respectivamente, la salida más tempranan del depósito y el retorno al depósito más tardío posible. Existen soluciones posibles solo si : e0 = E ≤ MIN[li − t0i ] i∈V −{0 }

•

• • •

and

ln +1 = L ≥ MIN[ei + si + ti0 ] i∈V −{0 }

Un arco (i,j) ∈A, con un tiempo de viaje tij puede eliminarse debido a consideraciones temporales si ei+si+tij>lj O debido a limitaciones de capacidad di+dj>C xijk, (i,j)∈A, k∈K, es igual a 1 si el arco (i,j) es utilizado por el vehículo k, y a 0 en caso contrario. N=V\{0,n+1} es el conjunto de clientes

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FORMULACIÓN DEL (VRPTW) COMO UN MODELO DE REDES CON FLUJO MULTIARTÍCULO CON VENTANAS DE TIEMPO Y RESTRICCIONES DE CAPACIDAD • Restricciones (2) ⇒ cada cliente es asignado solo a la ruta de un vehículo (1) MIN∑ ∑ cij xijk k∈K (i,j)∈A • Restricciones (3) a (5) = ∀ ∈ N (2) s.t. x 1, i ∑ ∑ ijk caracterizan el flujo en la k∈K j∈∆ (i ) ruta del vehículo k x = 1, ∀ k ∈ K (3) ∑ 0jk • Restricciones (6), (8) (9) j∈∆ ( 0 ) aseguran la factibilidad ∀k ∈ K, j ∈ N, (4) ∑ xijk − ∑ xjik = 0, en in términos de tiempo i∈∆ ( j ) i∈∆ ( j ) y capacidad ∀k ∈ K (5) ∑ xi,n+1,k = 1 , i∈∆ (n +1) • Para un vehículo dado k xijk (wik + si + tij − w jk ) ≤ 0, ∀k ∈ K,(i, j)∈ A (6) las restricciones (7) fuerzan wik=0 cuando el ei ∑ xijk ≤ wik ≤ li ∑ xijk ∀k ∈ K,i ∈ N (7) cliente i no es visitado j∈∆ (i ) j∈∆ (i ) por el vehículo k E ≤ wik ≤ L ∀k ∈ K,i ∈ {0,n + 1} (8) Las variables temporales di ∑ xijk ≤ C, ∀k ∈ K (9) • ∑ wik, i∈V, y k∈K i∈N j∈∆ (i ) especifican el principio xijk ∈ {0,1}, ∀k ∈ K,(i, j)∈ A (10) del servicio en el nodo i por el vehículo k • Xijk = 1 si el arco (i,j) es utilizado por el vehículo k +

+

-

+

-

+

+

+

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A UNIFIED TABU SEARCH HEURISTIC FOR VRPTW (Cordeau, Laporte and Mercier, JORS, Vol. 52, pp. 928-936, 2001)

• Tabu search, a local search meta-heuristic that explores the solution space by moving at each iteration from the current solution s to the best solution in its neighbourhood N(s). • Anti-cycling rules to prevent deterioration of the solution • Allow to explore infeasible solutions during the search • Diversification mechanisms to help the search process to explore a broad portion of the solution space • The heuristic has two main components: – A constructive phase that constructs at most K routes – An improvement phase 16/06/05

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CONSTRUCTIVE PHASE •

Constructs at most K routes as follows 1. 2. 3.

Randomly choose a customer j∈{1,…,n} Set k:=1 Using the sequence of customers j,j+1,….,n,1,…,j-1, perform the following steps for every customer i: I. II.

•

•

If the insertion of customer i into route k would result in the violation of load or duration constraints, set k:=MIN{k+1,K} Insert customer i into route k so as to minimize the increase in the total travel time (cost) of route k

Taking into account that the insertion of customer i can only be performed between successive customers j1 and j2 if ej1 ≤ ei ≤ ej2, otherwise customer i is inserted at the end of the route. At the end of the procedure routes 1,…,K-1 satisfy load and duration constraints, and route K may violate any of the three types of constraints.

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Let S denote the set of solutions that satisfy constraints (i) and (ii) • A solution s∈S is a set of K routes such that every customer belongs to exactly one route • This solution may violate: – The maximum load and duration constraints – The time windows constraints associated with the customers and the depot.

• The time window constraint at customer i is violated if the arrival time ai of the vehicle is larger than the time window upper bound li • Arrival before ei is allowed and the vehicle then has to wait the time wi=ei-ai

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IMPROVEMENT PHASE • • •

The tabu search starts from the solution of the construction phase and chooses at each iteration the best non-tabu solution in N(s). After each iteration the values of parameters α, β and γ are modified. This process is repeated for η iterations and the best feasible solution s* identified during the search is post-optimized by applying to each individual route a specialized heuristic for the Traveling Salesman with Time Windows 1. Set α:=1, β:=1 and γ:=1 If s is feasible set s*:=s and c(s*) = c(s) Otherwise set c(s*) = ∞ 2. For κ = 1,…., η, do a. Choose a solution s ∈ N(s ) that minimizes

f(s ) + p(s ) and is

not tabu or satisfies its aspiration criteria b. If solution s is feasible, and c(s ) < c(s * ) , set s* := s , and c(s * ) := c(s ) c. Compute

q(s ),d(s ) and w (s )

and

update

α,

β

and

γ

accordingly d. Set s := s 3. Appli post-optimization heuristic (Generalized Insertion Heuristic – GENI- for the TSPTW) to each route of s* 16/06/05

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Generalized Insertion (GENI Construction)

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Pickup and Delivery Problem with Time Windows (PDPTW) • A generalization of the VRPTW • Consisting on determining a route and the corresponding schedule for every vehicle in a fleet that services a collection of the transportation pickup and delivery requests, satisfying the time windows and the vehicle capacity constraints as well as the main objective function of minimizing the total cost of a trip. 16/06/05

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A Metaheuristic for PDPTW • • • • • • •

Initialization. Construct the initial routes using a Modified Solomon’s Insertion Algorithm. Evaluation of the solutions. According to objective function evaluate the initial solutions and choose the local optimal solution Sb. Configuration of the control parameters of the heuristics. Tabu Search procedure Combines a Descent Local Search based on PDShift and PD-Excahnge Operators Followed by the application of PD-Exchange Operator, with Output: Sb.

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METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (SHIFTING)

P

D

Route 1

Route 2

SHIFTING

Route 1 P

D

Route 2

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METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (EXCHANGING)

P1

D1

P2

D2

Route 1

Route 2

EXCHANGING

P1

D1

Route 1 P2

D2

Route 2

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METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (REARANGING)

P

D

Route

REARANGING

Route P

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UN ENFOQUE DINÁMICO INTEGRADO: ENRUTAMIENTO ⇔ SIMULACION MODELS FOR VEHICLE ROUTING AND SCHEDULING: - Ordinary - Time windows - Pick up and delivery - Dial a ride - Others

OPTIMAL ROUTING AND SCHEDULING

AVERAGE (Time depend.) Link travel time

DYNAMIC TRAFFIC SIMULATION MODEL

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¿QUÉ TIPO DE SIMULACIÓN DINÁMICA DE TRÁFICO? PROPUESTA: SIMULACIÓN MICROSCÓPICA

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El enfoque de la modelación microscópica de la simulación de tráfico • Requiere una representación detallada de la geometría de la red viaria • Se basa en la emulación del movimiento de los vehículos individualmente, vehículo a vehículo, teniendo en cuenta sus características particulares, y las múltiples clases. • La posiciones de los vehículos se actualizan mediante modelos de seguimiento, reglas de cambio de carril, etc., que incluyen componentes estocásticas. • Se modela explícitamente la variabilidad de los comportamientos de los conductores y las dinámicas de los vehículos. • Los vehículos viajan desde orígenes a destinos siguiendo rutas variables con el tiempo, elegidas según modelos estocásticos de selección de rutas. • Se utiliza una representación explícita de los planes de control (fijo, actuado, adaptativo…) en las intersecciones semaforizadas y reglas de cesión de paso, etc. en las no semaforizadas. 16/06/05

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Como trabaja la simulación microscópica

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Los modelos de simulación como laboratorios virtuales para la experimentación INPUTS (Alternativas, políticas, cuestiones ¿qué pasaría si?)

MODELO DE SIMULACION

OUTPUTS (Respuestas)

EXPERIMENTACION

•

• •

El modelo de simulación puede considerarse como un laboratorio virtual en el ordenador para realizar experimentos que permitan extraer concusiones válidas sobre el sistema estudiado La Simulación deviene así un proceso experimental sobre el sistema real por medio de su modelo La fiabilidad de este proceso de toma de decisiones depende de la capacidad de producir un modelo de simulación que represente el comportamiento del sistema con suficiente validez

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LA VALIDACIÓN DE LOS MODELOS

• Análisis estadístico comparativo de los resultados de la simulación y las observaciones del sistema de tráfico • Análisis e interpretación de las rutas utilizadas: estimación de tiempos de viaje

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Simulated

Detector

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INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: Tiempos de viaje en los arcos dependientes del tiempo

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Seguimiento de vehículos simulando AVL de un vehículo equipado con GPS

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INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: Ruta del Vehículo, Emulación de la localización automática (GPS)

Tracked Vehicle and Vehicle’s data (FCD)

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Emulación de la monitorización de un vehículo equipado con GPS en la simulación microscópica de tráfico

Possibility to follow a vehicle during the simulation and to gather dynamic data while following the vehicle

Vehicle information

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DIVERSION ISSUES IN REAL-TIME VEHICLE DISPATCHING

• How to deal with the situation when a new request appears? • How to divert a vehicle from its present destination to serve the new client? • Conceptual scheme of the diversion problem: Current movement

Current planned routes (including current destinations)

New request

Optimization procedure

New planned routes (with the new request) D

D

D’

A

D’

A B

B

Planned movement C

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Ad hoc Waiting strategies based on real-time and short term forecasted travel times (Adapted from MitrovicMinic and Laporte)

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Esquema conceptual para la evaluacion de sistemas de gestión de flotas en tiempo real DEMANDA INICIAL Y ESPECIFICACIONES DE LA FLOTA

MODULO DE CÁLCULO DE RUTAS Y PROGRAMACIÓN DE SERVICIOS

PLAN INICIAL DE OPERACIONES

INFORMACIÓN EN TIEMPO REAL •Nuevas demandas •Demandas insatisfechas •Condiciones de tráfico •Disponibilidad de la flota

MÓDULO DE REPROGRAMACIÓN Y CÁLCULO DE RUTAS DINÁMICO

PLAN DINÁMICO DE OPERACIONES

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Simulación de sistemas de gestión de flotas en tiempo real •

Calcular las rutas y programa inicial de servicios –

•

Ejecutar la simulación –

•

Seguir lo vehículos de la flota a lo largo de sus rutas

Demanda de los clientes en tiempo real –

•

Costes de los arcos cij∼ tiempos de viaje en los arcos tij

El nuevo cliente llama en el instante t

New route for vehicle 2 Position of vehicle 1 at time t

Position of vehicle 2 at time t

Inputs al sistema de ayuda a la toma de decisiones – – –

Posiciones de cada vehículo en el instante t Identificación de los vehículos candidato Identificación de nuevas rutas dependientes del tiempo •

•

New route for vehicle 1

New customer Calls at time t

Tiempos de viaje en los arcos, en curso y previstos, proporcionados por la simulación

Decisión –

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IMPLEMENTACIÓN DEL ESQUEMA CONCEPTUAL CON EL AIMSUN NG DYNAMIC ROUTER AND SCHEDULER (External Application) • Identifies the new demand • Reassigns vehicles • Changes stop points

AIMSUN NG • Makes available o The Link-node extended graph of the road network o Stop points in the graph o Type of stop • Provides access to o Current (and forecasted) link travel times o Fleet vehicles current routes and positions

DYNAMIC ROUTER AND SCHEDULER • Initializes the process o Defines the initial schedule • Provides o Stops changes, adding new stops o New routes for the fleet vehicles

AIMSUN MICROSCOPIC SIMULATION MODEL • Simulates traffic condition on the modelled network • Tracks fleet vehicles • Collects FCD

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TEST DEL PROTOTIPO DE SISTEMA DE AYUDA A LA TOMA DE DECISIONES: ESTUDIO DE DOS CASOS EN EL PROYECTO MEROPE (INTERREG III B MEDOC) LUCCA PIACENZA

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Modelo AIMSUN de Lucca con clientes y Centros Logísticos

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Lucca: Resultados para el Escenario 1

HUB 1

Total

Route Cost Route/Vehicle (Distance) 1 6270,020 2 4366,700 3 4267,540 4 5264,860 5 3160,160 6 5188,260 7 4711,240 8 4734,820 9 4926,380 10 5186,280 11 5732,640 12 6118,840 13 6200,120 14 5801,100 15 5906,580 16 5976,620 17 6514,460 18 7426,120 97752,74

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Rutas desde el Centro Logístico 2

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Piacenza: puntos de carga-descarga

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Modelo AIMSUN de Piacenza: detalles (Ubicaciones de clientes y puntos de carga-descarga)

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Resultados de Piacenza: Comparación de Escenarios (Por tipo de cliente, servicio directo/ Por puntos de carga-descarga; distancia/tiempo) HUB HUB 1 elettrodomestici HUB 2 elettrodomestici

by distance 105228,212 302901,380

by time 19436,123 21636,601

HUB HUB 1 carico-scarico HUB 2 carico-scarico

by distance 28263,186 177938,200

by time 13972,171 11881,131

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Reconocimientos y conclusiones •

• • • • •

•

AIMSUN es un simulador de tráfico desarrollado desde 1986 por el Laboratorio de Investigación Operativa y Simulación Del Departamento de Estadística e Investigación Operativa de la Universidad Politécnica de Cataluña, a través de la participación, entre otros, en más de 22 proyectos de los Programas de I+D de la Unión Europea. AIMSUN está comercializado desde 1998 por TSS-Transport Simulation Systems, una empresa spin-off de la UPC. Actualmente hay más de 350 licencias en uso en todo el mundo. Para información sobre AIMSUN visitar http://www.aimsun.com Las ideas presentadas sobre Simulación y City Logistics fueron desarrolladas inicialmente en el proyecto SADERYL de la DGICYT (TIC2000-1750-C06-03). El prototipo fue completado como parte del Programa Europeo INTERREG III B MEDOCC Project MEROPE Axe 3, Measure 4, Code 2002-02-3.4-I-091 Los tests se realizaron en las ciudades de Piacenza y Lucca, que han probado la viabilidad de la combinación de simulación y modelos de Vehicle Routing para el diseño y evaluación de aplicaciones City Logistics. El desarrollo y verificación de los conceptos de gestión de flotas en tiempo real es objeto del proyecto SADERYL-2 de la DGICYT (TIC2003-05982-C05-04 ).

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MUCHAS GRACIAS POR SU ATENCIÓN

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Chapter 9.4 CYCLES AND SYSTEMS J ON C. Y INGLING 9.4.1 INTRODUCTION Though mine production unit operations must be matched to the characteristics of the site at hand–sufficient power must be available at the excavator’s cutterhead for effective fragmentation, haulage vehicles must be matched to the physical characteristics of the roadways, bucket design must be matched to the handling characteristics of the material being excavated, etc.— the process of design is not finished when equipment is identified that satisfies these requirements. How the unit operations will work together must be considered. The integration of the unit operations discussed in previous chapters of this section into a system that can execute the production cycle efficiently requires great attention, both in initial design of the system and in managing its day-to-day operations. Some of the important decision areas are as follows: 1. Scheduling and sequencing unit operations executed in parallel (i.e., simultaneously) so that any one operation seldom results in excessive delay in execution of another. 2. Balancing production capacity of unit operations (e.g., sizing a truck fleet to match a loading shovel or a conveyor network to match the output of multiple production sections). A good solution to this problem is often much more involved than simply matching either the peak or the average material production capacities of the different unit operations. 3. Assessment of systems level design effects on availability. Overall, mine production systems tend to be highly interdependent and serial in nature. Failure of one unit operation may cause production in a number of other dependent operations to cease. Buffer storage capacity in transportation systems and use of fleet operations to perform a task (a number of smaller machines instead of one large one) are sometimes appropriate approaches to improving overall availability and, accordingly, the long-term rate of production output from these systems. 4. Assessment of working-section layout effects on the performance of the production system. For instance, entry layout and cut sequence in room and pillar mines influence the total nonproductive time spent moving equipment between the working places, the lengths of haulage runs, and tradeoffs between haulage distances and downtime due to extension of the section belts. 5. Real-time operations control strategies, such as the rules used to dispatch pooled truck fleets to service multiple loading operations at a surface mine. Mine production systems engineering aims at evaluating the many alternative designs and operational strategies that can be developed for a given application. It serves as a vehicle for identifying good, perhaps optimum, choices. It views the unit operations collectively as integrated systems rather than independent operations. The interfacing and interaction of the unit operations is explicitly considered. It evaluates performance in terms with overall relevance to mine management rather than in terms only locally relevant to the unit. Though some general rules of “good practice” can be stated (see 9.0.1.4) and should always be considered, these rules are not highly prescriptive of the detailed design and control of these systems. Production systems engineering is primarily a collection of techniques, that, if properly applied, can give good answers to often rather complicated questions. The tremendous incen-

tives for efficiency of mine production systems are powerful motivations for routine application of these techniques. At the many operations where profit margins are low, these incentives are often demands. Consistent with the scope of Section 9, this chapter focuses on topics of mine production systems engineering relevant to systems-level aspects of equipment selection and utilization. Specifically, the following three technologies are treated in some detail: 1. Simulation of mine production systems. This technology has taken a major role in detailed analysis of the performance of these systems. It uniquely can capture the stochastic (i.e., random) and dynamic character of these systems in models with little abstraction. Simulation models can be constructed to address any of the issues listed above. 2. Fleet dynamics and dispatch strategies. Addressed here are approaches for real time control of mine production systems involving fleet operations. These approaches are based on heuristic strategies, although the heuristics themselves sometimes employ solutions to rather sophisticated mathematical models. (The adjective “heuristic” is used in this chapter to refer to decision rules that arise from one’s intuition regarding approaches that appear appropriate for design or control of a system. The general performance of these rules cannot be characterized by deductive mathematical reasoning, and they lack complete theoretical foundation. However, they often provide a very useful and practical basis for decision making.) In the case of truck dispatch, this technology has been proven to utilize equipment more effectively. 3. Stochastic process models of mine production systems. Though simulation techniques can be used to model the performance of mining systems involving stochastic elements (e.g., truck queues at a loader, material flows on a conveyor network), a more detailed mathematical analysis using the theory of stochastic processes can sometimes lead to a concise analytical model. Relative to simulation models of the same process, these models can greatly simplify comparisons of system design and control alternatives and can thereby lead to stronger conclusions. They can be very useful in cases where the level of abstraction required to establish the model is not excessive. Other aspects of production systems engineering that are broader in scope and longer term in nature, such as mine development planning and production scheduling, are discussed from the perspective of mine exploitation in Chapters 8.3 and 8.4. Moreover, consistent with the theme of Section 9, the perspective of this chapter is general. Numerous other discussions of mine production systems engineering can be found throughout this Handbook, addressing specific application areas, including the examples listed.

