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The maximum capture per unit cost location problem

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  • Hua, Guowei
  • Cheng, T.C.E.
  • Wang, Shouyang
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    Abstract

    This paper considers the problem of siting p new facilities of an entering firm to a competitive market so as to maximize the market share captured from competitors per unit cost. We first formulate the problem as a mixed 0-1 fractional programming model, in which we incorporate the fixed cost and transportation cost. The model can deal with the case where some demand nodes have two or more possible closest servers. We then re-formulate the problem as a 0-1 mixed integer linear program. We use a one-opt heuristic algorithm based on the Teitz-Bart method to obtain feasible solutions and compare them with the optimal solutions obtained by a branch-and-bound algorithm. We conduct computational experiments to evaluate the two algorithms. The results show that both algorithms can solve the model efficiently and the model is integer-friendly. We discuss other computational results and provide managerial insights.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 131 (2011)
    Issue (Month): 2 (June)
    Pages: 568-574

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    Handle: RePEc:eee:proeco:v:131:y:2011:i:2:p:568-574

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    Web page: http://www.elsevier.com/locate/ijpe

    Related research

    Keywords: Competitive location Maximum capture Mixed integer fractional programming Branch-and-bound;

    References

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    1. ReVelle, Charles, 1993. "Facility siting and integer-friendly programming," European Journal of Operational Research, Elsevier, vol. 65(2), pages 147-158, March.
    2. Li, Han-Lin, 1994. "A global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 73(3), pages 590-596, March.
    3. Benati, Stefano & Hansen, Pierre, 2002. "The maximum capture problem with random utilities: Problem formulation and algorithms," European Journal of Operational Research, Elsevier, vol. 143(3), pages 518-530, December.
    4. D Serra & H A Eiselt & G Laporte & C S ReVelle, 1999. "Market capture models under various customer-choice rules," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 26(5), pages 741-750, September.
    5. Serra, Daniel & Marianov, Vladimir & ReVelle, Charles, 1992. "The maximum-capture hierarchical location problem," European Journal of Operational Research, Elsevier, vol. 62(3), pages 363-371, November.
    6. Hansen, Pierre & de Luna Pedrosa Filho, Eugenio & Carneiro Ribeiro, Celso, 1994. "Modelling location and sizing of offshore platforms," European Journal of Operational Research, Elsevier, vol. 72(3), pages 602-606, February.
    7. Carrizosa, Emilio & Conde, Eduardo, 2002. "A fractional model for locating semi-desirable facilities on networks," European Journal of Operational Research, Elsevier, vol. 136(1), pages 67-80, January.
    8. Daniel Serra & Samuel Ratick & Charles Revelle, 1994. "The maximum capture problem with uncertainty," Economics Working Papers 74, Department of Economics and Business, Universitat Pompeu Fabra.
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