RANDOM OPPORTUNITIES FOR REDUCED COST REPLENISHMENTS

In this paper we consider the situation where the typical assumptions underlying the EOQ model are appropriate for an item, in particular a reasonably level demand rate exists. However, opportunities for special replenishments at a reduced unit cost occur at random. The following type of 3-parameter policy is considered. When a non-special (regular) replenishment is made, an order-up-to-level, S1, is used. When a special opportunity arises we only take advantage of it if the current inventory is low enough (L2 or lower) and we order enough to raise the inventory level to S2. This situation was modelled earlier in the literature, but the solution procedure suggested involved a 3-dimensional search on the three control parameters, S1, L2 and S2. We develop an approximate solution method which is much easier to use and which performs excellently on a wide range of examples. The performance of an even more simple method, based on always taking advantage of a special opportunity to replenish at reduced unit cost (i.e., setting L2 = S2), is shown to be highly dependent upon the values of the five uncontrollable parameters of the problem.