9.4.2 GENERAL CONCEPTS AND TERMINOLOGY A vocabulary that helps one to characterize these systems and to understand the tools that may be used in predicting and analyzing their performance follows. A system is a collection of components on which processes operate, causing the components to interact for some objective

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purpose. Typically, the degree to which intended purposes of the system being met are assessed in terms of one or more performance measures, e.g., “production rate,” “tons per employeehour,” or “cost per cubic meter of material moved.” The options that management have in design and control of the system are expressed in terms of a set of decision variables. For example, in designing a materials handling system, management may be able to specify the number and size of trucks in its fleet or the width and speed of its belt conveyors. The natural objective of management is to specify the decision variables so that system performance in terms of the appropriate performance measures is good, preferably “optimum.” Production systems engineering relies extensively on the use of mathematical/logical system models. System models are established using knowledge of the performance of individual unit operations and the rules for interaction among these operations. The model should attempt to capture the essence of system performance and should adequately portray changes in performance as values of the decision variables are changed. An appropriate balance must always be sought with respect to the level of detail incorporated in the model. Too much detail unnecessarily consumes the analyst’s time. It may also hamper the tractability of obtaining a solution to the model or realizing extended analytical objectives such as mathematical optimization. Conversely, too little detail may result in a model that is an abstraction of little relevance to the problem at hand. The immediate utility of the model is that it enables examination and evaluation of alternative values of the decision variables. One can readily discern good options from bad ones. This typically is done at a fraction of the cost of experimenting with the real world system. The model provides considerable opportunity for both thoroughness and creativity on the part of the designer or analyst. It is sometimes possible to explore by mathematical techniques all possible specifications of the decision variables and to select the one that results in the best values for the performance measure(s). If one can accomplish this, optimization has been achieved. However, one often must be content at considering a limited number of alternatives and, therefore, has little assurance that the optimum solution has been found. The term optimization is frequently misused, referring to studies where the analyst simply selected the best from a few alternative designs that were examined rather than attempting comprehensive exploration of the range of the decision variables. The scope of the models, that is, the extent of the real world system that one attempts to represent explicitly in the system models, is an issue of considerable importance. One should attempt to keep the scope as small as possible consistent with the objectives in studying the system. For example, face operations might be the focus without special concern for outby transportation or vice versa. One stands a much better chance in arriving at a good, useful solution with small, focused problems. Scope is delineated by system bounds, partitioning the system under study from its environment. The internal workings of the system, within the system bounds, are said to be endogenous (endogenous variables, endogenous events), whereas external impacts on the system are termed exogenous. Typically, many transactions occur across the system bounds, both outputs from the system to the environment and exogenous inputs from the environment to the system. It is always assumed that the system outputs in no way determine the exogenous inputs. To clarify the issue of scope and system bounds, consider a belt network in an underground coal mine where shuttle cars are used for face transportation. Assume that spillage problems have been occurring at transfer points because of insufficient belt capacity for handling situations where peak loads from several

Case 1: Fixed Feeder Speed

Case 2: Real Time Control of Feeder Speeds

Fig. 9.4.1. Contrast of minimum system bounds for two approaches to control belt spillage

production sections are superimposed. One wishes to adjust speeds of the section feeders to reduce the incidence and extent of such problems. One approach might be just to reduce speeds permanently somewhat from current levels, spreading the discrete loads of material from the shuttle car into longer, thinner layers on the belt. Another might be to install belt load sensors, a data transmission network, and some type of intelligent control system to reduce speeds only on an “as needed” basis to prevent spills. Minimal system bounds (i.e., system bounds that keep the overall scope of the model as small as possible) will be contrasted for rigorous system models that one might construct to study these two alternative approaches to control of the system. In the first case, one could set the system bounds at the section feeder, including the conveyor network in the model but excluding face operations. One would need to input shuttle car interarrival times and loads exogenously to the model, but these inputs would in no way be influenced by outputs of the system model for a given, fixed feeder speed. For a rigorous model of the second case, however, one would have to broaden the model’s boundaries relative to the first case, explicitly incorporating the face operations in some fashion. The reason for this is that feeder speed would be varied with time by the control system in response to circumstances on the belt network. When feeder speed changes, the discharge time of any shuttle car currently unloading is affected. This, in turn, influences subsequent interarrival times. The face operations and the belt network are intimately coupled here and, if rigor is desired, should not be modeled independently (Fig. 9.4.1). The state of a system is defined in the model by the value of a collection of variables sufficient to characterize system operation

CYCLES AND SYSTEMS and performance. Static models are solved for a single value of the state variables. Dynamic models are solved to obtain a trace of how the state variables change over time or, perhaps, over space or through a series of stages. The first test for sufficiency of state variables is that one should be able to ascertain performance measures of interest with respect to making comparisons among alternatives. For example, consider a surface mine haulage system where trucks wait in line to be loaded by a shovel, travel to the dump site, dump (without having to wait in line), and return to the load site. One might be interested in analyzing the rate of production of this system for a given size of truck fleet. For this purpose, state might be characterized at any point in time by the number of trucks waiting to be loaded, the status of the loader (idle/ busy), and the number of trucks in the process of dumping (ignoring equipment breakdowns). The stated performance variable as well as others that might also be of interest, such as average haul cycle times, average truck delay times, etc., can obviously be inferred from knowledge of how these variables change through time. For dynamic models, such as the example just noted, a second test of sufficiency is also required. One must be capable of generating the subsequent state of the system given the current value of the state variables, exogenous inputs, and the known functional relationships among the system components. If one can do this, such a system is referred to as possessing the Markovian property. Specifically, this property states that the subsequent state of the system depends on the prior history of the process only through the present state. The next state may be generated from the model input using known relations describing single-step transitions. This criterion, in conjunction with the ability to infer performance variables of interest, provides a test to determine whether a given definition of state variables for the system is insufficient, sufficient, or superfluous. With discrete-event dynamic models, the state variables only change at a countable number of points in time. A plot of the state variables vs. time appears as a step function. Using the state variables mentioned previously, the truck haulage system might be modeled as a discrete event system. Events are those occurrences at discrete points of time that result in the state changes. For example, arrival of a truck to the loading site changes the number of trucks waiting to be loaded and may change the status of the loader unit from idle to busy. Fig. 9.4.2 shows a plot of the state variables “queue length” and “loader status” vs. time for this system. With continuous dynamic models, the state variables change continuously with respect to time. An example where a continuous model might be used would be in sizing the capacity of a mine drainage sump so that pumping can be shifted to off-peak periods to reduce power costs. The level of the sump, a state variable, would change continuously with respect to time as a function of inflow and outflow rates. As will be noted in the following with respect to a discussion of conveyor network modeling, sometimes one can convert from a continuous to a discrete model by making an appropriate selection of state variables. In general, discrete-event systems are easier to model than continuous systems. Some real world systems may require that a mixed discrete/continuous representation be used. Stochastic models are used where the exogenous input to the model is random in nature. Note that this input is characterized in the form of some appropriate type of probability distribution (e.g., a distribution fitted to dump cycle times obtained in a time study of haulage operations). The input distributions are known, both their form (e.g., normal, exponential, gamma) and appropriate parameters. The modeling effort is to see, for a given specification of the decision variables, how the system responds

785

Fig. 9.4.2. Plot of state variables vs. time for a discrete-event dynamic model.

Fig. 9.4.3. Output from a stochastic model of production system performance.

to this input. Such response will also be stochastic in nature (Fig. 9.4.3). By modeling, one attempts to infer or deduce the distribution of the response, or important properties of this distribution, such as mean levels of the performance variables. If, on the other hand, the input is not stochastic, the model is deterministic. In general, deterministic situations are easier to model and analyze. Many times, mean levels of input variables are inserted into a mathematical expression that represents performance of the system such as the equations given for cycle calculations for haulage systems in Chapter 9.3. For example, one might insert mean trip times, mean spotting times, mean loading cycle times, mean dipper fill ratio, truck volume, and long-term average unit availability into a mathematical equation representing the production rate of a truck/loader system. Note, however, that probability theory provides no guarantee that the resulting answer would represent the mean level of the performance variable. Such approaches, when randomness is significant, only provide approximations. It is an expressed role of the techniques discussed in this chapter to eliminate the errors inherent in such approaches

786 9.4.3 SIMULATION OF MINE PRODUCTION SYSTEMS

Elapsed time since previous arrival at the feeder

Fig. 9.4.4. Nonstationary input distribution required to describe shuttle car arrivals to the feeder.

Discrete-event and continuous simulation are the modeling techniques that have been most widely applied in mine production systems engineering for the detailed analysis of equipment interaction. There are several good reasons for this. Most importantly, these approaches can readily accommodate the strong dynamic and stochastic character of these systems. Further, great levels of detail can readily be incorporated in simulation models. If properly carried out, such detail can insure valid representations of the real system without undesirable abstractions. The technique is also one of the easiest to learn. The main prerequisites are a modest degree of computer literacy and a reasonably strong background in probability and statistics. Constructing the models is usually a conceptually easy process (though perhaps time consuming in some cases). Analysis of the output in proper scientific fashion is the more technically difficult issue.

9.4.3.1 Nature of Simulation Models

and establish more accurate and meaningful performance predictions. A model where the exogenous input and internal relationships do not vary systematically over time may yield what is called a steady-state solution. All static models are steady state. Such a solution represents an equilibrium behavior reflecting long-term performance of the system. A requirement for a stochastic model to provide a steady-state solution is that the parameters of the input distributions are held constant. Note that if the the foregoing condition is not true, the input is said to be nonstationary and the transient behavior of the system must be studied. Although one might think that study of transient behavior is more difficult than steady state, often the reverse is true. In simulation of production systems, particular short periods of interest in analysis of transient behavior can often be defined. For instance, performance of a rail transport system might be studied only during the hour around shift changes when demands on the system are at their peak (assuming both men and ore are being transported simultaneously). The model might appropriately focus on transient behavior for this interval of time. Input distributions to many mining models are nonstationary. For instance, the input to the belt network model discussed previously would systematically change as the mining machine proceeds through its cut sequence. The time between consecutive shuttle car arrivals should reflect this underlying cycle. When cuts are close to the feeder, interarrival times will be small. When cuts are far from the feeder, they will be large. If rigor is desired, interarrivals should not be taken as independent draws from a probability distribution since the influence of cut sequence on the sequence of interarrivals will be lost (Fig. 9.4.4). The concepts previously discussed are useful in characterizing a system, selecting an appropriate modeling technique, determining the proper structure of the model, and in assessing the output or results produced by the model. The chapter continues with an overview of techniques that may be employed for detailed performance analysis of integrated systems of mine unit operations.

Simulation models are distinguished from other systems models in that the basis for model construction and solution is the run. A run is used to generate an artificial history of the process, specifying how state variables change either through time or through a sequence of stages. These histories, in whole or in part, provide information useful to the analysis of system performance. To understand what is meant by a run and why the idea is so useful in constructing many types of process models, the following example will be considered. A number of boxes of different sizes, shapes, and weights are to be loaded on a cargo plane. The center of gravity of the boxes is of concern and some loading pattern that locates the center of gravity in a position acceptable for stable flying needs to be identified. Generating a candidate loading pattern in a single step is a mentally forbidding task. However, if the task is broken into a sequence of stages, it becomes much less intimidating. For instance, a candidate loading pattern might be generated step by step using a three-dimensional graphics package, putting one box alongside or on top of others as one would if the boxes were being physically stacked. This is an example of using a run to construct a candidate solution to the model. In this example, only the terminal state of the run is of interest; but in many cases the entire history of the process evolution is of value. The advantage of this approach to systems modeling is that it is often quite easy to specify the mechanics of the run. One can readily express rules for stacking boxes one atop the others. Given these rules, one can arrive at a candidate loading pattern by building up the pattern sequentially. However, given a collection of boxes of assorted weights, sizes, and shapes, a feasible loading pattern could not be deduced in a single step. In short, the mechanism of a run can generate information useful to the solution of a problem when attempts to summarize system behavior, via deductive mathematical analysis, cannot be made fruitful. However, as will be seen later in this chapter, the information provided by a run is often of weaker nature than that which might be obtained if analytical techniques can be applied to the problem. Note that many models called simulations are misnamed. For example, one often says that a chemical process, a coal preparation flowsheet, or a mine ventilation network has been simulated. However, if steady state flows through the system are

CYCLES AND SYSTEMS

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Fig. 9.4.5. System structure for truck haulage example.

being computed, one is really solving a model expressed as a system of equations in each of these cases. A run has not been executed, generating an artificial history of system behavior. This misnomer arises from the fact that many of the equation-solving techniques used for these models are similar to the run mechanism.

9.4.3.2 How Simulation Models Are Structured Discrete-event Models: In the next few paragraphs a simple example is introduced to help the reader gain some appreciation for discrete-event simulation. Consider a situation where two loading shovels are serviced by a pooled fleet of four identical trucks (Fig. 9.4.5). Trucks wait in line at a shovel, first-come, first-served, if they arrive and find the shovel busy loading another truck. The material from each loading shovel is dumped at a distinct site, but trucks need not wait for trucks ahead of them to dump. A dispatcher continuously keeps track of the trucks, and when a truck has finished dumping, it is assigned to return to one of the two shovels depending on the current situation. Specifically, assume the dispatcher keeps track of the number of trucks waiting in line at each shovel and the number in transit to that shovel from the dump site (previously dispatched). He calls this number “assigned transport capacity.” He sends any truck that has just completed dumping to the shovel with the lower value of assigned transport capacity. In evaluating system performance, assume one is interested in the production capacity of the system, that is, the amount of material dumped per unit time at each of the two dump sites, the utilization of each of the two shovels, and the amount of time the trucks spend waiting at the shovels. In constructing a simulation model for this system, the following input data for the model might be established: 1. Combined time to spot and load a truck at the shovel. 2. Time to transport the loaded truck between each shovel and its respective dump site. 3. Time to transport the empty truck from each dump site to either loading shovel. These data might come from time studies or from other sources (e.g., determination of haul cycle times using rimpull curves and data descriptive of haul road characteristics). Any or all of the input variables might be described as distributions rather than constant values. Depending on the detailed objectives of the study and needs for accuracy, it might be more appropriate to break the aggregate truck spotting/loading time into spotting and a sequence of swing cycles. But things will be kept simple here.

Fig. 9.4.6. Mechanism of a simulation model.

A set of state variables for the system might include: 1. Each shovel’s operating status (idle or busy). 2. Assigned transport capacity (ATC) for each shovel. 3. The number of trucks waiting in line at each shovel. The state variables for a given simulation are not unique; alternatives often exist. Moreover, the state variables employed depend on the objectives of the study. Progressing through the section, it should become clear to the reader that the shovel operating status is necessary as a state variable here only because of the interest in utilization of the shovels. In constructing the model, the objective is to generate a run, that is, an artificial history of the behavior of the loading/haulage system as it progresses forward in time. In general terms, the overall operation of a simulation model is described in Fig. 9.4.6. The initial conditions provide the starting point. They include, among other items, a specification of the initial state of the system. In the example, one might specify that one truck is waiting in line at each loader, loading by the shovel has just started for the second truck, ATC is two, and both shovels are busy. Time is subsequently advanced and state is updated as appropriate. Next, a check is made to see if it is time to stop the run. This might be ascertained by checking the current state with some terminating condition or by checking to see if the simulated time exceeds some predetermined stopping time specified by the analyst. If not, time is advanced and state is updated again as shown in the figure. The key issue is time advance. Changes in the values of the state variables for the example only occur at discrete points in time. In such a situation, it is clear that one knows the behavior of the system completely if a sequence of “snapshots” of the system at those points in time where state changes can be generated. For generating a run efficiently, time should advance from the time of occurrence of one event to the time of occurrence of the next event. Note, however, that some simulation models for mining systems advance time in fixed increments of short duration. Events and state changes may or may not occur at the end of these increments. Though appropriate for systems where continuous state variables are required for the analysis, for most discreteevent simulations, this technique loses not only in speed of execution but also in accuracy since state is not permitted to change, as it would in the real world, at arbitrary points in time.

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Fig. 9.4.8. Flowchart for the event scheduling approach to discreteevent simulation and corresponding program structure.

L: Load Truck

TF: Tram Full

TE: Tram Empty

Fig. 9.4.7. Possible run for truck/shovel example.

In discrete-event simulation, those input variables that specify a time duration are called activities. For the example, all three inputs—spotting/loading time, transport empty time, transport full time—are activities. Fig. 9.4.7 shows how the state variables might change with time for an example run of the truck haulage system. Referring to this figure, one sees that: 1. All events (an event corresponds to any change in the value of any of the state variables) occur upon the termination of activities. For instance, whenever a “transport empty” activity is terminated, an event occurs where the queue length increases by one and, if not already in the busy mode, shovel status changes to busy. 2. Upon termination of an activity, one might, using the external input to the model, be able to forecast the termination of some future activity. If this can be done, a point in time when some future event will occur has been identified. For instance, when the truck loading activity is finished, one can forecast, using the model input, when that particular truck will finish dumping. If “transport loaded” times are random, a typical time

that follows the input distribution of these times would have to be “drawn” from this distribution. Nonetheless, the forecast can be made just using the input to the model. Note that a future event cannot always be predicted upon termination of an activity. For instance, if a truck arrives and finds the shovel busy loading another truck, no activities are initiated, and no future events can be forecast. If the truck arrives and finds the shovel idle, a truck loading activity begins and the model input can be used to forecast when it will end. This illustrates that whether or not some future event can be forecast when the current event occurs is a function of the current state of the system. The names for events are usually derived from the activities used to predict their occurrence. In the example, there are three events: (1) truck arrival at a shovel, (2) completion of truck loading at a shovel, and (3) completion of truck dumping at a dump site. Now a position has been reached where it is possible to see how a computer might be programmed to execute a simulation run via what is known as the event scheduling approach. This is one of two major general purpose approaches for constructing discrete-event simulation models; the other is discussed later. Fig. 9.4.8 shows an overall flowchart for this approach. As noted previously, the initial conditions define the initial state of the system. In addition, they also give a few events for priming the model. For the example, if the initial state described above were to be used, a “completion of truck loading” event would have to

CYCLES AND SYSTEMS Table 9.4.1. Event Logic Tables for the Shovel Truck Problem

be specified for each shovel. In general, one priming event should be specified for each ongoing activity as the simulation run begins. The priming events, both their identity and time of occurrence, are stored on the future event list (FEL). The events on this list are kept in order from earliest to latest. The computer then removes the most imminent event from the list, advances simulated time to the time of occurrence of that event and executes an event subroutine (there is one for each type of event). The event subroutine does two things: 1. It updates state. 2. It forecasts any new events due to activities initiated at the time of the current event and puts these new events on the FEL. The results of both of these operations are determined strictly by the event type and the current value of the state variables using known functional relationships regarding the behavior of the system. No other information is required. Table 9.4.1 gives event logic tables for the three events of the example. These tables effectively describe the action of the event subroutines that one would incorporate with the event scheduling algorithm shown previously in Fig. 9.4.8 when coding the model.

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Note that at any point in time, the content of the FEL is determined by the ongoing activities. A new event placed on the FEL would not necessarily go at the bottom of the list. For example, when truck 3 finished loading at shovel 1, its dump completion event would be placed on the FEL. While it is traveling loaded to the dump site, truck 4 may have begun loading at shovel 2. Its load completion event would then be placed on the FEL, and it may be placed ahead of the dump completion event for truck 3. Further, in general, events may be removed from the FEL before they occur. This would happen if activities exist that preempt ongoing activities. Two new concepts, entities and attributes, useful for coding simulation models, are now introduced. Entities correspond to those dynamic objects in the physical system that require explicit representation in the model. In the example, entities might be used to represent the trucks and the shovels. Attributes are properties of a given entity, for example the operational status of the shovel, the size of the material load in a truck. In the computer program, entities are often represented as records and order is maintained using files. For example, a sorted first-in, first-out (FIFO) file of records representing truck entities might be used for the waiting lines at each of the shovels. When an end of loading event occurs, the top record of this list is removed to identify the next truck to be loaded by the shovel. Discrete-event simulation programs have much in common with standard data processing routines. Good codes (i.e., codes that are efficient in their use of computer memory and in speed of execution) written from scratch in a general purpose language such as FORTRAN or Pascal require the use of list processing techniques and search algorithms to handle properly dynamic representations of the system using entities and attributes. The event scheduling approach, discussed previously, is primarily an approach for organizing the simulation program. A quite different organization of simulation programs called the process interaction approach will now be discussed. Here coding is based on what are called process routines. One process routine is written for each type of entity in the system. In the example, two process routines would exist, one for truck entities and one for shovel entities. The process routine describes everything that can happen to the entity as it passes sequentially through the system. Fig. 9.4.9 gives a process routine for the truck entities in the example. To understand how a process interaction simulation program works, it is useful to imagine that each entity is given, as it enters the system, a copy of the process routine that corresponds to the type of entity it happens to be. The entity then executes the routine sequentially in a fashion described below until it exits the system or the run otherwise is terminated. The entity’s process routine is activated. It starts at some point in the routine and executes as many steps in the routine as possible with zero time advance. These steps might change the value of global state variables, change the value of attributes of the entity, or schedule future events and put them on the FEL. Note that the FEL is common to both the event scheduling and process interaction approaches. Both are variable time increment techniques that advance the clock from the time of one event to the next. Execution of the routine is temporarily suspended once time advance is required for the entity to take an additional step. These stop points correspond to the blocks before the dashed connection lines in the flowchart of Fig. 9.4.9. Note that some of the suspensions correspond to the beginning of activities. Here a future event will be placed on the FEL. Initiation of truck loading, block 6, is an example of this. Other stops correspond to indefinite delays, for example, wait in the queue at the shovel until removed, block 4.

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Fig. 9.4.9. Process routine for truck entity.

