Optimal policies for inventory models with multiple demand classes

Abstract

This dissertation consists of three essays that address issues in inventory management. We focus on the structural results, in particular on the structures of optimal policy for inventory systems with multiple demand classes. In the first essay, we consider a finite horizon periodic review, single product inventory system, with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand from the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s, S) policy, and we partially obtain the rationing structure based on the sub-convexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for a majority of our numerical examples. We study in more depth the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s, S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of a finite set of states, For each state in this set, the optimal policy is obtained by simply choosing a policy from at most two alternatives. An efficient algorithm is then proposed. In the second essay, we first consider a periodic review inventory system with a fixed setup cost and two demand classes: deterministic and stochastic, where the deterministic demand must be satisfied immediately and the stochastic demand can be backlogged. Assuming that the stochastic demand is never backlogged if there is stock in the system, a modified (s, S) policy was proved optimal under certain conditions in a previous paper. The objective is to weaken one of the conditions in the literature while still obtaining the optimality of the (s, S) policy.