The Impact of Demand Correlation on Replenishment Policies for Multi-Product Stochastic Inventory Systems with Joint-Replenishment Costs

Abstract

This paper analyzes optimal replenishment policies that minimize expected discounted cost of multi-product stochastic inventory systems. The distinguishing feature of the multi-product inventory system that we analyze is the existence of correlated demand and joint-replenishment costs across multiple products. While prior literature on multi-product stochastic inventory systems has focused on computation of heuristic policies that decouple the N product problem to N single product problems, our focus is on computing and finding the structure of the optimal policies for multi-product inventory systems, particularly when demand is correlated across products. The problem is formulated as a Markov Decision Process (MDP). A method to compute the optimal policy that uses a moving boundary based policy improvement scheme is proposed. Numerical examples show that the (s, c, d, S) policy closely approximates the optimal policy, and can significantly outperform the (s, c, S), P (s, S) and Q(s, S) policies analyzed in prior literature which assume independent demand.