Once the process interaction routine stops, the process routines for other entities may be activated to see if they can also be advanced with zero time delay. In the example, a shovel entity’s process routine would at some point in time remove a particular truck entity from the queue and subsequently stop execution. Before time advances, execution of that truck’s process routine would resume from block 5 in Fig. 9.4.9. Once all of the process routines have been advanced as far as possible with zero time advance, the most imminent event is removed from the FEL and time is advanced to the time of occurrence of that event. This corresponds to conclusion of an activity, and it reactivates the process routine of the entity that scheduled the event. The process routine of that entity is then executed sequentially starting from the block following the previous stop point. If one writes a simulation model in a general programming language such as FORTRAN, the event scheduling approach should be used rather than process interaction. If the program writer must take care of all details, process interaction routines become very complex and the organization of the code is not natural. However, most of the special purpose simulation languages, including all of the more recent languages, are based on the process interaction approach. When writing a program in these languages, one effectively defines a process interaction routine for the system entities. However, the statements available are at a macro level; a single statement may take care of many detailed operations automatically. These statements are geared to common situations that arise again and again in simulation models, and they are very powerful. Also some complete process interaction routines for common situations are built into these languages. In the example problem, one probably would not have to write any code for the shovel’s process routine, just one for the trucks. With these macro statements, writing a process interaction routine is often quite natural and is typically much less involved than writing an event routine for the event scheduling approach. Table 9.4.2 gives a process interaction routine for the example

problem written in the SIMAN simulation language. Note that only 18 lines of code were required for this model, and one need not explicitly write such a routine for the shovel. The use of simulation languages in mine systems simulation is discussed in more detail in a later section. Continuous Simulation Models: Continuous simulation differs from discrete-event simulation in that the state variables do not change strictly at discrete points in time. Rather, they change continuously with respect to time. Simulation is not required if a closed-form relation that gives the value of the state variable for any time and any specification of initial state can be established. However, often one can only specify the rate of change of the state variable with respect to time as a function of the current state. For instance, from basic mechanics, one can specify a differential equation relating the state variable x, position of the vehicle, to equipment performance data that describe acceleration av of the vehicle: (9.4.1) If av were a constant, it would be simple to establish a closedform expression of x as a function of time and initial position. However, av is determined by the the rimpull characteristic (a measure of available force for acceleration) and the motion resistance of the vehicle, both of which, for a given vehicle and operating conditions, change as a function of the vehicle’s velocity (see 9.4.2.4). If the rate of change of the state variable is described as a first-order ordinary differential equation (i.e., the highest-order derivative is one, and all derivatives are taken with respect to the same variable, e.g., time), then a first-order Taylor’s series expansion of x about t yields: (9.4.2) Ignoring higher order terms, this expansion suggests a simple

CYCLES AND SYSTEMS Table 9.4.2. SIMAN Code for Truck/Shovel Simulation

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numerical approach to computing x(t). Start with x(t 0 ), the initial state at time t0, then, ignoring the higher-order terms, use the expression and the expression for dx/dt as a function of the state variables to estimate x(t0 + ∆t) for some small increment ∆t. Repeat this procedure to estimate x(t0 + 2∆t), x(t 0 + 3∆ t), etc. The magnitude of ∆t is called the step size. The error in computing x for a single step is given by the unknown term O( ∆ t 2 ), which can be made small by selecting a small step size. This approach is seldom used directly because, relative to other available approaches, errors are large and computational efficiency is poor. However, this illustrates the basic idea behind a class of algorithms called Runge-Kutta methods that are routinely applied for this type of application. With minor extensions, these techniques can be applied to higher-order ordinary differential equations like the second-order one given previously to describe vehicle motion.

9.4.3.3 Coding Options for Mine Simulation Models One has three options for establishing a model for use in mine production systems analysis: (1) write the code from scratch in a general purpose programming language, (2) select an appropriate and existing, often commercial, mining simulation software package, or (3) write the code from scratch in a simulation language. The issues one should consider in selecting from among these alternatives are now briefly discussed. The first option is probably one that should only be considered by research institutions or engineering firms. The justification for considering this option is that a general purpose language offers complete flexibility in constructing the model. In contrast, the other two options might be constrained in the type of process they can model and/or in the efficiency with which they can execute a particular type of simulation run. These constraints do not exist for a general purpose language. However, this option is often a time-consuming one. These models typically involve thousands of line of code and have, in the past, taken months, even years, to code. One should become very familiar with list-processing techniques and data structures prior to attempting such programming. Note that execution speed for models written in a general purpose language should, if proper data processing routines are employed, at least equal that achieved by the simulation languages. Often these speeds can be exceeded because the situation being modeled may allow use of more specialized routines than those implemented by the simulation language. If one elects to code in FORTRAN, one might consider use of the GASP language. Though often referred to as a simulation language, GASP is a collection of FORTRAN subroutines that can be used to organize filing structure for the program, handle filing operations, handle input and output, and provide a clockadvance mechanism. The program would be coded using event scheduling. Several other simulation language packages also offer such utility routines for user-written FORTRAN codes. However, writing simulation models in general languages other than FORTRAN that have better data structures and dynamic storage allocation (e.g., Pascal or C) is often more natural. FORTRAN is only prominent in simulation because of tradition, not because of any special suitability of the language itself. Numerous simulation software packages exist for mine production systems, such as conveyor network models, truck/shovel models, surface mine simulators, continuous mining section simulators, longwall simulators, etc. Some of the more prominent of these packages are discussed in the next segment of this chapter.

These packages provide the core routines necessary for simulating these types of operations, and they accept alternative user specifications on system structure. The main advantage of such packages is that the user need not generate the code. Further, some of these packages have an impressive range of capability. For example, the General Purpose Surface Mining Simulator (GPSMS) package incorporates detailed ore body and spatial description of the mine along with capability to simulate a wide range of production operations and their interaction on this property (Albert, 1989). There are some limitations of these packages, however, that should also be kept in mind. Input requirements can be extensive and learning these requirements can be quite time consuming. The better packages have given considerable attention to simplifying the user interface. For packages with broad scope, one may not be interested in using all this capability, but the package may, regardless, require extensive input description. Many of the existing packages use discrete increment time advance. Though necessary for simulating systems with continuous state variables, this approach leads to very slow execution times and inaccuracy for discrete-event simulations, and is inappropriate for some of the systems modeled. Perhaps the most serious limitation of this class of software is that it is nearly impossible for the package developer to foresee all the systems alternatives that users might like to model. The scope of available options may not meet user needs. Moreover, since the software is written in general purpose languages with thousands of lines of code, major modifications of the package to accommodate user needs, other than by the original developer, is often a forbidding task. The third option is the use of simulation languages. Here the user must write his own code. However, because of the powerful nature of the statements of these languages, the amount of code required to write the model is typically dramatically reduced relative to that required when writing the model in a general purpose language. This is especially true when the process interaction approach is employed. For instance, a simulation model was developed by the author of a surface mine where a truck fleet serves as an intermediate transport link between a pair of loading shovels and two skip hoists. Features addressed in the model included a detailed description of the truck loading cycle, haul road segmentation with different operating conditions, pooled use of the truck fleet with special dispatch rules, modeling of truck failures, use of standby trucks that are activated when breakdowns occur, interfacing with a fixed capacity bunker at the hoist stations with special control logic for skip loading, and shift start-up and shutdown routines. Using a simulation language, a model for this system was written with fewer than 130 lines of code. This is substantially less than 5% of the amount of code that would be required to construct the same model using a general purpose programming language. The proficient programmer in these languages can write reasonably complex models in a matter of hours or days, not months. In the course of developing the code, the programmer becomes intimately familiar with how the process is being modeled. The level of model validity can be judged better relative to judgments made when using a package developed by others. Most importantly, the programmer has considerable flexibility in customizing the model and the output it provides to suit needs and analytical objectives. Simulation languages possess what is called a world view. This reflects the scope of the macro-statements used in the model and the type of real-world processes to which they are oriented. This is an important factor to consider since it influences the ease with which one might model a given situation or the ability

CYCLES AND SYSTEMS to model it at all using the language. Many simulation languages are oriented toward modeling queueing systems. The SIMAN language, developed for manufacturing applications, has a number of features useful for mine systems modeling. These include material handling modules for discrete vehicle and conveyor transport and special features for accommodating spatial aspects of the system. Other languages have recently started to introduce such features. It is not likely that one will find the world view of most simulation languages too restrictive or awkward for mining applications; most situations can be modeled using these languages. General constructs in the language can usually be combined to model specialized processes when the specialized constructs are absent. Differences may exist in the facility with which various situations can be modeled. Moreover, to overcome restrictions in scope, most of the modern simulation languages allow the user to interface routines written in a general purpose language with the routines written in the simulation language. One can thereby accomplish operations that the language cannot perform itself directly. At least in principle, one is not constrained in the scope of processes that may be modeled if user-defined routines can be integrated with the code. If possible, it is suggested that someone interested in modeling a particular process contact users of the various simulation languages to see if example codes they have developed for various mining applications are available. Because of their brevity, these codes can be readily “digested” by individuals familiar with the simulation language. These examples can aid the learning process and greatly speed development of a custom model for a particular application. The major simulation languages currently available include GPSS (GPSS/PC, GPSS/H), SLAM, SIMAN, and SIMSCRIPT II. Since these languages and their supporting software packages have been undergoing extensive updating and improvements in recent years and these trends are likely to continue for the foreseeable future, detailed comparisons of features will not be undertaken here. The following issues, however, should be considered when purchasing a license for a simulation language. 1. Availability of the package in a PC version. The computing power of today’s personal computers is adequate for many (but certainly not all) applications. OS/2 packages that are now becoming available will increase the size of model that can be investigated using a microcomputer. 2. Available modeling orientations supported by the language. Preferably the language should support process interaction, event scheduling, and continuous simulation. Process interaction is typically the main approach employed for discrete-event simulation using the language. User-written event routines may often be interfaced with the process routines to increase flexibility and scope of the language; the package will typically have utility subroutines available to the user for creating these programs. If modeling of systems with continuous state variables is supported, mixed continuous/discrete systems can be represented. Detailed examination of the approach used for interfacing user-written routines and for mixing discrete/continuous representations should be undertaken if one believes there will be need to use these capabilities. 3. Special application orientations for the language. Some languages are directed especially toward queuing systems simulations, which is a major aspect of many real-world simulations, including mining systems (see 9.4.5). Some packages have built in features to make the simulation of materials handling systems easy. 4. Output analysis software. Custom reporting capability should be provided, and it should be easy to gather a wide range of system performance statistics. Many packages enable one to

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create files with detailed performance data generated during a run and include rather sophisticated statistical software for analyses using these data. 5. Capability of animation of the simulation run. This includes a graphics interface to the simulation package that provides a dynamic display of the system state using symbolic representations that the user designs. Effectively, it provides an opportunity to obtain a dynamic, global view of system operation at a faster or slower pace than could be observed in the real world. The importance of this capability depends on user needs. It may provide a means for gaining insights into system operation and can be an effective communication tool when presenting results to management or clients. At present, costs for animation capability can be high. 6. Availability of good documentation with example programs to illustrate modeling approaches. A well-written manual with illustrative examples can greatly speed the process of learning the code. 7. Quality of debugging facilities. The language package should have convenient facilities for debugging with abilities to generate program traces, set break points, etc. Debugging effort for programs in a simulation language is, relative to typical computer programming applications, slightly disproportionate to the size of the programs because of the powerful nature of the statements. Animation capability can also aid the debugging process.

9.4.3.4 Using the Models in Systems Analysis The capability of simulation models to accommodate inputs that are described as random variables is most useful. Mining engineers are well aware of the ramifications such randomness has on the performance of real-world mine production systems. One might attempt to answer questions such as 1. How do truck breakdown rates and repair team performance influence the preferred size of a truck fleet? 2. How do different belt sizes and speeds influence the amount of spilled material at a transfer point, given the stochastic patterns of loaded material on the intersecting belts? 3. How much increased production can be expected if a bunker of a particular size is installed in the belt network to provide a storage buffer when outby belts fail? 4. What are the implications of the randomness in truck loading and haulage cycle times on the way a dispatcher should control the truck fleet so that production rate is maximized and blend qualities are maintained? In answering questions such as these, there is a key issue to recognize (an issue that, unfortunately, is often ignored by practitioners). If the input variables are random variables, the performance variable(s) also is a random variable. The proper goal, therefore, is to know the probability distribution for the performance variable as a function of the input variables and specification of the decision variables. However, the simulation model, because it is based on a run mechanism, does not give us this distribution directly. Rather, a single run gives one possible realization of this process. For example, it describes the way production might go for a particular shift. One must use multiple and/or extended runs and statistical inference to infer properties of the distribution of the performance variable (e.g., the mean level of the variable). Drawing conclusions on performance of a system from a single, short simulation run can be as misleading as management using, say, one shift’s production figures for evaluating a field-implemented system. The first issue of output analysis is to establish a clear definition of the performance variable(s) of interest. There is usually

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opportunity to collect observations on a large number of variables of interest during the simulation run. In the truck haulage model of 9.4.3.2, one might be interested in utilization of each loader, the average waiting time of the truck in the loader queue, the average production rate from each loader, the average total cycle time for the trucks, and perhaps others. Although any or all of these data are readily obtained from a simulation run of this system model, one is strongly discouraged from considering more than one or two variables in formal comparisons between alternative specifications of the decision variables. There are two reasons for this statement. First, as will become more clear in the discussion that follows, there is uncertainty involved in any estimate of performance from a stochastic simulation run. If one wants to ascertain the value of several performance variables with high accuracy, often an extreme amount of computer time will be required. Second, one is faced with difficulties in comparing alternative systems when multiple performance criteria are involved. In the example, if system A has higher loader utilization but higher average total truck cycle time than system B, how does one trade off a unit of loader utilization vs. a unit of total truck cycle time to decide which system is preferred? Multi-criteria decision making, that is, ranking alternatives while considering multiple performance variables of distinctly different natures, is an area of active research interest. However, most results from this field are not yet considered very practical. It should be noted that one can often aggregate many performance variables in terms of their contribution to cost or profit from the operation. In the truck haulage example, a revenue might be associated with each ton of ore produced, a cost might be imposed for each hour the vehicle is operated and for each failure incident. In turn, a single criterion such as net profit becomes the performance variable of interest in comparing alternative system design or control options. Other criteria might become performance constraints that all system designs must satisfy if they are to be considered true candidates for implementation. For instance, one might wish to select the production system alternative that produces at the lowest cost per ton subject to the constraint that the alternative produces at an minimum average rate of X tons per month. Here the performance variable “production rate” is not used directly in comparing alternatives. One just ensures that all candidates produce at the minimum acceptable level. Though it is strongly encouraged that the analyst establish a single performance criterion for formally comparing system alternatives, this is not to say that one should ignore the other criteria. Ad hoc, intuitive experiments with a simulation model can often provide considerable insight into system operation and often suggests useful design and control options. Within reason, such experimentation is strongly encouraged. Indeed, it is here where the animation of the simulation run can often serve a useful role in the analysis. Nonetheless, the study should conclude with formal, scientific comparisons. A final point must be emphasized regarding selection of performance criteria. Most of the literature discusses basing system comparisons on the value of the mean or average level of the performance variable (e.g., mean rate of production, mean availability). The mean is often, but not always, an appropriate basis for comparisons. The mean is so useful because it “boils down” the entire distribution to a single value. This value can be directly used in making comparisons in cases where total rewards or costs are proportional to the accumulated value of the performance variable over repeated or extended runs of the system. For example, total production revenues are likely proportional to the sum of individual tonnages produced during

Fig. 9.4.10. Performance variable of interest for conveyor spillage example.

future shifts. Here the mean is a reasonable basis for comparing two or more system designs. However, often other properties of the distribution of the performance variable, such as its variance, are also of interest. Consider the following example. In simulating material flows in a conveyor network, flow rate (cubic yards or cubic meters per hour) at each of the transfer points might be included among the system state variables. Belt width effects on flow rate at some critical intersection in the model might not be explicitly incorporated in the model (a fixed conveyor width would simply truncate the flow rate when it exceeds some fixed level). Rather, one might attempt to size the belt, ex post facto, once the model output has been obtained. Here one is using what some might call a functional model—a model where unit sizing or capacity effects on its operation are ignored. Such models are often appropriate when designing a system since unit size is typically a decision variable. What kind of performance variable would be of interest here? One that comes to mind is that time-persistent statistics might be gathered on the flow rate variable for the critical intersection. These data could be used, for instance, to generate a histogram (Fig. 9.4.10), where the magnitude of the vertical bars is equal to the proportion of time the flow rate is at any particular observed value. This histogram, assuming it accurately portrays long-run performance, could be used to provide information on expected spillage for any particular belt width. One would simply truncate the distribution at some fixed capacity level corresponding to a particular belt size; spillage rate would be proportional to the area above the point of truncation. Here it is clear that one would like to know the entire distribution of the performance variable. The information provided by the mean flow rate is insufficient for and, in fact, has little relevance to the needs of this analysis. As noted previously, simulation output does not give the distribution of the performance variable directly. Rather, this distribution, or properties of the distribution, must be inferred from data generated during a run using statistical techniques. There are some interesting complications that arise when applying statistical methods to simulation output. Consider again the truck haulage example. Assume that truck delay time in the loader queue is the primary performance variable of interest. It is quite clear that the delay times of individual trucks will be related to one another. If the delay time of one truck is long, it is very likely that the delay of the next truck will also be long. Similarly, if the delay for one truck is short, the delay of the next truck is also likely to be short. This illustrates a key feature of simulation output. Individual observations of output variables are likely to be correlated (positive correlation in this case). Classical methods of statistical inference that are based on assumptions that successive observations are independent and follow the same distribution, that is, they are independent and

CYCLES AND SYSTEMS identically distributed random variables (IIDRV), do not apply to simulation output. Two distinct cases can be identified for analysis of output: terminating simulations and steady-state simulations. Such distinction arises not from the nature of the simulated process itself but from the nature of the performance variable of interest to the analyst when evaluating that process. With terminating simulations, the desired measure of performance is defined relative to a specific interval of simulated time. With steady state simulation, the desired measure of performance is defined relative to the limiting distribution of the variable as simulated time goes to infinity. As an example of a terminating simulation, one might be interested in the volume of material moved for a production shift in the truck haulage example. A terminating simulation must have well-defined start-up conditions and terminating conditions. In the example, one might start as previously described in 9.4.3.2. One might terminate using a rule such that if a truck dumps its material within 10 min of quitting time, it returns to the service area. Often one might be interested in system performance only during periods of “peak demands” on the system. For example, for some performance variable, one might simulate a track haulage system only during the period around shift changes, say, from 3 pm to 5 pm. Such simulations are also terminating; however, definition of initial conditions may be more difficult than in the previous example since activities of the system that are in progress when the simulation run begins may not be known and might be random. As an example of a steady-state simulation, one might study, using a simulation model that accommodates unit failures, the availability of the furthest inby face conveyors as influenced by the size and location of surge storage bins in the belt network. If contemplating incorporating such buffer capacity in the network, one would certainly want to know implications on mine production over an extended time horizon. However, there are no natural starting or terminating conditions for considering performance of this system. Steady-state simulations are frequently employed where performance measures are long-term in nature and where there are no natural events to terminate the run. An inherent characteristic of steady-state simulation is that the initial state of the system influences the early observations of the performance variable. For instance, in the truck haulage example, assume that for some reason one is interested in the steady state value of the mean delay of the trucks at the loader queue. The simulation might be started with all trucks queued up at the two loaders. Under such circumstances, the early delays will be longer than they typically would be. If data from the early portion of the run are used in estimating the mean steadystate delay, the estimate will be biased high because of these long delays. Any other starting condition is also arbitrary and will introduce some type of bias. This is called initialization bias, and it should be dealt with carefully. The distributions for the exogenous input variables for steady-state simulations must remain constant throughout the simulation run. In contrast, terminating simulations are by nature transient. These distributions may change over simulated time. Moreover, no effort is made to eliminate the effect of initial state on the performance observations. In fact, one wants to explicitly capture the effects of initial state on performance. It is considered a fundamental aspect of the process under study. Terminating simulations are much easier to analyze than steady-state simulations. Assume interest is focused on the mean value of some performance variable. The analytical procedure is to make multiple runs of the simulation model, each spanning

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the performance period of interest. Each of these runs, or replications, would use a different sequence of random numbers. Then the mean value of performance variable, observed for each individual replication ii = 1,2, . . . , r, where r is the total number of replications, is calculated. Though the individual observations of the performance variable within a replication are not statistically independent, the i = 1,2, . . . , r, since they are generated using independent random number streams, clearly may be treated as IIDRV, and classical statistical techniques may be applied. Since the are averages, they will tend to be normally distributed in many applications. (There are central limit theorems for correlated random variables.) The data can be used to compute a confidence interval for the performance interval as follows. Let

(9.4.3)

(9.4.4)

Then compute a (100 – a)% confidence interval for the mean value of the performance variable as (9.4.5)

What has been discussed is a procedure that has high probability, specifically 100 – a, of constructing an interval that contains the unknown value of Preferably, the interval will be small in width, but this depends on the innate variability of X. One can overcome wide intervals by increasing the r, as is evident from the previous formulas. In using this approach to compute a confidence interval, one does not say that is contained in the interval with probability 1 – a. The probability statement is about the procedure. A probability statement about is inappropriate since it is a constant (though unknown), not a random variable. Fig. 9.4.11 illustrates two major approaches for characterizing the mean value of a performance variable in a steady-state simulation. The first illustrated approach is similar to that used in terminating simulations. One makes several replications of the model using different random number sequences. Like the terminating case, the mean level for each replication will be IIDRV. However, since interest is in steady-state performance, observations from the early part of each run are eliminated to prevent these observations from biasing the estimator. The second approach is called the batch approach. Rather than making several replications, a single long run is made. This long run is divided into a number of batches. For example, if 4000 truck delays are observed in the simulation run, the run might be divided into 40 batches of 100 observations each. (There is little incentive to ever create more than 40 batches.) Although consecutive individual observations of the performance variables are correlated, intuition suggests that if the batches are big enough, the means for each batch will tend to be uncorrelated. This is frequently observed to be true. These means will also tend to be normally distributed. The batch observations might thereby be treated as IIDRV.

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1. How to determine how many replications of a terminating simulation are necessary to characterize a performance variable with a level of precision specified by the analyst. 2. Procedures to determine how long the initialization period lasts for a steady-state simulation. However, these procedures can only be viewed as giving approximate answers to this difficult question. 3. Procedures for determining the batch size and run length necessary for determining the mean level of a steady-state performance variable with a certain level of precision using the batch approach. 4. Procedures for comparing system alternatives. These include techniques for computing confidence intervals on the difference between the mean levels of performance in two systems, for selecting the best of a number of distinct system alternatives, and the use of formal experimental design in characterizing system response to the adjustments of the decision variables. 5. Procedures for reducing the variance of the response variables by manipulations of the input data to the model. With these procedures, response variables can often be estimated with greater precision, and comparisons between alternatives can often be more easily made.

