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Probabilistic Demands and Costs in Facility Location Problems

Author

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  • P B Mirchandani

    (Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12181, USA)

  • A Oudjit

    (Operations Research and Statistics Program, Rensselaer Polytechnic Institute, Troy, NY 12181, USA)

Abstract

When deterministic assumptions in ‘classical’ location problems are relaxed some new theoretical and algorithmic problems arise. In this paper, the definition of medians is generalized to the cases: (1) when generated demands and travel costs are random, and (2) when the demand induced at the facilities is random because of competition . Under a particular set of assumptions, the well-known theorems on ‘optimality of node locations' hold for the underlying ‘probabilistic networks’. For case (1) the model is shown to be a generalization of the probabilistic and deterministic median location problems on networks. The relationship of the model to a multicommodity location problem is also pointed out. Additionally, within the framework of the problem formulation, certain parallels with multiobjective location problems are drawn. For case (2), the competitive median location problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for the 1-median and 2-median are discussed.

Suggested Citation

  • P B Mirchandani & A Oudjit, 1982. "Probabilistic Demands and Costs in Facility Location Problems," Environment and Planning A, , vol. 14(7), pages 917-932, July.
    • Handle: RePEc:sae:envira:v:14:y:1982:i:7:p:917-932
    DOI: 10.1068/a140917
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    References listed on IDEAS

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    1. Timothy J. Lowe, 1978. "Efficient Solutions in Multiobjective Tree Network Location Problems," Transportation Science, INFORMS, vol. 12(4), pages 298-316, November.
    2. Berman, Oded & Larson, Richard C. & Odoni, Amedeo R., 1981. "Developments in network location with mobile and congested facilities," European Journal of Operational Research, Elsevier, vol. 6(2), pages 104-116, February.
    3. Gerard Cornuejols & Marshall L. Fisher & George L. Nemhauser, 1977. "Exceptional Paper--Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms," Management Science, INFORMS, vol. 23(8), pages 789-810, April.
    4. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    5. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. 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.

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