New product introduction against a predator: A bilevel mixed‐integer programming approach |
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Authors: | J Cole Smith Churlzu Lim Ayd?n Alptekino?lu |
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Institution: | 1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611‐9565;2. Systems Engineering and Engineering Management Program, University of North Carolina at Charlotte, Charlotte, North Carolina 28223;3. Edwin L. Cox School of Business, Southern Methodist University, Dallas, Texas 75275 |
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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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Keywords: | mixed‐integer programming product introduction Stackelberg game |
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