A Multi-Period Model of Inventory Competition

26 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

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 multi-period 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.

Keywords: Inventory Games, inventory substitution, stock out based competition

Suggested Citation

Nagarajan, Mahesh and Rajagopalan, Raj S., A Multi-Period Model of Inventory Competition (April 1, 2009). Marshall School of Business Working Paper No. IOM 18-09, Available at SSRN: https://ssrn.com/abstract=1140311 or http://dx.doi.org/10.2139/ssrn.1140311

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 90089
United States

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