Annals of Operations Research

, Volume 122, Issue 1–4, pp 43–58 | Cite as

An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

  • Stefano Benati
Article

Abstract

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.

competitive location models random utility theory submodular functions heuristic concentration data-correcting method 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Stefano Benati
    • 1
  1. 1.Dipartimento di Informatica e Studi AziendaliUniversitá di TrentoTrentoItaly

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