GOTHAM CITY HOSPITAL BLOOD BANK The management of blood is an important area within health care delivery systems. Blood banks have been developed which perform the functions of procurement, storage, processing, and distribution of blood. The uncertainties associated with both supply and demand usually result in the maintenance of relatively large buffer stocks. Blood bank inventory models are complex, for several reasons: . (1) both supply and demand are random; (2) approximately 50 percent of all bloods demanded, cross matched, and held for a particular patient are eventually found not to be required for that patient; (3) blood is perishable, the present legal lifetime being 21 days in most areas; and (4) each blood bank typically interacts with a number of other banks. John B. Hennings, Blood Bank Inventory Control, Management Science, vol. 19, no. 6 (February 1973), p. 637. Assume that GCH is in the process of studying the inventory policies of its blood bank. It is interested in determining the optimal buffer stock to maintain. Needless to say, the assumptions of the model developed in the previous section need to be stretched to apply to the blood bank environment; however, assume that the analysts agree that the assumptions are close enough to use the model for a quick benchmark solution. The model is to be applied to the entire inventory of blood used by the hospital. Subsequently, further analyses can be conducted for each type of blood. Mean annual demand is 160,600 units of blood (based on 365 days). Lead−time for receiving replenishment supplies from the regional cooperative blood bank is deterministic and equal to two days. The carrying cost of blood is estimated at $2.25 per unit per year. Ordering cost is estimated at $63 per order. Based on the equation . Q* is approximately 3,000 units of blood per order. GCH has worked out a loan arrangement with a private blood bank in Gotham City whereby if GCH incurs a temporary shortage of blood, it can immediately borrow units at a cost of $1.50 per unit. The agreement also specifies the replacement of the borrowed blood units when GCH receives its next replenishment supply. Lead−time demand (that is, demand for any two day period) is stochastic. It is characterized reasonably well by the empirical distribution in the next table. According to

the mean of this distribution is 880 (Note that 880 is the mean demand per two days. Per day the mean demand is 440, which when multiplied by 365 days gives D= 160,600 units per year. Table LEAD TIME DEMAND GCH Class intervals for Lead Time Demand 790 but under 810 810 but under 830 830 but under 850

Lead Time Demand

Probability

Cumulative Probability

(dL) 800 820 840

f(dL) 0.02 0.05 0.07

F(dL) 0.02 0.07 0.14

1

850 but under 870 870 but under 890 890 but under 910 910 but under 930 930 but under 950 950 but under 970

860 880 900 920 940 960

0.18 0.36 0.18 0.07 0.05 0.02

0.32 0.68 0.86 0.93 0.98 1.00

In order to determine the optimal reorder point R* we first compute

We conclude that the lowest value of r satisfying Equation (11.20) is R*= 940. In other words, according to the Table, R must be 940 for the cumulative probability to exceed 0.9720, or F(940) 0.9720. Thus, 3,000 units of blood should be ordered whenever inventory drops below 940 units. Since the expected lead−time demand is 880, the recommended buffer stock is

2