9.4.3.5 Discussion of Specific Applications batch 1

batch 2

batch 3

batch r

Fig. 9.4.11. Two approaches to estimating a performance variable for a steady-state simulation.

The batch approach has the advantage over the replication approach in more efficient use of data since one only throws data away for the initial transient period once, not r times. Moreover, it is difficult to ascertain how many data should be eliminated to eliminate initialization bias. This differs from one system to the next. In the batch approach, initialization bias becomes less and less significant as more data are collected by extending the length of the run. However, with the replication approach, one might collect more data by adding replications. If the length of the initialization period has been underestimated, a narrow confidence interval might be constructed around a biased estimator of performance and such an interval can be very misleading. Both the batch and the replication approach would use the same formulas given previously for terminating simulations in the numerical computation of the confidence interval. Room exists here only to highlight some of the major points in analysis of output from simulation models. Hopefully, it is clear to the reader that simulation models with stochastic input variables do not directly describe performance of the system. Rather, they give data from which performance can be inferred with appropriate use of statistical techniques. Failure to consider formally these techniques is a weak point of many applications of simulation to mining problems. The reader is referred to the texts Law and Kelton (1982), Banks and Carson (1984), and Fishman (1978) for more detailed discussions of output data analysis. These texts address additional topics as follows:

The objective of this segment is to identify typical applications of simulation modeling in mine production systems engineering, to discuss some of the key technical issues in structuring these models, and to identify software packages that might be applied to these problems. Major differences in structure exist between models involving continuous material handling systems and discrete vehicle transportation systems, and this forms the basis for organizing this section. Continuous Material Handling Systems: The major continuous material handling application involves conveyor network modeling. Some of the problems that might be addressed using simulation models of these systems are as follows. 1. Design of systems for throughput capacity. When a belt handles the output from several production sections, designing capacity to meet the combined peak loads from all of the sections can lead to unneedful expense in terms of capital and operating costs. Simulators can describe the distribution of material flow rates into any belt transfer point. This in turn can be used to evaluate a particular system configuration—specified in terms of network structure, belt speeds, use of surge bins to trim peak flow rates, use of limit switches and other operating controls, etc.—for its ability to handle material flows without excessive spillage or curtailments of availability of the network to the production sections. 2. Assessment of network configuration impacts on availability of the transportation system to the production systems. In many applications the production section and belt system form an extensive serial chain of operations. Belt system failures frequently provide a major constraint on production output. The simulators provide a means for testing alternative configuration options to assess their impact on network availability. This includes assessing the impact of buffer storage capacity (e.g., bunkers), appropriately sized and inserted at strategic locations, which are a means to temporarily breaking the serial dependence of one portion of the network on other portions. 3. Testing control strategies for belt monitoring and control systems. The potential for computer-based monitoring and control in underground mines is now just becoming evident, with the belt system a major focus of attention. A variety of means for real-time control of the dynamic material flows potentially exist, such as variable speed belts and feeders and feedback to

CYCLES AND SYSTEMS the production operations. Simulation will no doubt play an important role in development of these strategies. Turning the discussion to highlight some of the key technical aspects of modeling these systems, there are two major approaches used to represent material flows. In the first approach, a conveyor is viewed as a collection of small adjacent cells, which is represented in the computer as an array. Attributes associated with each cell can denote properties of the material, for example, thickness on the belt or type of material. Time is advanced in small discrete time increments and, effectively, the attributes are shifted ahead a single register, representing material flow in the outby direction. At junctions or transfer points, cell attributes are combined in an appropriate fashion to represent superposition of material flows. For example, if the outby belt travels at the same speed as the inby belts, thickness attributes are simply added. This is, effectively, a simple form of continuous simulation. These models execute slowly relative to the approach discussed in the following, especially if one physically shifts records in the array to model material movement. It is much more efficient to shift a pointer to the array location that corresponds to the cell at the head of the belt, as done in some packages, than it is to move all of the records for each time advance. The second approach employs discrete-event simulation. For many analytical purposes, one obtains adequate information if the flow rates are known at each transfer point, into and out of each bin or feeder, and out of each discharge point. For example, spillage and throughflows can be ascertained directly using these rates. Though knowledge of position of material along the conveyor at any point in time requires continuous representation as discussed previously, flow rates may be modeled as variables that only undergo changes at discrete points in time. If a change in flow rate occurs at one transfer point, one simply uses belt speed to forecast the time when a resulting change in flow rate will occur at the next outby transfer point. The magnitude of this future rate change is determined by multiplying the ratio of the speed of the incoming belt to the outgoing belt times the current rate change. A change of flow rate into a feeder/bin can be used to schedule a feeder bin overflow event if the new input flow rate exceeds the maximum discharge rate of the feeder, an event that may be preempted if rates decrease in the future before the scheduled event occurs. It may also schedule an increase in discharge rate if the current outflow rate is not currently at maximum. Further, such a change in flow rate can be used to schedule a future decrease in the outflow rate of the feeder if the input rate is less than the current outflow rate. Models using this representation may be coded using the event-scheduling algorithm mentioned previously. Since a variable time increment approach is used, they operate much faster than the other class of models. The BELTSIM program uses an approach similar to this (Bucklen et al., 1969). Perhaps the most critical aspect of conveyor network modeling is obtaining a realistic representation of material arrival to the system. Exceeding the throughput capacity of units in a reasonably designed conveyor network will typically be a “rare event .” Predicting accurately, with a reasonable amount of run time, the incidence of rare events via stochastic simulation can be difficult. For this reason, it is important that the description of material arrivals accurately portray the real-world situation. For example, one might represent material arrivals from a continuous miner section in a coal mine using a sequence of discrete arrivals to the system. Shuttle car interarrivals would be random, but the parameters of the interarrival distribution would not be held constant through the simulation run. Rather, these parameters would be changed in a cyclic fashion to reflect the underlying cut sequence. A random place-change delay would also be allowed between each cut. The entire sequence of

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interarrivals may be preempted from time to time with delays representing major equipment failures. If additional realism is desired, interarrival times might alternate between high and low values for the two cars for those cuts where the tram paths differ substantially in length. One might also provide for shuttle car failure, changing the interarrival pattern when this event occurs. For a longwall unit, material arrivals would be continuous, but rates would vary for different portions of the cut. The overall arrival pattern would be cyclic and interruptions might be allowed to represent equipment failures. Available conveyor simulation packages vary in their ability to accommodate such detail. Some are quite flexible. A number of packages for simulation of conveyor networks exist. These include BELTSIM (Bucklen et al., 1969), Continuous Material Handling Simulator (CMHS) (Tan and Ramani, 1988), Coal Mine Belt Capacity Simulator (CMBCS) (Thompson and Adler, 1988), BETHBELT- (Newhart, 1977), and UnderGround Materials Handling Simulator (UGMHS), (Manula, 1974). The recent paper by Sturgul (1989), discusses the use of a simulation language to construct a belt simulator. Discrete Vehicle Transportation Systems: Simulation also provides a basis for analysis of many detailed aspects of mining systems employing discrete vehicle haulage in combination with excavation/loading equipment. Some of the issues one might attempt to address follow. 1. Design of haul road profiles. For example, should required climbs be achieved through use of short steep road segments or extended segments of lesser grade? 2. Fleet makeup of transporters. This addresses the determination of the best structure of a fleet of haulage vehicles at a mine, including the number of vehicles, their size, the number of units kept on standby in the event of breakdowns, and static allocation of the transport units among multiple loaders in order to maintain desired production ratios among the loaders. 3. Analysis of real-time fleet control strategies. Modern computer-based dispatching and fleet management systems often employ sophisticated computational schemes for improving the effectiveness of equipment utilization and maintaining control of quality of the mined product. However, the schemes are based on heuristic approaches (see 9.4.4). Simulation provides a technical basis for testing the quality of these heuristics and comparing alternative tactics. 4. Detailed analysis of equipment interactions on overall system performance. For example, one might consider modifications of the loading site to change maneuvering required for truck spotting or to allow double-sided loading at a shovel. 5. Analysis of working section and pit layout options. Examples of such analyses include where should an in-pit crusher be located to best serve multiple load sites and what are the ramifications of alternative cut sequences for a room and pillar section? The detailed description of vehicle motion may require use of continuous simulation. A basic differential equation (9.4.1) can be used to describe the spatial position of a vehicle. When the vehicle is increasing in speed, av is typically determined from the expression,

(9.4.6) In this relation, Fr is the rimpull force at the current velocity, which may be taken directly from the rimpull chart for the vehicle. Fm is the resistance force offered by the vehicle, which depends on rolling resistance, air resistance, and grade resistance. Corrections for rolling and air resistance are usually incorpo-

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rated as a function of current velocity of the vehicle when making such simulations. Mc is the corrected mass that accounts not only for the actual mass of the vehicle, but incorporates a corrective term, which is also a function of current velocity, to account for losses in the drive system of the vehicle. It is seen that av can be known given a collection of state variables that includes the current velocity of the vehicle, grade, and rolling resistance of the haul road. Given av, Eq. 9.4.6 can be integrated to forecast the velocity and position of the vehicle at the end of a subsequent time increment. Other factors taken into account in such simulations are speed limits for the road segment, which restrict maximum attainable speed, braking/retardation, and losses for the “dead time” when shifting gears (depending on the nature of the drive system). The VEHSIM package (Anon., 1984) is widely used for such simulations. It incorporates performance parameters of many Caterpillar vehicles and allows users to input parameters for other vehicles. Recall that the selection of state variables, in part, depends on the the objectives of the simulation study and is not directly defined by the physical nature of the system. In simulations of material excavation and handling systems, performance is typically addressed in terms such as material production or throughput rates, equipment utilization, average cycle or delay times, etc. Performance measures such as these may be reliably obtained from simulation runs that do not provide knowledge of vehicle position at each instant of time. If one is in a situation where travel times are not available for various hauls (e.g., from time study data), it is often a good practice to use a vehicle motion simulator to provide data descriptive of haulage times for various segments of the haulage cycle. Subsequently, one uses these data as a basis for the input to a discrete event simulation model of the mining operation. The discrete-event model will operate much more efficiently, will not be repetitively computing deterministic haulage times, will readily accommodate stochastic aspects of the process, and can flexibly handle detailed aspects of the process relevant to the performance variables of interest. A number of software packages have been developed for modeling these systems for both surface and underground mining. They include: 1. GPSMS, General Purpose Surface Mine Simulator (Albert, 1989), couples ore body modeling with operations simulation. Block models may be constructed to describe local geology and mine property boundaries. Operations descriptions are input to the package via a two-level structure. The first, “Equipment Face Activity Description,” details excavation operations. The second, “Equipment Deployment Description” describes equipment operations and activities spatially and sequentially (i.e., the overall mining plan) and ties extraction with materials handling. Support modules are incorporated for simulating dragline operation, truck haulage (continuous simulation using rimpull curves), and conveyor haulage. This package extends the capability of its predecessors, the Total System Surface Mine Simulator (Albert, 1979) and Open Pit Materials Handling Simulator (O’Neil, 1966), although these packages have unique modules that may be of value and are not supported in GPSMS. 2. FACESIM (Prelaz, et al., 1968; Suboleski and Lucas, 1969) and UnderGround Material Handling Simulator (UGMHS) (Manula, 1979) can be used to simulate room and pillar mining operations, including ancillary operations. The input structure for UGMHS is similar to that for GPSMS. Motion of haulage vehicles may be established using continuous simulation in UGMHS, whereas distributions or constant values are input using FACESIM. The paper by Bise and Albert (1984) compares these packages and the use of simpler deterministic models of the mining cycle.

3. LHDSIM (Beckett et al., 1979) is a package for simulating a load-haul-dump system for room and pillar mining operations. 4. SCSMLT (Peng et al., 1988), simulates haulage in open pit mines and has features for interfacing discrete vehicle haulage systems to a crusher/continuous haulage system. Examples of applications where the modeling was executed using a simulation language include Sturgul (1987), where alternative locations for an in-pit crusher were investigated; Mutmansky and Mwasinga (1988), who examined the general applicability of SIMAN to modeling mine production systems and applied the language to model a truck/loader system; Weyher (1976) who modeled room and pillar operations using GPSS; and Harrison and Sturgul (1988), who examined the main haulage system for a large underground mine and modeled several alternative transportation systems mixing both truck and train transport.

9.4.3.6 Simulation Case Study A case study will illustrate the process of conducting a simulation study. The study has been “manufactured” by the author, but it is intended to portray major aspects of the execution of a simulation study in a realistic fashion. Statement of Problem: A multi-mine coal operator has recently experienced some difficulty in meeting sulfur specifications for one of its major clients. Although construction work will begin shortly for new operations in a low-sulfur reserve owned by the company, in the interim, a greater quantity of low-sulfur coal is being obtained through the addition of two continuous miner sections at one of its existing operations working a low-sulfur seam. The addition of the two units brings the total number of working sections at the mine to four. A problem has been experienced because of the inadequate size of mainline belts to handle the peak production capacity of the four units. Several overload-related spills have occurred in the past few weeks since the new units have come on-line, and action needs to be taken so that this situation does not continue. Decision Alternatives: The mine is nearing the end of its life, and since the belt line carrying the combined flow from the four units is quite long, the capital expenditure for modifying the existing conveyors so that they have higher capacity cannot be justified. However, one option that is easy to implement and is believed to have potential for alleviating this problem is fine tuning the feeder discharge rates at the production sections. By slowing the feeders from their current levels, the discharge of an individual shuttle car is spread on longer, thinner layers on the conveyor belt. This, in turn, directly reduces the magnitude of the load observed at the transfer point where flows from the four units converge. Such a modification is expected to reduce the incidence and severity of spills. Note that it may not be desirable, from the perspective of overall production output from the mine, to set all of the feeders at the same speed. Hence the decision alternatives considered in this case study may be expressed in terms of four setpoint values, one for each of the four section feeders. Of course, there are other control options that probably should be considered. With minor modifications, the model presented in the following is flexible enough to consider many other decision alternatives that one might conceive such as, for example, staggering start-up times of the production units so that the duration of the periods when all four units are active is minimized. However, for the purpose of this study, only feeder discharge rates will be considered. Structure of the Simulation Model: The simulation model will incorporate (1) face operations for the four production units, (2) the feeders, and (3) the belt network to the transfer point

CYCLES AND SYSTEMS where the material flow from the four units converges. The third component of the model is actually quite trivial for this study. A fairly detailed model of face operations is necessary for two reasons. First, for the units where feeder speed will be reduced from current values, there is no direct way of predicting what the shuttle car interarrival times will be after the change is implemented. Certainly, there is a chance that on some cycles, the car dumping time will be increased from its current value if the material from the previous car has not cleared the feeder, but there is no direct way of knowing how often this will occur and what the net effect will be on total shuttle car cycle time. Second, for this particular problem, there is a coupling between the belt network and face operations that should be considered. Changing feeder speeds has potential for both positive and negative impact on overall economics at the mine. By increasing shuttle car dump times on occasion, the short-term rate of production output from the mine will be negatively affected. On the other hand, if a major spill is avoided, one prevents shutting down the face units while the spill is cleaned up and production is increased through the increase in available operating time. As discussed in more detail in the following, the average rate of production output is employed to compare decision alternatives. To accurately reflect the coal output, the serial dependency of the face units on the operation of the belt should be incorporated in the model. It is interesting to note that the coupling exists in this case due to the nature of the performance criterion that is used in making the comparisons. An issue that is believed to be important for the study is the effect of cut sequence. The variable distance between the cut and the feeder might have a pronounced influence on the effect of changing feeder speeds. If the cuts are close to the feeder, shuttle car interarrivals will be short and the feeder is likely to have more surge when the arrival occurs. Short hauls also have more dead time, and a delay in dumping is not as likely to turn into an overall delay in cycle time. For this reason, the model was constructed to incorporate the cut sequence followed by each section. The model was coded in the SIMAN simulation language. Process interaction routines (in SIMAN, these are called “block models”) were written to describe operation of the face units and the belts. Coal flow through the feeders and belts were modeled using flow rates as state variables since this approach has considerable advantages when modeling bulk material flows on continuous haulage systems (see 9.4.3.4). The SIMAN language does not readily accommodate such a representation for a surge storage device like a feeder, and for this reason the following event routines were written: (1) shuttle car arrival at feeder event, (2) feeder full event, (3) shuttle car empty event, and (4) feeder surge depletion event. Table 9.4.3 gives, as an example, the event logic table for event 1. There are several interesting features of the block model. First, as one might expect, a separate process routine is not required for each face unit. The sequence of operations undertaken by a continuous miner, a shuttle car, and a roof bolter is very similar among the four units. The SIMAN macro concept (similar mechanisms are available in other simulation languages) allows entities from each of the four units to share the same process routines that describe the overall sequence of operations. Moreover, details necessary for describing spatial aspects of the process are readily decoupled from the process routine. In the model that has been developed, the shuttle car routine is roughly defined as follows: 1. Wait at the miner change point if the other shuttle car has not cleared the change point. 2. Once access to the miner is possible, seize a resource to block entry of the other shuttle car and tram to miner.

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Table 9.4.3. Event Logic Table for Event – Shuttle Car Arrival at Feeder First compute the current surge level in the feeder, E, as

where D is the current discharge rate of the feeder, t is the current time, and Te is the time that the next surge depletion event (event 4) has been scheduled. (If D > 0 such an event is always scheduled.) Condition

Action

Always

Set feeder input rate I to the shuttle car discharge rate R. Schedule a shuttle car empty event (event 3) at time t + L/I where L is the payload of the shuttle car. Schedule a feeder full event (event 2) at time t + (K – E)/(l – D) where K is feeder surge capacity. Also, delete any previously scheduled surge depletion event (event 4). Schedule a surge depletion event (event 4) at time t + E/(D – I )

If D < I (feeder filling)

If D > I (emptying) and E > 0

3. Wait while loaded. 4. Tram to miner change point and release the resource that allows the other shuttle car to enter. 5. Tram along a sequence of stations until arriving at the feeder change point. 6. Seize a feeder access resource and tram to feeder. 7. Activate a shuttle car arrival event (user-written event routine 1) and wait. 8. Release the shuttle car from the wait state when shuttle car empty event (user-written event routine 3) has occurred. 9. Return to the feeder change point and release the feeder access resource. 10. Tram along a sequence of stations until returning to the current miner change point. Externally defined input data to the model define stations that correspond to physical locations of the crosscuts and entries. In addition, sequences of these stations are defined that control vehicle movements. Equipment moves along the cut sequence are handled in similar fashion. Only a few statements were required to model the four continuous miner units and movement of material along the belts. Input data to the program, in addition to the station layouts and tram sequences noted above, are as follows: 1. Feeder discharge rates and surge capacity. 2. Belt transit times from the section feeder to the point of convergence. 3. Tonnage per cut. 4. Distribution of shuttle car, miner, and bolter tram rates. 5. Distribution of shuttle car payload size. 6. Distribution of time to load a shuttle car. 7. Distribution of time to bolt a cut. 8. Distribution of downtime when an overload spill occurs. 9. Distribution of time between unscheduled delays in the face production cycle and duration of such delays.

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As can be seen, the amount of field work to obtain the various input distributions required by the model is not excessive. Simulation can usually proceed with a rather small investment in time studies. Moreover, these studies typically should focus on the various elemental times of the production operation, spending perhaps a few hours observing each of the major parts of the operation. Simulation is a means of synthesizing time study data and drawing meaningful conclusions from this data that otherwise cannot be obtained. In this case, perhaps the most difficult data to obtain would be the distributions involving unscheduled delays in the face production cycles. For the purpose of relative comparisons among the decision alternatives that have been studied, it might be reasonable to ignore such delays. Ignoring such delays would, however, be inappropriate if one hoped to obtain accurate cost figures from the simulation study. Application of the Model: From examination of the capacity of the belts handling the combined flow from the four units, it is clear that the overload incidents occur at this mine only when peak loads from all four units meet simultaneously. In such a situation, reducing the frequency of overloading incidents can only be accomplished by reducing the sum of the discharge rates of the feeders to the minimum capacity of the belts handling the combined flow of the four units. Moreover, there is clearly no incentive to reduce the discharge rates below this level since this will only reduce the rate of production from the working faces. These questions remain: 1. Will the reduction in feeder discharge rates cause an excessive decrease in the rate of production that cannot be offset by the gains in operating time? 2. How should one best go about allocating the discharge rate reductions among the four units? To help answer these questions, four alternative strategies have been investigated. Alternative 1 represents the status quo. Alternatives 2, 3, and 4 all specify the same combined feeder discharge capacities equal to the capacity of the belts handling the combined flows. With alternative 2, the rate reduction is split equally among the four units; with 3, it is split equally among three units; and with 4, it is split among just two units. Allocating all of the reduction to one unit was not considered since this would clearly be an excessive choke on output from that unit. Though there is some cost associated with cleaning up a spill, the costs are an order of magnitude less than the lost production costs associated with any belt shutdowns that might occur. These shutdowns are reflected directly in the simulation model. Ignoring cleanup costs, the alternatives have been compared in terms of the time average flow rate on the mainline belts, a measure of total production output from the mine. Simulation runs were made for a single production shift since this represents a natural termination point for the run, and the output is analyzed as realizations from a terminating simulation. To deal with the potentially significant influence of cut locations and the cut sequence, the starting cuts were randomized for each run. (One could perhaps find better ways to handle the influence of the cut sequence, which introduces a long cycle into the operations, than through randomization; this appears to be a rather complex issue from a technical perspective.) A total of 20 runs was made for each alternative and the results are given in Table 9.4.4. As the histogram for the performance variable for alternative 1 in Fig. 9.4.12 shows, there is considerable variability of the output response. The sample mean production rate for each alternative is shown in the table along with a 95% confidence interval for the mean. The results appear to imply that a reduction in feeder speed is desirable and that it is best to allocate the reduction equally among the four units (alternative 2). An equal allocation in this case is not surprising, but such a result probably would not

Table 9.4.4. Output for the Four Alternatives Considered in the Case Study

Fig. 9.4.12. Production rate distribution for alternative 1, current feeder setpoints.

hold if there were significant differences in the production cycle among the four units. Though a comparison of sample means is the device for selecting the best alternative, such a selection cannot be made with certainty. The sample means only represent estimates of the true, but unknown, mean. The fact that the confidence intervals of several alternatives overlap provides an indication that one might expect some difficulty when coming to a decision about the best alternative.

CYCLES AND SYSTEMS In this problem, one might apply a procedure where the results of the first 20 runs are used as a basis for determining how many more runs to make before making a final decision on which alternative is best. These initial runs give considerable information in the inherent variability of system performance for each alternative. Using these measures of variability, the number of additional runs might be established on the basis of (1) the level of probability of a wrong decision that one is willing to accept, and (2) the minimum difference in performance among alternatives that one considers to be of significance. Once these additional runs are made, a final decision could be made by comparing the means, and one would have assurance that the two stated conditions on uncertainty are satisfied when making the decision. Further discussion of the nature of such procedures are beyond the scope of this presentation; interested readers are referred to the texts cited at the end of 9.4.3.4.

9.4.4 FLEET DYNAMICS AND DISPATCH The stochastic aspects of mine operations—an equipment failure incident, variation in tram times or loading rates, etc.,— preclude development and field implementation of a fully prescriptive plan for operations. Rather than attempt to follow a rigid sequence of operations, often much can be gained from ongoing, real-time analysis of the current status and recent history of the operations. This analysis might then be used as a basis for taking control actions to improve subsequent performance of the system. This is perhaps most evident, and the technology is most fully developed and accepted, for real-time management (dispatch) of pooled truck fleets serving multiple loading units. Ideas similar to these might be applied to any type of mine production system employing discrete vehicles, although a large size of operations and the ability to allocate flexibly the transport vehicles among multiple excavators/loaders enhances the potential utility of such approaches. The field is one with little theory; the basis for control actions involves application of heuristic approaches. Though innately heuristic, some procedures prescribe control actions on the basis of solutions to quite sophisticated mathematical models. The proof of the pudding is in the eating, and though heuristic, these techniques have been reported to be quite effective in increasing the rate of production from these mines for a given level of loading and transport equipment (Clevenger, 1983). Some approaches have also helped in simultaneously meeting a number of additional operational objectives such as better control of oregrade targets. An opportunity one has in certain discrete vehicle material transport systems involves the fact that the vehicle may be flexibly routed. Rather than running the vehicle in a locked cycle between a particular loader and dump site, one may use the vehicle to service multiple loaders and dump sites. Moreover, rather than following a predetermined, rigid sequence of movements, routing can be dynamically controlled, switching the sequence that loader and dump sites are visited by the truck from one cycle to the next. The underlying reasons why advantages in system performance can be gained by such dynamic control include: 1. One can respond to information on the current state of the system that reflects the realization of particular random variables (e.g., the observed cycle time to load a particular truck) that could not have been predicted exactly ahead of time; 2. One can appropriately respond to deviations from the expected levels of performance that were used to develop the operational plan (e.g., one shovel is having an easy time digging and is completing its load cycle more quickly than expected and

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this provides opportunity for increased production over what was expected if levels of truck capacity allocated to the shovel are increased). In examining truck dispatch strategies that have been employed, distinctions among them can be made with respect to two major factors as follows. 1. The extent a forecast of future states of the system is employed to make the current dispatch decision. Some approaches consider only the current truck (e.g., immediately upon completion of dumping) when making the dispatch decision prescribing where the truck should next be routed. Others attempt to forecast the state of the system for a number of future dispatches and make the current dispatch while cognizant of this forecast. For instance, one might send the current truck to its “best” shovel (e.g., the one that will be ready to load the truck at the earliest future point in time), but there is a good second choice for this truck. The next truck that will complete dumping also has the same “best” shovel but no second choice that is very good. Considering performance of the two trucks together, it would be better to send the current truck to its second-best choice. 2. The scope of the operational objectives that drive the selection of dispatch assignment. Some strategies base dispatch decisions on narrow criteria (e.g., send the truck to the shovel where it is expected to be loaded first). Other strategies base dispatch decisions in accordance with how well the decision contributes to conformance with a production plan. The plan is developed to enhance specific performance criteria such as overall mine production rate. It may also recognize various operational constraints such as achievement of grade targets with the ore blend from the multiple loading sites and desirable ore/gangue production ratios. These production plans are typically short term in nature, are routinely updated, and are frequently based on solution to math programming models for short-term production scheduling and equipment allocations. Two examples of some simple “one truck at a time” dispatch heuristics are as follows: 1. As mentioned before, “send the current truck to be dispatched to the loader where it is expected to be loaded first.” One would use figures on average load times and tram rates and current positions of previously dispatched trucks headed to the loader in question to forecast when the loader will have serviced all of these previously assigned trucks. Then travel time to this loader for the truck to be dispatched is compared to the forecast time when the loader will be free to estimate the future point in time that truck loading for the dispatch vehicle would begin. This is done for all loaders and the truck is sent on the shortest path to the one that is expected to load it at the earliest point in time. 2. “Send the current truck to be dispatched to the loader that is next expected to become idle (after servicing all previous trucks assigned to that loader).” One would forecast the time each loader is expected to become idle as discussed in the first example, and without consideration of the distance to that loader, the current truck is sent to the loader expected to become idle at the earliest point in time. These rules are very simple and have some intuitive appeal. Note that one may use recent history on load time and tram rates to obtain better forecasts as operating conditions change at the mine. The first rule is noted to cause loader utilizations to become unbalanced (Lizotte and Bonate, 1987), since trucks tend frequently to be sent to the closest shovels, ignoring the remote ones. In the second case, production ratios will be more controlled but are primarily influenced by allocation of the shovel to the available loading sites. Both rules may result in shortsighted decisions because the current decision may be unfavorable when considered in conjunction with dispatches that might be made

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in the near future. Further, the objective criteria for both rules are very narrow and may not conform to overall operating objectives for the operations. To see how one might approach overcoming the shortcomings of these simple rules, the operation of one of the more sophisticated dispatching systems, DISPATCH, which has been developed recently and is described by White and Olson (1986), is now discussed. The DISPATCH system first solves a sequence of two linear programming problems to establish a short-term production plan. This plan is updated routinely as will be discussed in the following. When the plan is established, it is based on the current status of mine operations, reflecting siting and current availability of the loading shovels, estimates of quality characteristics of ore at working faces and stockpiles, and operational status of the process plant. The first linear programming (LP) model defines “optimum” production rates for the various shovels, including those operating from stockpiles. The objective function of this optimization accounts for penalties associated with failure to meet process-plant input demands and violations of blend-quality constraints, and weights established by management reflecting the current relative desirability that plant feed originate from stockpiles or from active faces. Given these overall flows from the material sources (stockpiles and working faces), a second LP is solved to determine the allocation of truck resources to move material flows efficiently along available haulageways. The model prescribes how many cubic yards (cubic meters) of haulage capacity should be allocated to all “paths” in the system. The second model is set up to maximize production rate from the system. It is loosely coupled to the first model in that the first model prescribes minimum production from working faces and stockpiles for the second model. Any excess production from working faces that can be achieved would be stockpiled. The use of the output of the second model is to provide a criterion for truck assignments in real-time dispatch. Roughly speaking, the objective of the dispatch will be to implement and maintain the “optimum” haulage allocation determined by the second model, which is given in terms of the volume of haulage capacity that should be allocated to each path. Contrast this to the objectives of dispatch decisions for the two simple heuristics cited. As mentioned previously, the two LP models form a shortterm production plan. Whenever a major upset such as a shovel breakdown or process plant outage occurs, the models are solved again to establish a new short-term plan. Moreover, blend constraints in the first-level model are structured to allow some slack in conformance to rigid bounds on ore grade. An estimate of the moving average quality of the ore feed to the process plant is continuously maintained. There is a bound imposed on the maximum period of time that can pass without replanning so that excessive and sustained deviations from target grades do not occur. The more slack permitted in complying with grade requirements when solving the first-level model, the more frequently operating plans must be updated. The actual dispatching procedure uses the deviation between actual current assignment of trucks to a path and the optimum assignment levels determined by the second stage LP as a basis for evaluating dispatch decision alternatives. All trucks that are in transit from a loader to a dumpsite are considered collectively with the current truck to be dispatched when making assignments. At the time of a dispatch, the time each loader will “need” a truck assignment (typically in the future) is forecast. “Need” is determined by the LP haulage capacity prescription. The loader with the earliest need is considered first. The truck closest

to this shovel is nominally assigned to it. Eliminating this loader and truck from consideration, the shovel with the second earliest need is considered in the same fashion, etc., until all loaders have been considered. This will typically result in an assignment for the current truck to be dispatched. The point of this discussion is to illustrate a way that dynamic dispatch systems can be used to (1) help achieve a goaloriented production plan that, because of its short-term nature, is itself responsive to changing conditions at the mine, and (2) make decisions using updated forecasts of expected future states of the system rather than making each truck assignment independent of such forecasts. The overall logical structure of most of the more recently developed dispatch systems will resemble the one discussed here. However, they will vary considerably in details. Although the mathematical models are described rather than explicitly reported, the system at the Mount Wright mine (Soumis et al., 1989) apparently differs from DISPATCH in a number of respects. Some of these include (1) consideration of alternative loader site locations when making preliminary equipment assignments, (2) use of a nonlinear objective function in determining optimum haulage allocation, which results in a more balanced distribution of truck capacity assignments, (3) use of a simple process-plant model for estimating the actual costs of deviations from blend targets (in the previous procedure these were, more or less, guesses), and (4) solution of a classical assignment model for dispatch decisions where the objective function minimizes the squared difference between current forecast waiting times for the shovels and trucks and average waiting times expected for implementing the operational plan. This segment is concluded with two additional notes. First, the dispatch algorithm (but not the planning models) for these systems must be able to execute in a very short period of time (a matter a few seconds). With careful consideration of the mathematical techniques employed, one can use rather extensive models, as evidenced by the Mount Wright system, for making dispatch decisions. Second is a reminder that the procedures are heuristics, and many modifications are conceivable. Simulation, as discussed in the previous section, can serve to evaluate alternative dispatch heuristics and tactics for a given mining operation.

9.4.5 STOCHASTIC PROCESS MODELS OF MINE PRODUCTION SYSTEMS The weakness of simulation as a tool for systems analysis should be evident from the discussion of 9.4.3. One wants to know the distribution of performance variables, perhaps, even how these distributions change as a function of time, but simulation only gives data from which one may infer some of the major properties of these distributions. It does not give the distributions directly. Moreover, it is typically quite cumbersome to make generalizations regarding system performance and its response to the decision variables on the basis of simulation output. On the other hand, the theory of stochastic processes provides a basis for analytical modeling of these processes. The field is comprised of a number of basic topics including Poisson processes, Markov chains, renewal theory, continuous-time Markov processes, semi-Markov processes, Brownian motion, etc. These, in turn, service many applications including results in queuing theory, inventory theory, reliability theory, sampling plans for quality control, and inference-based measurements using signals gathered by sensing instruments, among many others. The analytical results may, in some cases, give the distributions of the performance variables directly. They may also facilitate comparisons among alternative values of the decision vari-

CYCLES AND SYSTEMS ables, perhaps permitting mathematical optimization. Often they give valuable insights in to the nature of system operation that would not have otherwise been obtained. An example of this for a mining application is given in the following. Typically, more assumptions are required in order to progress with this approach to systems analysis than are required when using simulation. If one is not careful, the result of the modeling effort may be an abstraction of little relevance to the real-world system. One is cautioned against “pulling a formula from a book” without understanding the assumptions and nature of the result. Nonetheless, the results that can be obtained by using these approaches often justify the efforts. Subsequently, some examples of the more recent work in mining-related applications of stochastic process models that have resulted in—or with more work may lead to—practical achievements are discussed. These applications are in the area of modeling of continuous material handling systems and queueing theory applications. Space exists here only to present a descriptive discussion. Readers interested in learning about fundamental aspects of these techniques are referred to the well-known texts by Ross (1983), Cinlar (1975), and Karlin and Taylor (1975).

9.4.5.1 Stochastic Process Models of Continuous Material Handling Systems As examples of the type of issues that can be addressed in applying this technology to analysis of continuous material handling systems, the work of Baral et al. (1987) and Sevim (1987) are discussed. Baral et al. Model: This work addresses the implications of installing a bunker as a storage buffer in a serial arrangement of conveyors to increase the availability of that system to the production section it services. The role of such bunkers is to hold production for intervals of time when outby conveyors have failed, temporarily isolating the production section from its dependence on the outby transport network. They must be larger than bins used to reduce surge loading on an outby belt to control spillage. The service of the system depends on the availability of the conveyors between the face and the bunker and between the bunker and the end of the conveyor line. For the bunker to increase production, the inby belts must be available to haul material to the bunker when the outby belts fail. Moreover, the outby belts must be capable of clearing a substantial portion of the stored material between successive failures of the outby belts, else the effective capacity of the bunker might be reduced to the point where it provides little isolation. The availabilities of the bunker inflow and outflow belts are a function of where the bunker is located in the sequence of belts. Thus both the size of the bin and its location in the network are decision variables with important ramifications on performance of such a system. It was assumed by the authors that the time between failures and time to repair the belts are exponentially distributed random variables. This permits the system to be modeled as a continuoustime Markov process. For a simple two-conveyor system with a bunker between the first and second conveyor, state is described by the triplet (up/down status of the inby conveyor, up/down status of the outby conveyor, and proportion of bin volume currently filled). It is clear that one can assess the availability of the system to the production section given the value of these variables. For larger networks, it was shown that the belts inby the bunker and the belts outby the bunker may be considered in aggregate analogous to the two-belt system to reduce the state space and simplify computations. Expressions were derived for steady-state availability of the conveyor/bunker system to the production system as a function of the bunker volume, and

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the time to failure and the time to repair distributions for the individual conveyors. Analysis of these expressions suggested the following strategy for optimal specification of bunker storage. The bunker should be located at the location where the differential between the availability of the inby belts and the outby belts is the smallest, that is, at the location where these availabilities are closest to being equal. (Simple expressions can be used to compute the availability for an arbitrary serial chain of belts.) It is shown that the rate of increase of availability decreases and reaches an asymptote as bunker volume increases. Volume should be set prior to reaching the asymptote. Plots can be constructed to aid this decision. Perhaps the most serious criticism of this work might be the assumption of constant flow on the belt when the system is up. The ramifications of this assumption are not known. It appears that additional work might also be done on how one combines multiple production sections serviced by the same network, although this was addressed by the authors to a limited extent. Sevim Model: The work of Sevim (1987) focused on a different aspect of performance: the use of a bin to smooth outflow from multiple production sections that operate in a discontinuous fashion. Here, in contrast to the work just discussed, greater attention was given to modeling the production sections. Output from the face was modeled as a semi-Markov process, which allows for an arbitrary form of distribution of the times between up and down states as well as different classes of up and down states. It was assumed that the rate of production was constant during the up periods. Transient distributions of the probability of coal flow from a section were established for the first halfshift (from arrival at the section until the lunch break). It was also shown how these could be combined for multiple sections serviced by the same belt network. One thereby has knowledge of the probabilities (as a function of time of day) associated with the various aggregate levels of material flow on a belt. These distributions were then used to describe the inflow into a bin installed for the purpose of smoothing flow. A heuristic approach was established for sizing this bin. Both constant and controlled outflow rates from the bin were considered. Similar work applied to control of flow in slurry transport systems is presented in Sevim and Yegulalp (1984).

9.4.5.2 Queuing Models of Mine Production Systems The basic structure of queuing systems is as follows. A calling population provides a source of customers who request service at some service station. One should take a broad interpretation of the term customers; in a mining context it might refer to shuttle cars waiting to be filled, belts needing repair, or even, as will be seen in an example that follows, working faces requesting an operation in the cut, drill, blast, load, roof-bolt sequence of coal mining operations. The calling population may either be finite or infinite. The latter is most common in queuing models and is simpler analytically. It typically refers to a large source of customers external to the system such as the body of potential customers for a fast food restaurant. In each of the three mining cases discussed before, and probably in most queuing systems of interest in mining, the calling population is finite and fixed. The service station referred to previously contains one or more parallel service channels; each such channel is called a server. If the number of channels is finite, there is a limit in the number of customers that can be serviced simultaneously. Arriving customers finding all channels filled must wait for service in a queue. The queue may or may not correspond to a waiting line in the real-world system being modeled. For in-

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stance, broken machines (customers) may have to wait for the repair crew (servers) to finish a number of jobs before being serviced. But the machines are never “lined up” physically. The queue itself provides an opportunity for controlling the system. It may be desirable to service some waiting customers ahead of others independent of their order of arrival to the queue. For example, one might load 80-ton (72-t) trucks ahead of 50ton (45-t) trucks regardless of which truck arrived first. These controls are specified in terms of a queue discipline, which gives rules for determining the priority for removing customers from the queue when a service channel becomes available. The queue may have limited capacity, and customers arriving when the queue is full may be balked from the system or sent to another service station. Each server is typically assumed able to service only one customer at a time. This customer is retained and occupies the server for a period of time called the service time. For example, an empty, spotted truck ties up the loading shovel until it is filled. Once service is completed, the server is now available to service another customer and the customer is released. The system may consist of multiple service stations. A single customer may progress from one service station to the next in a fixed or a flexible sequence. This arrangement is frequently called a queuing network. In many mining systems, the customer is cycled among a number of service stations. For example, the truck goes from a loader to a dump site and back again. When multiple services stations are involved, state is often described in terms of the number of customers at each station. Overall, the structure of queuing models is quite broad and flexible. Hopefully this brief discussion of structure has left the reader with the impression that a number of mining processes might potentially be modeled in this framework. Two assumptions are frequently made to make queuing models more tractable analytically. First is that one is interested in equilibrium probabilities at steady state as opposed to transient performance of the system. As explained in 9.4.3.4, the acceptability of this assumption depends on the objectives of the study, not the system itself. Second is that the temporal variables of the system—customer interarrival times, customer service times, interstation transfer times—are exponentially distributed. This allows the theory of continuous-time Markov processes to be applied to compute the steady-state probabilities. The latter assumption is a restrictive one. Though the exponential distribution is an excellent model for many situations such as time between failures of certain types of components, time between arrivals to a system from a large external calling population where customers act independently, it is not a good model for service times (e.g., time to load a truck) and interstation transit times (e.g., time to travel from the loader site to the dump-site) in many mining applications. An approach that may be used to overcome this limitation is to employ what are called generalized Erlangian distributions or phase-type distributions. The general idea is to view a temporal variable with an arbitrary distribution, such as a service time, as being executed in a sequence of phases. The order of the phases is defined by either series or parallel structures or a combination of both. A serial structure implies that one phase is executed sequentially after another until the required number of phases in the series is completed. A parallel structure implies that multiple serial structures are available and one of these is selected with a specified probability then executed as just described. Time for each phase in the sequence is exponentially distributed. The phase structure and parameters of these exponential distributions may be determined so that as customers pass through the sequence of phases, the distribution of total elapsed time closely matches the arbitrary distribution that the modeler wants. Since

all times are now exponentially distributed, the result is that a continuous-time Markov process model can be employed, with accompanying advantages in tractability. This, however, comes at the expense of an expansion of the state space relative to the initial problem. The theory of stochastic networks (Kelly, 1979) provides means for computing the steady state probabilities for the various states of the system. Recently, this approach has been applied to mining systems in the work by Kappas and Yegulalp (1987). In their model of a room and pillar coal mining operation, working faces are viewed as customers that transit through a fixed series of service stations corresponding to the undercutting, drilling, blasting, loading, and roof-bolting operations of the conventional mining cycle. Distributions of general form were fitted to field data on the time required to complete each of these operations. A phase structure was fitted for each service station that resulted in a distribution of total elapsed time that matched the first two moments of the general distribution exactly (mean and variance) and was close to the third moment (skewness). They used specialized versions of computational algorithms for computing steadystate probabilities of the various states, which were given in terms of the number of faces undergoing each operation of the mining cycle. From these probabilities, various aspects of performance, such as steady-state production rate, could be obtained. They compared the effect of various numbers of working faces on production rates. Though a number of shortcomings were noted by the authors, including the uncertain utility of steady-state measures and inadequacies in accommodating spatial aspects of entry layouts when comparing system alternatives, the work certainly shows promise in bridging the major gaps in applying queuing theory to mining systems over previous applications where exponential times for activities were assumed.

