Replenishment Policies for Multi-Product Stochastic Inventory Systems with Correlated Demand and Joint-Replenishment Costs
Haolin Feng, Qi Wu, Kumar Muthuraman, Vinayak Deshpande
Production and Operations Management · 2015 · Volume 24 · Issue 4
Abstract
This study 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. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real-world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s,c,d,S)-policies, and also develop an algorithm to compute good policies in this class, for large multi-product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.
Keywords
multi-item inventory management, joint replenishment, stochastic inventory control, correlated demand, fixed ordering cost
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