4.100 How much to order?

CASE 4.2 Faced with the demand for the perishable product in blood, hospital managers need to establish an ordering policy that deals with the trade-off between shortage and wastage. As it turns out, this scenario, referred to as a single-period inventory problem, is well known in the area of operations management, and there is an optimal policy. What we need to know is the per item cost of being short and the per item cost of being in excess . In terms of the blood example, the hospital estimates that for every bag short, there is a cost of $80 per bag, which includes expediting and emergency delivery costs. Any transfusion blood bags left in excess at day's end are associated with $20 per bag cost, which includes the original cost of purchase along with end-of-day handling costs. With the objective of minimizing long-term average costs, the following critical ratio needs to be computed:

Recognize that will always be in the range of 0 to 1. It turns out that the optimal number of items to order is the smallest value of such that is at least the value.