REFERENCES Anon., 1984, “VEHSIM Hauling Unit Simulation Manual,” Caterpillar, Inc., Peoria IL. Albert, E.K., 1979, “A Complete Surface Mine Simulator,” MS Thesis, Dept. of Mineral Engineering, Pennsylvania State University, University Park, PA. Albert, E.K., 1989, “A New General Purpose Surface Mining Simulator,” Proceedings 21st APCOM Symposium, Society of Mining Engineers, Littleton, CO, pp. 366–374. Banks, J., and Carson, 1984, J.S., Discrete-Event System Simulation, International Series in Industrial and Systems Engineering, Prentice-Hall, Englewood Cliffs, NJ. Baral, S.C., Daganzo, C., and Hood, M., 1987, “Optimum Bunker Size and Location in Underground Coal Mine Conveyor Systems,” International Journal of Mining and Geological Engineering, Vol. 5, pp. 391–404. Beckett, L.A., Haycocks, C., and Lucas, J.R., 1979, “LHDSIM—A Load-Haul-Dump Simulator for Room-and-Pillar Mining Operations,” Proceedings 16th APCOM Symposium, SME-AIME, New York, pp. 408–413. Bise, C.J., and Albert, E.K., 1984, “Comparison of Model and Simulation Techniques for Production Analysis in Underground Coal Mines,” Trans. SME-AIME, Vol. 276, pp. 1878–1884. Bucklen, et al., 1969, “Computer Applications in Underground Mining Systems Volume 4-Beltsim Program,” Virginia Polytechnic Institute and State University, Research and Development Report No. 37, Office of Coal Research, US Dept. of the Interior. Carmichael, D.G., 1987, Engineering Queues in Construction and Mining, Wiley, New York. Cinlar, E., 1975, Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, NJ. Clevenger, J.G., 1983, “DISPATCH Reduces Mining Equipment Requirements,” Mining Engineering, Vol. 35, No 9. Fishman, G.S., 1978, Principles of Discrete Event Simulation, Wiley, New York.

CYCLES AND SYSTEMS Kappas, G.P., and Yegulalp, T.M., 1987, “Application of Closed Queuing Networks to Room and Pillar Mining,” Proceedings, 3rd International Conference on Innovative Mining Systems, J.M. White, ed., University of Missouri-Rolla, Nov. 2–4. Karlin, S., and Taylor, H., 1975, A First Course in Stochastic Processes, 2nd ed., Academic Press, New York. Kelly, F.P., 1979, Reversibility and Stochastic Networks, Wiley, New York. Law, A.M., and Kelton, W.D., 1982, Simulation Modeling and Analysis, McGraw-Hill, New York. Lizotte, Y. and Bonates, E., 1987, “Truck and Shovel Dispatching Rules Assessment Using Simulation,” Mining Science and Technology, Vol. 5, pp. 45–59. Manula, C.B., et al., 1974,“A Master Environmental Control and Mine System Simulator for Underground Coal Mining: Production Subsystem,” Vol. 5, Open File Report 84(6)-76, US Bureau of Mines, NTIS PB-225426. Manula, C.B., and Albert, E.K., 1980, “Evaluation of Operational Constraints in Continuous Mining Systems - Underground Materials Handling Simulator (UGMHS/79), Vol. IV, User Manual,” Report to US Dept. of Energy, 1980. Mutmansky, J.M., and Mwasinga P.P., 1988, “An Analysis of SIMAN as a General-Purpose Simulation Language for Mining Systems,” Preprint No. 88-185, SME Annual Meeting, Phoenix, AZ, Jan. 25– 28. Newhart, D.D., 1977, “BETHBELT-1, a Belt Haulage Simulator for Coal Mine Planning,” Research Report File 17202, Bethelehem Steel Corp., Bethelehem PA. O’Neil, T. J., and Manula, C.B., 1966,“Computer Simulation of Materials Handling in Open-Pit Mines,” Special Research Report SR 56, Coal Research Section, The Pennsylvania State University. Peng, S., Zhang, D., and Xi, Y., 1988, “Computer Simulation of a SemiContinuous Open Pit Mine Haulage System,” International Journal of Mining and Geological Engineering, Vol. 6, No. 3, pp. 267–272.

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Prelaz, L.J., et al., 1968, “Optimization of Underground Mining,” Report No. 6, Vols. 1-3, Office of Coal Research, US Dept. of the Interior. Ross, S.M., 1983, Stochastic Processes, Wiley, New York. Sevim, H. and Yegulalp, T.M., 1984, “Optimization of Hydraulic Haulage Systems in Underground Coal Mines,” Trans. SME-AIME, Vol. 276, pp. 1659–1666. Sevim, H., 1987, “A Heuristic Method in Bin Sizing,” Mining Science and Technology, Vol. 5, pp. 33–44, 1987. Soumis, F., Ethier, J., and Elbrond, J., 1989, “Evaluation of the New Truck Dispatching in the Mount Wright Mine,” Proceedings 21st APCOM Symposium, SME, Littleton, CO, pp. 674–682. Sturgul, J.R., 1978, “How to Determine the Optimum Location of In-Pit Movable Crushers,” International Journal of Mining and Geological Engineering, Vol. 5, No. 2, pp. 143–148, 1987. Sturgul, J.R., 1989, “Simulating Mining Conveyor Belt Systems,” Preprint, 2nd World Congress on Non-Metallic Minerals, Oct., Beijing, China. Suboleski, S.C., and Lucas, J.R., 1969, “Simulation of Room and Pillar Face Mining Systems,” A Decade of Computing in the Mineral Industry, A. Weiss, ed., AIME, New York, 1969, pp. 373–384. Tan, S., and Ramani, R.V., 1988, “Continuous Materials Handling Simulator: An Application to Belt Networks in Mining Operation,” Preprint No. 88-179, SME Annual Meeting, Phoenix AZ, Jan. 2528. Thompson, S.D., and Adler, L., 1988, “New Simulator for Designing Belt System Capacities in Underground Coal Mines,” Mining Engineering, Vol. 40, No. 4, pp. 271–274. Weyher, L.H.E., 1976, “Innovative Computer Use for Underground Coal Mine Planning, Development of a Comprehensive Program System for Bethelehem’s Mines,” Proceedings 14th APCOM Symposium, AIME, New York, pp. 112–124. White, J.W., and Olson, J.P., 1986, “Computer-Based Dispatching in Mines with Concurrent Operating Objectives,” Mining Engineering, Vol. 38, No. 11, pp. 1045–1054.

Modelling open pit shovel-truck systems using the Machine Repair Model by A. Krause* and C. Musingwini†

Shovel-truck systems for loading and hauling material in open pit mines are now routinely analysed using simulation models or offthe-shelf simulation software packages, which can be very expensive for once-off or occasional use. The simulation models invariably produce different estimations of fleet sizes due to their differing estimations of cycle time. No single model or package can accurately estimate the required fleet size because the fleet operating parameters are characteristically random and dynamic. In order to improve confidence in sizing the fleet for a mining project, at least two estimation models should be used. This paper demonstrates that the Machine Repair Model can be modified and used as a model for estimating truck fleet size in an open pit shoveltruck system. The modified Machine Repair Model is first applied to a virtual open pit mine case study. The results compare favourably to output from other estimation models using the same input parameters for the virtual mine. The modified Machine Repair Model is further applied to an existing open pit coal operation, the Kwagga Section of Optimum Colliery as a case study. Again the results confirm those obtained from the virtual mine case study. It is concluded that the Machine Repair Model can be an affordable model compared to offthe-shelf generic software because it is easily modelled in Microsoft Excel, a software platform that most mines already use. This paper reports part of the work of a MSc research study submitted to the University of Witwatersrand, Johannesburg, South Africa. Keywords: simulation, bunching, probability distributions, cycle time, queuing, matching, shovel-truck, OEM.

Introduction Shovel-truck systems are a prevalent loading and hauling system in surface mining operations. The loading units are typically wheel loaders (WL), hydraulic excavators (HEX) or rope excavators. The trucks can be off-highway trucks (OHT), articulated dump trucks or coal haulers as in coal mining. Generally truck fleet sizes increase with progressive mining or when expansion projects are envisaged. Haulage distances invariably increase with increasing pit depth as mining progresses, consequently reducing individual truck productivity and demanding more trucks to maintain the same level of production. Expansion projects require higher The Journal of The Southern African Institute of Mining and Metallurgy

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* Endeavor Mine, CBH Resources Ltd, North Sydney, Australia. † School of Mining Engineering, University of Witwatersrand, Johannesburg, South Africa. © The Southern African Institute of Mining and Metallurgy, 2007. SA ISSN 0038–223X/3.00 + 0.00. Paper received Mar. 2007; revised paper received Aug. 2007. REFEREED PAPER

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production rates, and with same level of truck productivity, it means more trucks will be required to meet the increased production rate. The stochastic-dynamic nature of shoveltruck production cycle variables renders deterministic calculations inadequate to estimate the required shovel-truck fleet sizes. Consequently, simulation models are used to estimate the additional truck requirements. Several simulation models or software packages are available for this purpose. However, these models yield different fleet sizes for the same input parameters. The main reason why these different models each yield unique results is based on the assumed probability distributions fitted to the main cycle variables and the corresponding calculation of waiting time for both trucks and loaders. Of-the-shelf simulation software packages can be very expensive for once-off use and mines would need to be able to analyse their new truck requirements using affordable and reliable models. Consequently, most mines have to rely on the original equipment manufacturers’ (OEM) fleet size recommendations. Mines can increase their confidence in the OEM estimations by using simple models to substantiate the estimations. The modified Machine Repair Model based on Markov chains and running on an MS Excel platform, can used for this purpose because mines have computers that run MS Excel. The Machine Repair Model can therefore be used as an affordable model for checking OEM recommendations. The shovel-truck sizing problem is a twostage problem even for a shift start-up (Ta et al., 2005). The first stage is truck resource

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Modelling open pit shovel-truck systems using the Machine Repair Model allocation or fleet size estimation. The second stage, which is a truck dispatching stage, is a real-time implementation of the estimated truck resource and is done either manually or using computerized truck dispatch systems such as Dispatch®. Truck allocation is critical because if it is incorrectly done then the dispatch stage inherently carries over errors made in the first stage, resulting in sub-optimal truck dispatching decisions. This is the reason why at project inception the fleet size has to be estimated as accurately as possible. Two extreme undesirable trucking conditions can exist if truck allocation is done incorrectly. These are an ‘over-equipped’ condition where there are more trucks than are required or an ‘under-equipped’ condition when there are fewer trucks than required. There are consequences associated with these conditions. For example overestimating truck fleet size by one extra CAT 777D truck implies about R10 million (in 2006 monetary terms) unnecessary extra capital expenditure, while underestimating truck fleet size carries the risk of loss of potential revenue due to production shortfalls. Central to the estimation of shovel-truck fleet size is the determination of the load-and-haul cycle time. The number of cycles a haulage unit can complete per hour are then determined. Subsequently, the system’s productivity in tons per hour is determined as the aggregate of the productivity of all haulage units, hence sizing the shovel-truck fleet system. However, in any load-and-haul system there exist variations in the cycle variables such as loader bucket payload, truck payload, haul road distances, haul road conditions, operator proficiency, truck waiting times and truck loading time, to name but a few. Variations in these variables and their subsequent interaction contribute to the complication in the estimation of real-time waiting time, hence the estimation of the cycle time in real-time. Waiting time is an inherent but undesirable part of any load-and-haul system because it represents real-time equipment mismatch and ultimately production loss from idling equipment. Any shovel-truck analysis must therefore include estimation of waiting time. Accordingly, optimization of shovel-truck systems must aim to minimize or eliminate the total waiting time for both shovels and trucks (Temeng, Francis and Frendewey, 1997).

Models for analysing shovel-truck systems To date, a number of off-the-shelf commercial simulation software packages have been developed to estimate shoveltruck fleet size requirements for given mining production rates and conditions. The various models associated with these packages and considered in this study can be broadly classified as: ➤ Iterative models that fit discrete empirical values to cycle variables. Examples are the Elbrond (1990) model and Machine Repair Model (Winston, 2004). In this paper, the Machine Repair Model is also alternatively referred to as the Winston model ➤ Regressive models that treat waiting time as a function of fleet matching and bunching correction factors. These models are based on static simulation algorithms that are driven by prescribed processing flow that is not dependent on time or interaction of resources. An example is the Fleet Production and Cost model (FPC®)

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developed by Caterpillar Inc. and discussed in detail by Morgan (1994) ➤ Stochastic Monte Carlo type models which fit probability distributions to cycle variables. An example is the Talpac® model developed by Runge Software Ltd ➤ Stochastic graphic simulation methods in which trucks and shovels (or loaders) are represented by physical entities (icons) within a virtual environment following probability distributions within a Monte Carlo simulation environment. The simulation progress can be viewed as an animation. An example is the Arena® model developed by Rockwell Software Inc. The reasons for the choice of the above models are firstly, that the Elbrond (1990) and Winston (2004) models are iterative models, which can easily be programmed in MS Excel. The Talpac and FPC models were chosen because they are commonly used in the mining industry for shovel-truck analysis although they are limited to fitting probability distributions to a maximum of five major shovel-truck cycle variables. Lastly, Arena was chosen because it can be programmed with any number of probability distribution models fitted to an unlimited number of cycle variables and is therefore a very flexible model for use in analysing several variables in shovel-truck analysis. This characteristic of Arena gives it the potential to closely imitate real systems and was therefore chosen as the benchmark model in this study to compare the output from other simulation models. Other useful models that were not considered in this study, due to reasons of non-availability and financial constraints, include Shovel Truck Analysis Package (STRAPAC®), General Purpose Simulation System (GPSS/H®) developed by the Wolverine Software Corporation, and Vehicle Simulation (VEHSIM®). Panagiotou and Michalakopoulos (1994) discussed the STRAPAC framework and its application to a shovel-truck system in a bauxite open pit mine. Today the STRAPAC® name is associated with plastic holding ties produced by Sublett Co. The GPSS/H® program, which has been used for both surface and underground mine simulations, is discussed in detail both in terms of architecture and application by Sturgul (2000). Dowborn and Taylor (2000) successfully used GPSS/H® to simulate a production system for an underground narrow reef platinum mine on the Bushveld Complex in South Africa. Other mining applications of GPSS/H® are reported by Sturgul, Jacobsen and Tecsa (1996), Sturgul and Jacobsen (1994), and Sturgul and Tecsa (1996). VEHSIM® was developed by Caterpillar Inc. in the late 1960s primarily for sales and technical support of the CAT 779 (85 ton) electric drive OHT truck, but was discontinued due to the decline in the truck’s use. FPC® has essentially the same program setup and functionality as VEHSIM®.

Review of the machine repair model In queuing theory, models in which arrivals (or customers) are drawn from a small population are called finite source models (Winston, 2004). The Machine Repair Model is an example of a finite source model. The model or system consists of K machines and R repair bays. The length of time that a machine spends away from the repair bays before coming back for repair follows an exponential distribution The Journal of The Southern African Institute of Mining and Metallurgy

Modelling open pit shovel-truck systems using the Machine Repair Model with rate λ and the time to repair a broken down machine at a repair bay follows an exponential distribution with rate μ. In other words, λ is the inter-arrival rate and μ is the service rate. Using the Kendall-Lee notation (Winston, 2004), the Machine Repair Model can be described as an M/M/R/GD/K/K model, where the first M is the inter-arrival rate, the second M is the service rate, R represents the number of repair bays, GD states that the machines are serviced following some general queue discipline, the first K is the number of machines being serviced in the system, and the last K states that the machines are drawn from a population of size K. Typical queue disciplines include first-come, first-served (FCFS), last-come, first-served (LCFS), service in random order (SIRO) and priority queuing disciplines. In FCFS customers are serviced in the order of their arrival, in LCFS the most recent arrivals are serviced first, and in SIRO the order in which customers arrive has no effect on the order in which they are served. In priority queue discipline, each arrival is classified into one of several categories, each category is allocated a priority level, and within each priority level, customers are serviced on an FCFS basis. For most shovel-truck systems, trucks are serviced on an FCFS basis. When arrivals to a system are drawn from a small population, the arrival rate may depend on the state of the system. For example, if the Machine Repair Model is in a state where j ≤ R machines are broken down, then a machine that has just broken down will be assigned for repair immediately, and if in a state where j > R machines are broken down, then j - R machines will have to queue in a line waiting for the next available repair bay. The state of a system can be described as stable or unstable. Winston (2004) describes the conditions under which a system will be stable or unstable, as explained below. Let ρ represent the traffic intensity for an M/M/1/GD/∞/∞ system with exponential inter-arrival and service rates. [1] where λ is the number of machines arriving for repair per unit time and μ is the number of machines successfully repaired per unit time. Further, an M/M/1/GD/∞/∞ can be modelled as a birth-death process with parameters as described in Equations [2] to [4].

future. The sum of the probabilities should be equal to unity as indicated in Equation [6], since at any given time the system must be in some state. [6] This infinite sum will diverge to infinity should ρ ≥1 and no steady state will exist, resulting in an unstable system.

Adapting machine repair model to shovel-truck system analysis In this study the Machine Repair Model was modified to model shovel-truck systems and the modelling results obtained compared to output from other simulation models/packages. The Machine Repair Model equivalents are shown in parenthesis. A truck is sent for loading (repair) every cycle with the number of shovels or shovel loading sides or number of tipping bins (repair bays) being equal to R and the inter-arrival and service times both assumed to have an exponential distribution. Therefore, a shovel-truck system can be described as M/M/R/GD/K/K, where the first M is truck arrival rate, the second M is loader service rate, R is the number of shovels or shovel loading sides that are loading K trucks drawn from a population of size K, whereby the loading follows some general queue discipline, GD. As with the Machine Repair Model, trucks are drawn from a finite population and their arrival pattern will therefore depend on the state of the system. For example, should all the trucks within a particular circuit be present at the loading unit, such as when a loading unit is experiencing an unexpected breakdown, then the truck arrival rate will be zero. At any other instant when there is less than the maximum number of trucks at the loading unit, the arrival rate will be positive. Under steady state conditions, the length of time that a truck spends away from the shovel follows an exponential distribution with rate λ, and the length of time that a shovel takes to load a truck follows an exponential rate μ. λ If we define ρ = μ as in Equation [1], the steady-state probability distribution will be given by Equations [7] and [8].

[7]

[2] [3] [4]

[5] where π is described as the probability that at a future instant, j machines will be present or may be perceived as the fraction of time that the j machines are present in the distant The Journal of The Southern African Institute of Mining and Metallurgy

[8] For any queuing system under steady-state conditions, Little’s queuing formulae can be applied to the system (Winston, 2004). Under steady-state conditions, an analogy of the shovel-truck system and the Machine Repair Model (Winston model) is illustrated in Table I. By applying Little’s queuing formulae, the model parameters are obtained from the calculations in Equations [9] to [12]. [9]

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These equations describe the flow balance of a birthdeath process where: expected no. of departures from state j per unit time = expected no. of entrances to state j per unit time The steady state probabilities that j machines will be present are given in Equation [5].

T r a n s a c t i o n

P a p e r

Modelling open pit shovel-truck systems using the Machine Repair Model Table I

An analogy of shovel-truck system and Machine Repair Model Notation

Machine Repair Model Description

L

Repair model adjusted for load and haul

Expected number of broken trucks or destination server (plant or dump)

Expected number of trucks at the loading unit

Lq

Expected number of trucks waiting for service at the workshop repair bays

Expected number of trucks waiting for service at the loading unit or dumping distination

W

Average time a machine spends broken (down time)

Average time a truck spends at the loading unit or dump destination

Wq

Average time a truck spends waiting for service

Average time a truck queues at the loading unit or the plant/dump

[10] [11] [12] The average number of arrivals per unit time is given by λ , where:

—

[13]

If Equation [11] is applied to trucks being loaded or trucks tipping at a bin, then the trucks that are waiting for service, W, are given by Equation [14]. [14]

If Equation [12] is applied to trucks waiting to be loaded, Wq, we obtain the relationship shown in Equation [15]. [15]

1 The inter arrival time λ at the loading unit is thus a function of the truck’s waiting time at the dumping destination, Wq (and vice versa for trucks at the dumping destination). This system of equations defining the Machine Repair Model was then programmed into MS Excel.

