Single-Period Multiproduct Inventory Models with Substitution

Yehuda Bassok, Ravi Anupindi and Ram Akella
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Yehuda Bassok: Department of Management Sciences, School of Business Administration, University of Washington, Seattle, Washington 98195
Ravi Anupindi: J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208
Ram Akella: Department of Engineering Economic Systems, Stanford University, Stanford, California 94305

Operations Research, 1999, vol. 47, issue 4, 632-642

Abstract: We study a single period multiproduct inventory problem with substitution and proportional costs and revenues. We consider N products and N demand classes with full downward substitution, i.e., excess demand for class i can be satisfied using product j for i ≥ j . We first discuss a two-stage profit maximization formulation for the multiproduct substitution problem. We show that a greedy allocation policy is optimal. We use this to write the expected profits and its first partials explicitly. This in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution. In a limited computational study using two products, we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering. Specifically, we show that the benefits are higher with high demand variability, low substitution cost, low profit margins (or low price to cost ratio), high salvage values, and similarity of products in terms of prices and costs.

Keywords: inventory/production; stochastic; substitution; multiproduct (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (94)

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