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The Maximum Capture Problem with Uncertainty

Author

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  • D Serra

    (Department of Economics, Universitat Pompeu Fabra, Balmes 132, 08008, Spain)

  • S Ratick

    (Department of Geography, The George Perkins Marsh Institute, 950 Main Street, Worcester, MA01610, USA)

  • C ReVelle

    (Johns Hopkins University, Baltimore, MD 21218, USA)

Abstract

The strategic location of servers by a firm in a competitive environment is basic in the determination or division of market shares. Let us suppose that a firm wants to locate p servers so as to maximize market capture in a region where competitors are already located but where there is uncertainty—there are several possible future scenarios with respect to demand and/or the location of competitors. The firm will want a strategy of positioning that will do as ‘well as possible’ over the future scenarios. In this paper we will present a discrete location model formulation to address this maximum capture problem with uncertainty.

Suggested Citation

  • D Serra & S Ratick & C ReVelle, 1996. "The Maximum Capture Problem with Uncertainty," Environment and Planning B, , vol. 23(1), pages 49-59, February.
    • Handle: RePEc:sae:envirb:v:23:y:1996:i:1:p:49-59
    DOI: 10.1068/b230049
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    References listed on IDEAS

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    1. Karkazis, John, 1989. "Facilities location in a competitive environment: A promethee based multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 42(3), pages 294-304, October.
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    Cited by:

    1. Diego Ruiz-Hernández & Javier Elizalde & David Delgado-Gómez, 2017. "Cournot–Stackelberg games in competitive delocation," Annals of Operations Research, Springer, vol. 256(1), pages 149-170, September.
    2. Daniel Serra & Vladimir Marianov, 1996. "The P-median problem in a changing network: The case of Barcelona," Economics Working Papers 180, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Rosa Colomé & Helena Lourenço & Daniel Serra, 2003. "A New Chance-Constrained Maximum Capture Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 121-139, September.
    4. Gunhak Lee & Morton E. O'Kelly, 2009. "Exploring Locational Equilibria In A Competitive Broadband Access Market: Theoretical Modeling Approach," Journal of Regional Science, Wiley Blackwell, vol. 49(5), pages 953-975, December.
    5. Drezner, Zvi & Guyse, Jeffery, 1999. "Application of decision analysis techniques to the Weber facility location problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 69-79, July.
    6. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    7. 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.
    8. Tolga H. Seyhan & Lawrence V. Snyder & Ying Zhang, 2018. "A New Heuristic Formulation for a Competitive Maximal Covering Location Problem," Transportation Science, INFORMS, vol. 52(5), pages 1156-1173, October.
    9. Francisco Silva & Daniel Serra, 2007. "Incorporating Waiting Time in Competitive Location Models," Networks and Spatial Economics, Springer, vol. 7(1), pages 63-76, March.
    10. Tammy Drezner, 2009. "Location of retail facilities under conditions of uncertainty," Annals of Operations Research, Springer, vol. 167(1), pages 107-120, March.
    11. Carreras, Miquel & Serra, Daniel, 1999. "On optimal location with threshold requirements," Socio-Economic Planning Sciences, Elsevier, vol. 33(2), pages 91-103, June.
    12. Gang Chen & Mark S. Daskin & Zuo‐Jun Max Shen & Stanislav Uryasev, 2006. "The α‐reliable mean‐excess regret model for stochastic facility location modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(7), pages 617-626, October.
    13. Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
    14. Shiode, Shogo & Drezner, Zvi, 2003. "A competitive facility location problem on a tree network with stochastic weights," European Journal of Operational Research, Elsevier, vol. 149(1), pages 47-52, August.
    15. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    16. Daniel Serra & Rosa Colomé, 2000. "Supermarket key attributes and location decisions: A comparative study between British and Spanish consumers," Economics Working Papers 469, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Francisco Silva & Daniel Serra, 2008. "Incorporating waiting time in competitive location models: Formulations and heuristics," Economics Working Papers 1091, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Current, John & Ratick, Samuel & ReVelle, Charles, 1998. "Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach," European Journal of Operational Research, Elsevier, vol. 110(3), pages 597-609, November.
    19. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.

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