550 m to loading area flat/haul

550 m to dump/plant flat/haul

Bench height: Ramp length: Half cycle distance: Rolling resistance:

10 m (depth: 10–135 m) 168–2828 m 1268 m–2932 m 4% constant

Figure 1—Layout of the virtual mine

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Application of Machine Repair Model to virtual mine The virtual mine has 10 m benches that extend from surface to a depth of 135 m (Figure 1). The ramp is constructed at 8% up-grade (GR) with a 4% rolling resistance (RR) kept constant throughout the haul route. A wheel loader loads OHT trucks that dump material at either a plant tipping bin or waste dump. For the virtual mine three loader cycle times were simulated, these being 3 minutes (for Caterpillar 777 OHT), 4 minutes (for CAT 777 OHT) and 5 minutes (for CAT 793 OHT). The dump and manoeuvre time was kept constant at 2.5 minutes, assuming a consistent operator proficiency. Simulations were performed using the five models described earlier on. The Arena model was used as the benchmark model for the reason stated in Section 2.0 of this paper. The shovel-truck model created in Arena for this study is illustrated by the screen snapshot in Figure 2. By using different loader service times of three minutes, four minutes and five minutes, the five estimation models were run to produce estimates of attainable loads per shift. A comparison of the Winston (Machine Repair Model), FPC, Elbrond and Talpac to Arena in terms of the loads per shift is shown in Figure 3. Several observations and accompanying explanations can be made in relation to Figure 3. Generally, the loads per shift obtained from the models are quite close to those obtained using Arena, with estimates from the other models ranging between 97% and 99.7% of the Arena estimates. The Talpac model with predominantly lognormal distributions fitted to cycle variables (standard distribution spreads embedded in program) produced estimates that were very close to those obtained from the Machine Repair Model, which has predominantly exponential distributions. Although FPC does not specify its embedded distributions, its estimates were closer to the estimates produced from lognormal and exponential distribution based models and appears to produce intermediate estimates compared to estimates from the other two models. The Elbrond (1990) model produced estimates that had the lowest percentage in comparison to Arena estimates compared to the rest of the models. This is primarily due to underestimation of waiting time by the FPC model when compared to the other models. By increasing the standard deviation of service time to return time ratios by 0.2 to 0.5, the difference of the Elbrond from with other models decreases, improving its percentage estimation compared to the other models. With an increase in service time the estimates of loads per shift deviate further away from Arena The Journal of The Southern African Institute of Mining and Metallurgy

Modelling open pit shovel-truck systems using the Machine Repair Model T r a n s a c t i o n

Plant Arrive arrive 2

Dispatch to Plant Spot at plant Arrive at shovel shovel arrive no.

count entrance

P a p e r

Back to shovel

Figure 2—Screen snapshot of shovel-truck simulation process in Arena

Correlation %

Model correlation with Arena: across service time

Loader service time (min.)

Figure 3—Comparison of loads per shift of other models with arena for virtual mine

The Journal of The Southern African Institute of Mining and Metallurgy

Application of machine repair model to Optimum Colliery’s Kwagga section Optimum Colliery is a surface coal mine owned by Ingwe Coal Corporation and BHP Billiton. Kwagga section is part of Optimum Colliery. Coal from Kwagga section is mined from three areas namely the North (or Rail), Central and South sections. The haulage routes for all three areas were considered in the study. Figures 4 depicts the haulage routes for the North (or Rail) section to show a typical haul route layout for the mine. The general geology of the North section is illustrated by a geological section (Figure 5). The strata consist mainly of a relatively thick, white, coarse grained massive sandstone layer followed by a thick shale layer below. Thinner alternating shale and sandstone bands occur VOLUME 107

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estimates. Arena reported slightly higher loads per shift with a possible explanation that the other models are more conservative, which could be a benefit to the user because the risk of potential loss of planned production is reduced. The slight improvement in the estimates from the Winston, FPC and Talpac models compared to those from the Arena model with the increase in service time from four minutes to five minutes can partly be explained by the difference in machine characteristics between the CAT 777D and CAT 793D OHT trucks. The reason why Talpac does not show this improvement can partly be explained by the tendency of the Talpac program to underestimate the performance of Caterpillar trucks. Overall, the results show that the Winston (Machine Repair) model produces productivity estimates in terms of loads per shift that closely match those of the other models.

Modelling open pit shovel-truck systems using the Machine Repair Model KGM-B12

North

Figure 4—Aerial photograph showing haulage routes for the North (Rail) section

KWN99 KWN57

KWN78

KWN76 K0261 K4344

NO. 2 NO. 2A

Figure 5—Section through North (Rail) section

in places. The top 8 metres consist of soft unconsolidated material. The geology illustrated in Figure 5 dictates that the general mining direction should be up-dip so that the gradient can be used to drain water away from the loading operations. Consequently, in-face haulage roads on the mine are developed with a slight dip. Major segments constituting the haulage profiles and their associated haulage resistances, for the three sections are presented in Table II. Prior to the study, the haulage equipment fleet complement for Kwagga section was constituted as follows: ➤ 4 x Caterpillar 776D coal haulers (CAT 776D) ➤ 7 x Caterpillar 777D OHT (CAT 777D) ➤ 2 x Caterpillar 992G Wheel Loader (WL) with a high lift (HL) design (CAT 992 G WL HL) ➤ 1 x Caterpillar 992D WL HL (CAT 992D WL HL). At the North section one CAT 992D WL and four Caterpillar 776D coal haulers are used. At the Central and South sections seven Caterpillar 777D OHT and two Caterpillar 992G WL are used. The travel distances are moderate for the Central and South sections while the North (or Rail) section has longer haul routes. It is for this reason that the CAT 776D coal haulers are predominantly confined to the North (Rail) section since they are more suited for longer hauls. Three Marion draglines are used for overburden stripping. Front end wheel loaders load blasted coal into the OHT trucks and coal haulers. The trucks haul the coal to two

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tips situated at the Central and South sections from where two main conveyors feed the washing plant that delivers coal to the Hendrina Power Station. The above equipment suite hauls about 10.5 million tons of run-of-mine (ROM) coal per annum with the distribution by section as shown in Table III for a planned 8 322 site-scheduled hours per year. As can be derived from Table III, the fleet has a scheduled production rate of about 1 260 t per site-scheduled hour. It was required to estimate the additional trucks required to raise the production rate to 3 022 t per scheduled site hour. Simulation runs were performed using five different models including the Machine Repair Model. The simulated truck fleet requirements for a production rate of 3 022 t per site-scheduled hour are presented in Table IV. From Table IV it can be seen that the Arena and Winston models, which are both modelled on exponential cycle time variable distributions, yield the same truck requirement. The Elbrond model also yields the same truck requirement as the Arena and Winston models. Although the Elbrond model yields the same result as the Arena and Winston models, the difference between its estimation of tons per hour (THP) and the required TPH is double the difference between estimated TPH and required TPH for other models. This can be directly attributed to the Elbrond model reporting zero waiting time for the coal haulers at the loaders. The FPC and Talpac The Journal of The Southern African Institute of Mining and Metallurgy

Modelling open pit shovel-truck systems using the Machine Repair Model T r a n s a c t i o n

Table II

Distances, grade and rolling resistance of the haulage profiles Face to ramp Ramp to haulage Distance

Grade %

RR%

Distance

Grade %

RR%

distance

4% 4% 6 800

800 500 9.5%

9.5% 9.5% 4%

4% 4% 10 000

4 100 8 715 0%

0% 0% 3%

3% 3% 10 600

5 950 9 615

5% 5% 5% 5%

4% 4% 4% 4%

400 450 400 5 800

9.5% 9.5% 9.5% 9.5%

4% 4% 4% 4%

2 000 1 300 700 400

0% 0% 0% 0%

3% 3% 3% 3%

2 600 2 100 1 500 1 500

500 5% 450 5% 350 5% 300 5% 250 5% 350 5% 12 600 Distance = travel in metres (one way) Grade % = grade resistance % RR% = rolling resistance %

4% 4% 4% 4% 4% 4%

1 000 700 700 400 600 700

9.5% 9.5% 9.5% 9.5% 9.5% 9.5%

4% 4% 4% 4% 4% 4%

1 000 400 400 1 100 1 500 1 900

0% 0% 0% 0% 0% 0%

3% 3% 3% 3% 3% 3%

2 500 1 550 1 450 1 800 2 350 2 950

Central Ramp 1 Ramp 2 Ramp 3 Ramp 4

1 050 5% 400 5% Load from stockpile 26 165 200 350 400 650 7 750

South Ramp 2 Ramp 3 Ramp 4 Ramp 5 Ramp 6 Ramp 7

RR%

Haulage to tip Total Distance

North Ramp 1 Ramp 2 Ramp 3

Grade %

Table III

Table IV

Planned production distribution by section

Simulated truck fleet size estimates from the five models

Section

Site schedule hours

Tons per annum planned

Model

North Ramp 1 Ramp 2 Ramp 3 Sub-total

3 177 2 951 2 194 8 322

1 046 093 971 373 722 303 2 739 769

Central Ramp 1 Ramp 2 Ramp 3 Ramp 4 Sub-total

1 040 1 820 2 081 3 381 8 322

598 357 1 047 125 1 196 714 1 944 661 4 786 857

South Ramp 2 Ramp 3 Ramp 4 Ramp 5 Ramp 6 Ramp 7 Sub-total Total

1 891 1 702 1 324 1 135 946 1 324 8 322 8 322

663 278 596 951 464 295 397 967 331 639 464 295 2 918 425 10 445 051

models estimate one additional truck requirement compared to the other models for the Central section. The Talpac model estimates an additional coal hauler for the North section compared to the other models. This can be attributed to Talpac reporting higher truck travel times, which result in higher waiting times at both loader and dumping tips. Consequently, individual truck total cycle times are higher The Journal of The Southern African Institute of Mining and Metallurgy

Section 776D

Truck type 777D 776D

P a p e r

Total truck no. 777D

Elbrond

North Central South

6 -

5 4

6

9

FPC

North Central South

6 -

6 4

6

10

Winston

North Central South

6 -

5 4

6

9

Arena

North Central South

6 -

5 4

6

9

Talpac

North Central South

7 -

6 4

7

10

compared to other models. Ultimately, in order to meet the required TPH, more trucks are required compared to other models. Overall, it can be seen again that the Winston (Machine Repair) model produces truck fleet size estimates that closely match those from other models. Subsequent to this study the mine decided to purchase two extra CAT 777D OHT trucks to bring the total CAT 777D fleet size to six. They also decided not to supplement the coal hauler fleet due to a change in the North section mining VOLUME 107

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Modelling open pit shovel-truck systems using the Machine Repair Model strategy. This decision was supported by a road improvement strategy using mobile crushers to provide sound underfoot conditions. This improvement will result in a reduction of rolling resistance and travel time and thus total cycle time and the number of coal haulers required.

Concluding remarks Each of the five truck fleet size estimation models produced different estimates for the same project input parameters. The underlying reason for the differences, as was observed from the two case studies, derives from the way the models assign probability distributions to the individual cycle time components. The simulations showed that the Arena model with exponential distributions fitted to the cycle time components yielded similar results to the Winston model. The Elbrond and FPC programs, which do not have a specified underlying distribution model and can be described as field models, yielded similar results compared to that of Arena and Winston (Machine Repair) models. The case studies demonstrate that the Winston (Machine Repair) model produces truck fleet size estimates that closely match the estimates produced by other models. The Winston (Machine Repair) model is an affordable model, even for once-off use, for mines needing to estimate project truck requirements because it can be programmed on an MS Excel platform, a software package that most mines already use.

Acknowledgements The authors wish to acknowledge Coaltech 2020 for funding the research and granting permission to publish this paper. Optimum Colliery is also acknowledged for allowing access to their mine and providing data used in the second case study.

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References 1. DOWBORN, M. and TAYLOR, W. Simulation modelling of platinum operations using GPSS/HTM, Proceedings of the 30th Application of Computers and Operational Research in the Mineral Industry, 2000. pp. 365–382. 2. ELBROND, J. Queuing Theory, Surface Mining, 2nd Edition, Society for Mining and Metallurgy and Exploration (SME), Littleton, Colorado, 1990. pp. 743–748. 3. MORGAN, B. Optimizing truck-loader matching, Proceedings of the Third International Symposium on Mine Planning and Equipment Selection, Istanbul, Turkey, 18–20 October 1994, pp. 313–320. 4. PANAGIOTOU, G.N. and MICHALAKOPOULOS, T.N. Analysis of shovel-truck operations using STRAPAC, Proceedings of the Third International Symposium on Mine Planning and Equipment Selection, Istanbul, Turkey, 1994. pp. 295-300. 5. STRUGUL, J.R. and JACOBSEN, W.L. (1994). A simulation model for testing a proposed mining operation: Phase 1, in Proceedings of the Third International Symposium on Mine Planning and Equipment Selection, Istanbul, Turkey, 1994. pp. 281–287. 6. STURGUL, J.R. and TECSA, T.L. Simulation and animation of a surface iron ore mine, Proceedings of the Fifth International Symposium on Mine Planning and Equipment Selection, Sao Paulo, Brazil, 22–25 October 1996, pp. 81–86. 7. STRUGUL, J.R., JACOBSEN, W.L., and TECSA, T.L. Modeling two-way traffic in an underground one-way decline, Proceedings of the Fifth International Symposium on Mine Planning and Equipment Selection, Sao Paulo, Brazil, 22–25 October 1996, pp. 87–90. 8. STURGUL, J.R. Mine Design: Examples Using Simulation, ISBN 0-87335181-9, Society for Mining, Metallurgy, and Exploration, Inc. (SME), Littleton, Colorado. 2000. 9. TA, C.H., KRESTA, J.V., FORBES, F., and MARQUEZ, H.J. A stochastic optimization approach to mine truck allocation, International Journal of Surface Mining, Reclamation and Environment, vol. 19, no. 3, September 2005, pp. 162–175. 10. TEMENG, V.A., FRANCIS, O.O., and FRENDEWEY, JR., J.O. Real-time truck dispatching using a transportation algorithm,International Journal of Surface Mining, Reclamation and Environment, 1997, vol. 11, 1997. pp. 203–207. 11. WINSTON, W.L. Operations Research: Applications and Algorithms (4th Edition), pp. 1104–1165, ISBN 0-534-38058-1. Indiana University, Brooks Cole. 2004. ◆

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Simpósio Brasileiro de Pesquisa Operacional

A pesquisa Operacional e o Meio Ambiente 6 a 9 de novembro de 2001 - Campos do Jordão - SP

MODELOS DE PROGRAMAÇÃO MATEMÁTICA PARA RESOLUÇÃO DE PROBLEMAS DE MISTURA DE MINÉRIOS E ALOCAÇÃO DE EQUIPAMENTOS EM MINAS A CÉU ABERTO Luiz Henrique de Campos Merschmann COPPE / UFRJ Rio de Janeiro –RJ [email protected]

Luiz Ricardo Pinto Escola de Minas / UFOP Ouro Preto – MG [email protected]

Resumo O trabalho apresenta modelos matemáticos para resolução de problemas operacionais relacionados com o planejamento de lavra de minas a céu aberto. Os modelos se prestam à determinação do ritmo de lavra a ser implementado em cada frente de lavra, levando-se em consideração a qualidade do minério em cada frente, a relação estéril/minério desejada, a produção requerida, as características dos equipamentos de carga e transporte e as características operacionais da mina. Os modelos também consideram a possibilidade de alocação estática e dinâmica dos caminhões. No caso de alocação dinâmica, o modelo determina qual deve ser a produção de cada frente e aloca os equipamentos de carga às frentes escolhidas. No caso da alocação estática, além da alocação dos equipamentos de carga, o modelo também faz alocação dos caminhões às frentes. Palavras-chave: programação matemática, mineração, mistura de minérios Abstract This paper presents mathematical models to solve operational problems in open pit mining design such as ore blending and equipment assignment. The models determine the productivity of each working bench in one mine. They also consider the ore quality in order to make the blending, production goals, truck and shovel characteristics and availability, and support both static and dynamic allocation. The dynamic allocation model provides productivity and haulage equipment assignment. The static allocation model also provides truck assignment. Keywords: Mathematical programming, mining, ore blending 1) Introdução A lavra de uma mina geralmente é feita em diversas frentes de modo que, realizando a mistura dos minérios retirados das frentes, seja possível fornecer para a usina de tratamento um minério que esteja de acordo com as especificações de qualidade necessárias. Deste modo, precisa-se conhecer qual o ritmo de lavra a ser implementado em cada frente, que atende as especificações quantitativas e qualitativas da usina. Entende-se por ritmo de lavra a produção horária da frente. Uma mina possui equipamentos como caminhões, carregadeiras e escavadeiras que viabilizam a lavra nas diversas frentes. Mesmo mantendo uma frota com um número fixo de equipamentos, a quantidade disponível em condições de operar pode variar ao longo do tempo. Isso pode acontecer por motivo de quebra desses equipamentos, manutenção preventiva, atrasos operacionais, etc. Sendo assim, o cumprimento do ritmo de lavra com objetivo de atender as especificações da usina depende da disponibilidade dos equipamentos na mina. Diante deste cenário diversas questões podem surgir, tais como:

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A pesquisa Operacional e o Meio Ambiente 6 a 9 de novembro de 2001 - Campos do Jordão - SP

9 Com quais frentes deve-se trabalhar para atender as especificações de qualidade da usina de tratamento? 9 Com a frota de equipamentos disponíveis será possível atender um ritmo de lavra que possibilita o atendimento das especificações da usina? 9 A partir de uma determinada frota de equipamentos e das especificações impostas pela usina, qual é a máxima produção que pode ser obtida? E qual é o ritmo de lavra de cada frente? Cada uma das questões apresentadas anteriormente pode ser respondida mediante a construção de modelos distintos de programação matemática. Pinto (1995) fez uma abordagem sobre o tema relacionado à mistura de minérios. Naquele trabalho, no entanto, não foram consideradas diversas questões relacionadas às características dos equipamentos, nem à relação estéril/minério. A seguir, dois modelos serão apresentados. Ambos têm como objetivo determinar o ritmo de lavra de cada frente disponível e alocar os equipamentos existentes às mesmas, de forma a maximizar a produção. Os modelos se diferem pela forma de alocação dos caminhões. Um trabalha com alocação estática, ou seja, cada caminhão trabalha fixado a um único par de pontos de carga e descarga. Desta forma, cada caminhão atenderá uma única frente e descarregará sempre no mesmo ponto. O outro modelo trabalha com alocação dinâmica, onde a definição da frente a ser atendida por cada caminhão e seu ponto de descarga, acontece ao término de cada viagem, sendo o controle desta alocação realizado por um sistema de despacho automático. No modelo de alocação dinâmica, a alocação de equipamentos fica restrita a carregadeiras e/ou escavadeiras. Já o segundo modelo considera um sistema de alocação estática e, deste modo, o modelo contempla também a alocação de caminhões.

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2) Modelo matemático - alocação dinâmica de caminhões Seja uma mina a céu aberto onde, durante a lavra, exista um controle dos teores das diversas variáveis envolvidas. Neste trabalho, considerou-se o controle dos teores das variáveis químicas, mas o mesmo poderia ser feito para o controle das variáveis físicas, como a granulometria, por exemplo. A cada plano de lavra de curto prazo elaborado, existem n frentes disponíveis, onde a lavra pode acontecer simultaneamente em m (m ≤ n) dessas frentes, dependendo da disponibilidade de equipamentos de carga (carregadeiras e/ou escavadeiras). Caso entre em operação, por razões técnicas e econômicas, cada equipamento de carga deve trabalhar entre limites preestabelecidos de produção. Além disso, uma relação estéril/minério mínima preestabelecida deve ser cumprida. O modelo matemático para o problema descrito anteriormente é o seguinte: Seja: M o conjunto das frentes de minério E o conjunto das frentes de estéril Pi o ritmo de lavra da frente i (t/h) 0, se o equipamento de carga j não trabalhar na frente i xji =

1, se o equipamento de carga j trabalhar na frente i

t v i o teor da variável v na frente i (%) linf v o teor mínimo admissível para a variável v (%) lsup v o teor máximo admissível para a variável v (%) Pmin j a produção mínima admissível para o equipamento de carga j (t/h) Pmax j a produção máxima admissível para o equipamento de carga j (t/h) R a relação estéril minério mínima requerida Preq a produção mínima requerida (t/h) Função Objetivo: Maximizar

∑ Pi

i∈M

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Restrições de Qualidade:

∑ Pi t vi

l inf v ≤ i∈M

≤ l sup v

∑ Pi

∀v

(1)

i∈M

Restrições de Alocação:

∑ x ji ≤ 1

∀ i ∈ M ,i ∈ E

(2)

j

∑ x ji ≤ 1

∀j

(3)

i∈ M i∈ E

Restrições de Produção:

∑ P min j x ji ≤ Pi ≤ ∑ P max j x ji j

∀ i ∈ M ,i ∈ E

(4)

j

∑P

i∈M

i

≥ Pr eq

∑P ∑P i∈E

i∈M

Pi ≥ 0

i

(5)

≥R

(6)

i

∀i ∈ M , i ∈ E

(7)

As restrições de qualidade (1) garantem que o produto resultante da mistura dos minérios das diversas frentes esteja com a qualidade exigida pela usina de tratamento. As restrições de alocação (2) e (3) fazem com que cada frente possua somente um equipamento de carga – restrições de alocação (2) – e que cada equipamento de carga atenda somente uma frente – restrições de alocação (3). Já as restrições de produção estão divididas em quatro grupos: (4) essas restrições garantem que os equipamentos de carga trabalhem entre os limites de produção preestabelecidos; (5) restrição opcional, caso se deseje impor uma produção mínima; (6) restrição que garante a relação estéril/minério preestabelecida e (7) é a restrição que garante produção em nível positivo em todas as frentes de lavra. 3) Modelo matemático - alocação estática de caminhões Inicialmente, será considerada a mesma situação apresentada no caso do modelo anterior. A diferença é que no caso de alocação estática tem-se também que realizar a alocação de caminhões às frentes de lavra. Para isso, deve-se levar em consideração dois fatos: 9 Cada caminhão deve atender uma única frente de lavra, sendo que, uma frente pode ter mais de um caminhão alocado a ela. 9 Um caminhão somente poderá trabalhar numa determinada frente se o seu modelo for compatível com o modelo do equipamento de carga que foi alocado àquela frente.

