Inventory Models for Substitutable Products: Optimal Policies and Heuristics

35 Pages Posted: 4 Jun 2008 Last revised: 19 Apr 2009

See all articles by Mahesh Nagarajan

Mahesh Nagarajan

University of British Columbia (UBC) - Sauder School of Business

Raj S. Rajagopalan

University of Southern California - Marshall School of Business

Date Written: April 1, 2009

Abstract

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 multi-period 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 de-coupled 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.

Keywords: Inventory/Production, stochastic multi-period inventory models, stockout-based substitution

Suggested Citation

Nagarajan, Mahesh and Rajagopalan, Raj S., Inventory Models for Substitutable Products: Optimal Policies and Heuristics (April 1, 2009). Marshall School of Business Working Paper No. IOM 17-09, Available at SSRN: https://ssrn.com/abstract=1140309 or http://dx.doi.org/10.2139/ssrn.1140309

Mahesh Nagarajan (Contact Author)

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

Raj S. Rajagopalan

University of Southern California - Marshall School of Business ( email )

701 Exposition Blvd
Los Angeles, CA California 90089
United States

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