Replenishment Policies for Multi-Product Stochastic Inventory Systems with Correlated Demand and Joint-Replenishment Costs
Authors
-
Haolin
Feng
-
Qi
Wu
-
Kumar
Muthuraman
-
Vinayak
Deshpande
Published
Production and Operations Management , vol.
24, issue
4,
April (2nd Quarter/Spring)
2015
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. Our objective is to understand the structure of the optimal policy and use this understanding
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
as well.