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A pesquisa Operacional e o Meio Ambiente 6 a 9 de novembro de 2001 - Campos do Jordão - SP

Sendo assim, o modelo matemático é o seguinte: Seja: M o conjunto das frentes de minério E o conjunto das frentes de estéril Pi o ritmo de lavra da frente i (t/h) 0, se o equipamento de carga j não trabalhar na frente i xj i =

1, se o equipamento de carga j trabalhar na frente i 0, se o se o caminhão k não trabalhar na frente i

dk i =

1, se o se o caminhão k trabalhar na frente i 0, se o equipamento de carga j não trabalhar com o caminhão k

yj k =

1, se o equipamento de carga j trabalhar com o caminhão k

t v i o teor da variável v na frente i (%) linf v o teor mínimo admissível para a variável v (%) lsup v o teor máximo admissível para a variável v (%) C k i a produtividade do caminhão k quando ele trabalha na frente i (t/h) Pmin j a produção mínima admissível para o equipamento de carga j (t/h) Pmax j a produção máxima admissível para o equipamento de carga j (t/h) R a relação estéril/minério mínima requerida Preq a produção mínima requerida (t/h) Função Objetivo: Maximizar

∑ Pi

i∈M

Restrições de Qualidade:

∑ Pi t vi

l inf v ≤ i∈M

∑ Pi

≤ l sup v

∀v

(1)

∀ i ∈ M ,i ∈ E

(2)

i∈M

Restrições de Alocação:

∑ x ji ≤ 1 j

∑ x ji ≤ 1

∀j

(3)

i∈ M i∈ E

∑ d ki ≤ 1

∀k

i∈ M i∈ E

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x ji + d ki − 2 y jk ≤ 1

∀ i ∈ M , i ∈ E, j, k

(5)

Restrições de Produção:

∑ P min j x ji ≤ Pi ≤ ∑ P max j x ji j

∀ i ∈ M ,i ∈ E

(6)

j

Pi ≤ ∑ C ki d ki

∀ i ∈ M ,i ∈ E

(7 )

k

∑ P ≥ Pr eq ∑ Pi

(8)

i

i∈M

i∈ E

∑ Pi

≥R

(9)

i∈M

Pi ≥ 0

∀i ∈ M , i ∈ E

(10)

Com relação ao primeiro modelo (alocação dinâmica) três grupos de restrições foram acrescentados, cujas funções são: 9 Restrições de alocação (4): garantem que cada caminhão atenderá somente uma frente. 9 Restrições de alocação (5): permitem que somente modelos compatíveis de equipamentos de carga e de caminhões trabalhem numa mesma frente. 9 Restrições de produção (7): garantem que a produção de cada frente fique limitada a produtividade dos caminhões que a ela estão alocados. A produtividade dos caminhões é calculada dividindo-se a sua capacidade de carga pelo tempo de ciclo total. Entende-se por tempo de ciclo total o somatório dos tempos de carga, deslocamento carregado, descarga e deslocamento vazio. 4) Implementação computacional Os modelos propostos devem ser resolvidos com a utilização de software específico, já que sua resolução manual é inviável devido ao grande número de restrições. Existem no mercado, diversos destes softwares, tais como o LINDO e “What’s Best” da Lindo Systems Inc ou CPLEX da Cplex Optimization Inc. Para geração do modelo matemático que servirá como entrada destes softwares, aconselha-se o uso de um programa construído especificamente para este fim, pois isso evita erros na construção do modelo. Estes programas podem ser desenvolvidos a partir de linguagens genéricas como C++, Pascal, Fortran, Delphi, Visual Basic, etc. 5) Exemplo de aplicação Seja uma mineradora de ferro que disponibiliza em seu plano de curto prazo 6 frentes de minério e 2 de estéril. Todo minério lavrado é descarregado no britador primário que alimenta a usina de tratamento de minério e todo estéril é depositado em uma única pilha. As variáveis controladas nesta mina correspondem aos teores de ferro, fósforo, alumina e sílica e para o plano de lavra em questão seus valores são mostrados na tabela 1. Os limites requeridos pela usina para cada uma das variáveis são mostrados na tabela 2.

Frente/Tipo

Tabela 1 – Teores das frentes de lavra Ferro (Fe) - % Fósforo (P) - % Alumina (Al2O3) - % Sílica (SiO2) - % 1407

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F1 / Minério F2 / Minério F3 / Minério F4 / Minério F5 / Minério F6 / Minério F7 / Estéril F8 / Estéril

45,34 48,87 53,76 52,56 47,00 50,12 34,00 41,00

0,038 0,059 0,038 0,041 0,032 0,039 0,058 0,055

1,21 1,35 0,87 0,91 1,10 1,31 0,97 1,89

3,56 4,94 3,05 4,74 4,57 4,58 6,65 5,95

Tabela 2 – Limites admissíveis para usina Variável Limite Inferior (%) Limite Superior (%) 48,50 58,00 Ferro (Fe) 0,030 0,043 Fósforo (P) 0,50 1,15 Alumina (Al2O3) 4,00 4,50 Sílica (SiO2) A empresa dispõe de 4 equipamentos de carga (carregadeira e/ou escavadeira) e 15 caminhões fora-de-estrada. Por razões operacionais cada equipamento de carga deve trabalhar com uma produtividade entre 450 e 900 t/h. Os caminhões têm capacidade média de 120 t. Os tempos de ciclo médios para cada uma das frentes estão mostrados na tabela 3. A usina requer no mínimo 2500 t/h de R.O.M. (run of mine) e a relação estéril / minério mínima deve ser de 0,3.

Frente T Carga (min) 2,3 F1 2,3 F2 2,3 F3 2,3 F4 2,3 F5 2,3 F6 2,3 F7 2,3 F8

Tabela 3 – Tempos de ciclos T Desl Car (min) T Desc (min) T Desl Vaz (min) 5,33 0,8 4,16 6,24 0,8 4,42 7,28 0,8 5,85 4,81 0,8 3,9 5,2 0,8 4,16 9,75 0,8 8,06 8,45 0,8 7,15 10,92 0,8 8,97

T Total (min) 12,59 13,76 16,23 11,81 12,46 20,91 18,70 22,99

T Carga: tempo de carga, T Desl Car: tempo de deslocamento carregado, T Desc: tempo de descarga, T Desl Vaz: tempo de deslocamento vazio, T Total: tempo de ciclo total

O problema proposto foi resolvido utilizando-se os dois modelos apresentados anteriormente, sendo sua implementação computacional feita com o uso do sistema LINDO da LINDO Systems Inc. A geração do modelo de entrada foi feita por meio de programa desenvolvido em Borland Delphi 5.0. Os resultados de produtividade e alocação de equipamentos obtidos para cada um dos modelos são apresentados a seguir nas tabelas 4 e 5. Frente Ritmo(t/h) Eqpto carga

Tabela 4 – Resultados para alocação dinâmica F1 F2 F3 F4 F5 F6 F7 0 900 900 0 900 0 900 -nº 3 nº 1 -nº 4 -nº 2

Eqpto carga: equipamento de carga

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Simpósio Brasileiro de Pesquisa Operacional

A pesquisa Operacional e o Meio Ambiente 6 a 9 de novembro de 2001 - Campos do Jordão - SP

Tabela 5 – Resultados para alocação estática Frente F1 F2 F3 F4 F5 F6 0 0 900 900 0 900 Ritmo(t/h) --nº 2 nº 1 -nº 4 Eqpto carga --3 2 -3 Quant. Caminhões

F7 810 nº 3 3

F8 0 ---

Eqpto carga: equipamento de carga, Quant. Caminhões: quantidade de caminhões alocados

Em ambos casos, a qualidade da mistura e a relação estéril/minério atendem às especificações como pode ser observado na tabela 6. Como pode ser observado o exemplo admite mais de uma solução. Além disso, não houve necessidade, para operacionalizar este plano, de se utilizar todos os caminhões disponíveis, apenas 11 deles. Tabela 6 – Resultados de qualidade e relação estéril/minério Variável Modelo Alocação Estática Modelo Alocação Dinâmica 52,15 49,89 Ferro 0,039 0,043 Fósforo 1,03 1,11 Alumina 4,12 4,19 Sílica 0,30 0,33 Rel. Est/Min Rel. Est/Min: relação estéril/minério

6) Conclusões Os modelos apresentados contemplam diversos aspectos operacionais do planejamento de lavra de curto prazo e seu uso simplifica substancialmente a programação da lavra. A implementação computacional dos modelos, apesar de não trivial, devido ao grande número de restrições, pode ser feita utilizando qualquer software de programação matemática. Na maioria das minas brasileiras, a resolução de problemas deste tipo ainda é feita pelo método de tentativas e erros, utilizando planilhas eletrônicas, o que não garante uma solução otimizada e demanda muito tempo. Espera-se que, em breve, muitas dessas empresas adotem soluções deste tipo visando à otimização de suas atividades, de forma a atender às exigências de um mercado cada vez mais competitivo. Referências bibliográficas PINTO, L. R. Uso de técnicas de pesquisa operacional na otimização das operações de lavra. In: Congresso Brasileiro de Mineração, VI, 1995. Salvador. Coletânea de trabalhos técnicos. Salvador: IBRAM, 1995. p. 53-61

1409

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

“LA TECNOLOGÍA MODERNA, A PARTIR DE LA REVOLUCIÓN

INDUSTRIAL,

CONFIGURA

DE

FORMA DECISIVA TODO EL ÁMBITO DE LA EXPERIENCIA HUMANA. ALTERA LA REALIDAD, E.T.S.I. Telecomunicación

NUESTRA

FORMA

EXPLICARLA

Y

DE

REPRESENTARLA

NUESTROS

CRITERIOS

Y

PARA

VALIDARLA” M.A. QUINTANILLA. 1988

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

“Lo que nadie puede dudar es que, desde hace mucho tiempo, la técnica se ha insertado entre las condiciones ineludibles de la vida humana de suerte tal que el hombre actual no podría, aunque quisiera,

E.T.S.I. Telecomunicación

vivir sin ella. Es pues, hoy, una de las mayores ingredientes que integran nuestro destino” Ortega y Gasset, José Santander, 1932

INTRODUCCIÓN A LA INGENIERÍA

SOBRE LA TECNOLOGÍA

Universidad Politécnica de Madrid

E.T.S.I. Telecomunicación

D.R.A.E.

“Conjunto de los conocimientos propios de un oficio o arte industrial

ETIMOLOGÍA

Estudio racional de la técnica Ciencia tratada según las normas del arte

CARÁCTER ANFIBOLÓGICO ACTUAL UTILIZACIÓN INTERESADA ¡ TO GET MORE OUT OF LESS ¡

INTRODUCCIÓN A LA INGENIERÍA

TECNOLOGÍA

Universidad Politécnica de Madrid

E.T.S.I.

TÉCNICA Procedimientos

CIENCIA Conocimientos

+

Telecomunicación

PROCESOS INDUSTRIALES

TECNOLOGÍA

INTRODUCCIÓN A LA INGENIERÍA

Universidad

ÁMBITO CULTURAL

Politécnica

Fines, valores, creencias, costumbres, ideas, creatividad, progreso

de Madrid

ÁMBITO ORGANIZATIVO T E C N O L O G Í A

Actividad económica, actividad industrial, organizaciones profesionales, sindicatos consumidores

E.T.S.I.

ÁMBITO CIENTÍFICO -TÉCNICO

Telecomunicación

Ciencia, conocimientos, máquinas, aparatos, productos, recursos

Tecnología: “Aplicación del conocimiento científico y de los procedimientos técnicos a la realización de tareas prácticas por medio de sistemas organizados que comprenden personas y organizaciones, seres vivos y máquinas” [Pacey, 1983]

INTRODUCCIÓN A LA INGENIERÍA

Universidad

INTRODUCCIÓN:

Politécnica

Problemas que plantea la definición de Ingeniería

de Madrid

Un concepto que se relaciona con otros: E.T.S.I. Telecomunicación

- CIENCIA - TÉCNICA - TECNOLOGÍA

I N G E N I E R Í A

- UN TÍTULO ACADÉMICO - UNA ACTIVIDAD PROFESIONAL - UNA MANERA DE ACTUAR: “EL MÉTODO INGENIERIL”

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

INGENIERÍA: Arte de transformar las materias primas y usar las fuentes de energía de la naturaleza en la producción de bienes y servicios para el bienestar del hombre. [“Engineering and Western Civilization”, James H. Finch. MGH, 1952] PROCREAD Y MULTIPLICAOS

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Y HECHID LA TIERRA. Y SOJUZGARLA, Y DOMINAD EN LOS PECES DEL MAR Y EN LAS AVES DEL CIELO Y EN TODO ANIMAL QUE SE MUEVA SOBRE LA TIERRA [Génesis 1,28]

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

E.T.S.I.

OTRA DEFINICIÓN DE INGENIERÍA: Aplicación creativa de los principios científicos al diseño de estructuras, máquinas, aparatos y procesos de fabricación, y al manejo de todo ello con un buen conocimiento de sus usos y propiedades, pudiendo predecir su funcionamiento bajo condiciones específicas de trabajo.

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DIMENSIÓN: FÁBRICA, MÁQUINAS, APARATOS, ... PERFIL: INGENIERO REVOLUCIÓN INDUSTRIAL (1825)

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

E.T.S.I. Telecomunicación

INGENIEROS INDUSTRIALES: ESPAÑA 1855 DIMENSIÓN: SERVICIOS Planificación Gestión Administración Organización Dirección DIMENSIÓN: ECONÓMICA Coste Tiempo Mercado

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica

DEFINICIÓN SINTÉTICA QUE “ACEPTAREMOS” EN ESTE CURSO

de Madrid

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INGENIERÍA: Es la actividad profesional que consiste en la aplicación creativa de los conocimientos científico-técnicos a la invención, desarrollo y producción de bienes y servicios, transformando y organizando los recursos naturales para resolver las necesidades del hombre, haciéndolo de una manera óptima, tanto económica como socialmente.

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

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DEFINICIÓN “PROVOCADORA”: La ingeniería es el arte de modelar materiales que no entendemos plenamente en formas que no podemos analizar con precisión, para que soporten fuerzas que no sabemos evaluar correctamente, de modo que la opinión pública no tenga motivos para sospechar el alcance de nuestra ignorancia.

INTRODUCCIÓN A LA INGENIERÍA

Universidad de Madrid

DEFINICIÓN DE INGENIERÍA COMO ACTIVIDAD PROFESIONAL:

E.T.S.I.

Actividad profesional que usa el método científico para transformar de una manera económica y óptima los recursos naturales en formas útiles para el uso del hombre.

Politécnica

Telecomunicación

ACTIVIDAD PROFESIONAL ™ Empleo, facultad u oficio que se ejerce públicamente ™ No confundir titulación con profesión

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

E.T.S.I. Telecomunicación

DEFINICIÓN DE “INGENIERO” SEGÚN FEANI (Federación Europea de Asociaciones Nacionales de Ingenieros):

Un ingeniero es una persona que ha adquirido y sabe utilizar conocimientos científicos, técnicos y cualesquiera otros necesarios que le capacitan para crear, operar y mantener sistemas eficaces, estructuras, instalaciones o procesos, y para contribuir al progreso de la ingeniería mediante la investigación y el desarrollo. ™ CONOCIMIENTO (Posesión y utilización) ™ CAPACITACIÓN (Legal y profesional) ™ INNOVACIÓN (I+D, optimización)

INTRODUCCIÓN A LA INGENIERÍA INGENIERO Universidad

(FEANI)

Politécnica de Madrid

Práctica Profesional

Telecomunicación

Formación Universitaria

E.T.S.I.

CONOCIMIENTO B. Física, matemáticas y fundamentos de su especialidad C. Práctica de su rama de ingeniería D. Instrumentación en nuevas tecnologías y manejo de información técnica y estadística H. Relaciones industriales, dirección empresarial O. Dominio de otra lengua europea

CAPACITACIÓN A. Responsabilidad profesional E. Uso de modelos teóricos de simulación del mundo físico F. Enjuiciar problemas técnicos G. Trabajo multidisplinar I. Comunicarse oralmente y por escrito L. Solución ingenieril más favorable (costes/calidad/tiempos)

INNOVACIÓN J. Soluciones que combinen calidad-sencillez-coste K. Actitud innovadora y creativa, apreciación positiva del cambio técnico M. Consideración y respeto por los factores medioambientales

INTRODUCCIÓN A LA INGENIERÍA

EJEMPLO

Universidad Politécnica

FARADAY

de Madrid

PRINCIPIO DE INTRODUCCIÓN ELECTROMAGNÉTICA (1831)

E.T.S.I.

SIEMENS (1816-1842)

EDISON (1847-1931)

DINAMO (1867)

DINAMO (1879)

EMPRESA

EMPRESA

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INTRODUCCIÓN A LA INGENIERÍA MÉTODO CIENTÍFICO Universidad Politécnica de Madrid

E.T.S.I. Telecomunicación

MÉTODO INGENIERIL

1. Observación de un fenómeno

1. Identificación de un problema

2. Conocimiento existente

2. Recopilación de información

3. Formulación de hipótesis

3. Búsqueda de soluciones creativas

4. Deducción:lógica,matemáticas, etc

4. Diseños preliminares: modelización, simulación, cálculos, etc

5. Contraste teorías-hechos 5. Evaluación y selección de soluciones 6. Comunicación científica 7. Aceptación científica

a

por

la

comunidad 6. Elaboración del proyecto: planos, mediciones, pliegos.condiciones, etc.

la

comunidad 7. Producción, construcción, etc.

8. Nuevo conocimiento, mejora del 8. Mercado, público, sociedad. existente

INTRODUCCIÓN A LA INGENIERÍA REFORMA Universidad

HOMBRE

Politécnica

PIENSA (H. SAPIENS) HACE (H.FABER)

de Madrid

NATURALEZA ACTIVIDAD TÉCNICA

SUJETO

ADAPTACIÓN

DIFICULTADES FACILIDADES

MEDIO

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ADAPTACIÓN

ANIMALES PLANTAS

ACTIVIDAD BIOLÓGICA

SUJETO REFORMA

NATURALEZA MEDIO

INTRODUCCIÓN A LA INGENIERÍA

Universidad

REFORMA DE LA NATURALEZA

Politécnica de Madrid

NATURALEZA

OBJETO: “EL QUE” FINALIDAD: “PARA QUE” E.T.S.I. Telecomunicación

+

PROGRAMA HUMANO

TÉCNICA

INTRODUCCIÓN A LA INGENIERÍA

Universidad

NECESIDAD .................... HAMBRE

Politécnica de Madrid

ACTO NATURAL ............... COMER LO QUE SE ENCUENTRA ACTOS TÉCNICOS ............ CAZAR, SEMBRAR, RECOLECTAR, SEGAR, MOLER, ETC

E.T.S.I. Telecomunicación

INGENIERÍA ....................... SISTEMAS Y REDES DE RIESGOS UTILIZACIÓN DE MAQUINARIA PLANIFICACIÓN, PRODUCCIÓN BIOTECNOLOGÍA TRANSGÉNICOS, ETC

¿Existe hambre en el mundo?

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

NECESIDAD .................... DESPLAZARSE ACTO NATURAL ............... ANDAR, CORRER, SALTAR ACTOS TÉCNICOS ............ USO DE ANIMALES NAVEGACIÓN ENERGÍAS NATURALES:

E.T.S.I. Telecomunicación

AGUA, VIENTO

INGENIERÍA ....................... FERROCARRIL, BARCOS, AUTOMÓVIL ENERGÍAS ARTIFICIALES MÁQUINAS

Volar,¿Era necesario?

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

OPTIMIZACIÓN ECONÓMICO-SOCIAL LA TOMA DE DECISIONES SOBRE: ™ OPCIONES CON ALTO GRADO DE CERTEZA ¾ Factores y variables cuantificables ¾ Modelos, simulación, etc. ¾ Consecuencias conocidas

E.T.S.I. Telecomunicación

™ OPCIONES CON RIESGO E INCERTIDUMBRE ¾ Factores y variables no cuantificables ¾ Ausencia de modelos ¾ Consecuencias conocidas con un margen de seguridad

™OPCIONES CON RESULTADOS

DESCONOCIDOS ¾ Largo plazo ¾ Sistemas complejos

INTRODUCCIÓN A LA INGENIERÍA

CONCEPTO DE INGENIERÍA

Universidad Politécnica de Madrid

DEFINICIÓN GLOBAL: DIMENSIONES I. DIMENSIÓN CIENTÍFICO-TÉCNICA

E.T.S.I. Telecomunicación

¾ ¾ ¾ ¾ ¾

Aplicación creativa: innovación Principios científicos Diseño, desarrollo, construcción Estructuras, máquinas, aparatos, sistemas Funcionalidad, utilidad

II. DIMENSIÓN ECONÓMICO-SOCIAL ¾ ¾ ¾ ¾

Organización Recursos: materiales – económicos - humanos Organización y dirección empresas Planificación y gestión de servicios Optimización costes: económicos - sociales

INTRODUCCIÓN A LA INGENIERÍA

Universidad Politécnica de Madrid

CONCEPTO DE INGENIERÍA RESOLVER PROBLEMAS TÉCNICOS

ECONÓMICOS

SOCIALES

™ ECONÓMICOS: “Un ingeniero es una persona capaz de hacer por una peseta lo que un no ingeniero haría por cien” Hacer que una cosa funcione bien de la forma más barata posible E.T.S.I. Telecomunicación

COMPROMISO: CALIDAD / COSTE

™ SOCIALES. Importancia de LA SEGURIDAD LA SALUD EL MEDIO AMBIENTE CALIDAD TÉCNICA

COMPROMISO

COSTE ECONÓMICO COSTE SOCIAL