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Technical Note—A Multiperiod Model of Inventory Competition

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

This paper explores when it is important for firms to consider stockout-based substitution and competitor's inventory levels in making inventory decisions in the context of a duopoly model. To address this question, we consider a model where two newsvendors sell substitutable products in a market with aggregate market demand D. The two firms get a proportion p and (1 – p) of this demand, where p is random. We characterize the equilibrium inventory levels of the two firms in a single-period model and show the striking property that, under certain reasonable conditions on the cost parameters, the two firms ignore their competitor's inventory levels and potential substitution demand, i.e., their inventory decisions are decoupled. Furthermore, we show under slightly more restrictive conditions on the cost parameters that the single-period results can be extended to the case where D is random. Finally, we extend the decoupling property to a multiperiod periodic review scenario and show that the resulting Nash equilibrium can be characterized simply as the solution to a single-product dynamic newsvendor problem that ignores substitution demand.

Subject classifications: inventory/production applications; uncertainty.
History: Received April 2006; revision received February 2008; accepted April 2008.