This Article Full Text (PDF) e-companion References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Nagarajan, M. Articles by Rajagopalan, S. Search for Related Content

Inventory Models for Substitutable Products: Optimal Policies and Heuristics

Operations and Logistics, Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Information and Operations Management, Marshall School of Business, University of Southern California, Los Angeles, California 90089
mahesh.nagarajan{at}sauder.ubc.ca
srajagop{at}marshall.usc.edu

In this paper, we examine the nature of optimal inventory policies in a system where a retailer manages substitutable products. We first consider a system with two products 1 and 2 whose total demand is D and individual demands are negatively correlated. A fixed proportion of the unsatisfied customers for an item will purchase the other item if it is available in inventory. For the single-period case, we show that the optimal inventory levels of the two items can be computed easily and follow what we refer to as "partially decoupled" policies, i.e., base stock policies that are not state dependent, in certain critical regions of interest both when D is known and random. Furthermore, we show that such a partially decoupled base-stock policy is optimal even in a multiperiod version of the problem for known D for a wide range of parameter values and in an N-product single-period model under some restrictive conditions. Using a numerical study, we show that heuristics based on the decoupled inventory policy perform well in conditions more general than the ones assumed to obtain the analytical results. The analytical and numerical results suggest that the approach presented here is most valuable in retail settings for product categories where the level of substitution between items in a category is not high, demand variation at the aggregate level is not high, and service levels or newsvendor ratios are high.

Key Words: inventory/production; stochastic multiperiod inventory models; stockout-based substitution
History: Received: June 12, 2006;