Optimal inventory control of lumpy demand items using (s, S) policies with a maximum issue quantity restriction and opportunistic replenishments

This paper presents a modified (s, S) inventory model which describes the characteristics of an inventory system with lumpy demand items. A maximum issue quantity restriction of w units and a critical inventory position of A units are incorporated into the inventory control policy. Customer orders with demand sizes larger than the maximum issue quantity will be filtered out from the inventory system and satisfied by using special replenishment orders in order to avoid disruption to the inventory system. The option of opportunistic replenishments is introduced to further minimize the total replenishment cost. An opportunistic replenishment is initiated if the level of the current inventory position is equal to or below the critical level when a customer demand with a size exceeding the maximum issue quantity arrives, which does not only initiate a direct shipment to the customer, but also raises the inventory position to S. Two effective algorithms are developed to determine the optimal values of w, A, s and S simultaneously. The first algorithm is based on the branch-and-bound tree search technique, and the second one is based on the concept of genetic algorithms. Numerical examples are used to illustrate the effectiveness of the algorithms developed. The effects of changes in the cost and system parameters on the optimal theory control policy are also studied by using sensitivity analysis.