Bank of Bloond

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