Title: Game theoretic analysis of an inventory problem with substitution, stochastic demand, and uncertain supply

Authors: Tugce Martagan; Burak Ekşioğlu

Addresses: Department of Industrial and Systems Engineering, University of Wisconsin-Madison, 3163 Engineering Centres Building, WI 53706, USA ' Department of Industrial and Systems Engineering, Mississippi State University, P.O. Box 9542, Mississippi State, MS 39762, USA

Abstract: A game theoretic approach is used to analyse an inventory problem with two products, stochastic demand, and uncertain supply. The supply chain analysed includes two competing retailers selling two substitutable products and those retailer' suppliers. Retailers face stochastic demand and replenish the inventory from the suppliers. However, both suppliers provide an indeterminate fraction of the quantity requested, due to randomness in capacity and quality. Some customers with unmet demand will substitute that product with one sold by the other retailer. We assume that the retailers are rational players with conflicting objectives. We model the retailers' single period expected payoffs and identify the ordering decisions using Nash strategy. We prove the existence and uniqueness of the Nash solution, and provide results for numerical examples. We analyse the combined impact of product substitution and supply uncertainty on the retailers. Results suggest that supply uncertainties do not always hurt retailers' expected payoffs.

Keywords: inventory management; product substitution; game theory; random supply and demand; substitution; stochastic demand; uncertain supply; uncertainty; substitutable products; supply chain management; SCM; modelling; Nash strategy; expected payoffs; ordering decisions; retailers.

DOI: 10.1504/IJIR.2013.058339

International Journal of Inventory Research, 2013 Vol.2 No.1/2, pp.27 - 43

Available online: 17 Dec 2013 *

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