IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v14y1982i7p917-932.html
   My bibliography  Save this article

Probabilistic Demands and Costs in Facility Location Problems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a140917
    Download Restriction: no
    File URL: https://libkey.io/10.1068/a140917?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. 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).
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rolland, Erik & Schilling, David A. & Current, John R., 1997. "An efficient tabu search procedure for the p-Median Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 329-342, January.
    2. Michael Brusco & Douglas Steinley, 2015. "Affinity Propagation and Uncapacitated Facility Location Problems," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 443-480, October.
    3. Hakimi, S.Louis, 1983. "Network location theory and contingency planning," Energy, Elsevier, vol. 8(8), pages 697-702.
    4. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Rosing, K. E. & ReVelle, C. S. & Schilling, D. A., 1999. "A gamma heuristic for the p-median problem," European Journal of Operational Research, Elsevier, vol. 117(3), pages 522-532, September.
    6. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    7. Rosing, K. E. & ReVelle, C. S., 1997. "Heuristic concentration: Two stage solution construction," European Journal of Operational Research, Elsevier, vol. 97(1), pages 75-86, February.
    8. Wu, Dexiang & Wu, Desheng Dash, 2020. "A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition," Omega, Elsevier, vol. 91(C).
    9. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    10. Heidari, Mehdi & Asadpour, Masoud & Faili, Hesham, 2015. "SMG: Fast scalable greedy algorithm for influence maximization in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 124-133.
    11. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2019. "An Exact Algorithm for Multilevel Uncapacitated Facility Location," Transportation Science, INFORMS, vol. 53(4), pages 1085-1106, July.
    12. