Annals of Operations Research

, Volume 34, Issue 1, pp 177–202 | Cite as

Heuristic algorithms for delivered price spatially competitive network facility location problems

  • Tan Miller
  • Terry L. Friesz
  • Roger L. Tobin
Article

Abstract

We review previous formulations of models for locating a firm's production facilities while simultaneously determining production levels at those facilities so as to maximize the firm's profit. We enhance these formulations by adding explicit variables to represent the firm's shipping activities and discuss the implications of this revised approach. In these formulations, existing firms, as well as new entrants, are assumed to act in accordance with an appropriate model of spatial equilibrium. The firm locating new production facilities is assumed to be a large manufacturer entering an industry composed of a large number of small firms. Our previously reported proof of existence of a solution to the combined location-equilibrium problem is briefly reviewed. A heuristic algorithm based on sensitivity analysis methods which presume the existence of a solution and which locally approximate price changes as linear functions of production perturbations resulting from newly established facilities is presented. We provide several numerical tests to illustrate the contrasting locational solutions which this paper's revised delivered price formulation generates relative to those of previous formulations. An exact, although computationally burdensome, method is also presented and employed to check the reliability of the heuristic algorithm.

Keywords

Location Problem Small Firm Heuristic Algorithm Price Change Facility Location 

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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1992

Authors and Affiliations

  • Tan Miller
    • 1
  • Terry L. Friesz
    • 2
  • Roger L. Tobin
    • 3
  1. 1.Temple, Barker and Sloane, Inc.LexingtonUSA
  2. 2.George Mason UniversityFairfaxUSA
  3. 3.GTE Laboratories IncorporatedWalthamUSA

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