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New product introduction against a predator: A bilevel mixed‐integer programming approach

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  • J. Cole Smith
  • Churlzu Lim
  • Aydın Alptekinoğlu

Abstract

We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

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  • J. Cole Smith & Churlzu Lim & Aydın Alptekinoğlu, 2009. "New product introduction against a predator: A bilevel mixed‐integer programming approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 714-729, December.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:8:p:714-729
    DOI: 10.1002/nav.20375
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