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Joint Inventory and Pricing Decisions for an Assortment

Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109
Graduate School of Business, Stanford University, Stanford, California 94305
ayding{at}umich.edu
eporteus{at}stanford.edu

We seek optimal inventory levels and prices of multiple products in a given assortment in a newsvendor model (single period, stochastic demand) under price-based substitution, but not stockout-based substitution. We address a demand model involving multiplicative uncertainty, motivated by market share models often used in marketing. The pricing problem that arises is known not to be well behaved in the sense that, in its deterministic version, the objective function is not jointly quasi-concave in prices. However, we find that the objective function is still reasonably well behaved in the sense that there is a unique solution to the first-order conditions, and this solution is optimal for our problem.

Subject classifications: inventory/production; multi-item; pricing; stochastic; marketing; choice models; pricing; retailing; wholesaling.
History: Received October 2003; revision received December 2006; accepted August 2007.

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