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The maximum capture per unit cost location problem

Author

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

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.

Suggested Citation

  • Hua, Guowei & Cheng, T.C.E. & Wang, Shouyang, 2011. "The maximum capture per unit cost location problem," International Journal of Production Economics, Elsevier, vol. 131(2), pages 568-574, June.
  • Handle: RePEc:eee:proeco:v:131:y:2011:i:2:p:568-574
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    References listed on IDEAS

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    1. 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.
    2. D Serra & S Ratick & C ReVelle, 1996. "The Maximum Capture Problem with Uncertainty," Environment and Planning B, , vol. 23(1), pages 49-59, February.
    3. 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.
    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. 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.
    6. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    7. ReVelle, Charles, 1993. "Facility siting and integer-friendly programming," European Journal of Operational Research, Elsevier, vol. 65(2), pages 147-158, March.
    8. 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.
    9. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.
    10. 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.
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    Cited by:

    1. Zhang, Yue, 2015. "Designing a retail store network with strategic pricing in a competitive environment," International Journal of Production Economics, Elsevier, vol. 159(C), pages 265-273.

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