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

30 Pages Posted: 5 Jun 2007 Last revised: 23 Nov 2008

Haolin Feng

Lingnan (University) College, Sun Yat-sen University

Kumar Muthuraman

University of Texas at Austin - McCombs School of Business

Vinayak Deshpande

Purdue University - Krannert School of Management

Date Written: October 1, 2008

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.

Suggested Citation

Feng, Haolin and Muthuraman, Kumar and Deshpande, Vinayak, The Impact of Demand Correlation on Replenishment Policies for Multi-Product Stochastic Inventory Systems with Joint-Replenishment Costs (October 1, 2008). McCombs Research Paper Series No. IROM-08-08. Available at SSRN: https://ssrn.com/abstract=991356 or http://dx.doi.org/10.2139/ssrn.991356

Haolin Feng

Lingnan (University) College, Sun Yat-sen University ( email )

135 Xin Gang Xi Road
Guangzhou, Guangdong 510275
China

Kumar Muthuraman (Contact Author)

University of Texas at Austin - McCombs School of Business ( email )

Austin, TX 78712
United States

Vinayak Deshpande

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

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