Suppose that there is a finite replenishment rate m (as discussed in Section 4.8).

a. Modify the Silver–Meal heuristic to take account of this fact.

Note: For simplicity, assume that m is large enough so that, if a replenishment is initiated at the start of period j, then, the demand for period j, D(j), can be met from that replenishment. In addition, assume that it is now necessary to include in the analysis the carrying costs of D(j) during its period of consumption, j. To do this, assume a uniform demand rate during any single period (without the extra cost included, the finite replenishment rate would have no effect on the decision).

b. For the item of Problem 5.4 suppose that m = 150 units/month. Now, use the modified heuristic to find the timing and sizes of the replenishments.

c. For this example, what is the percentage cost penalty over the 12-month horizon associated with ignoring the finite m value, that is, using the unmodified heuristic?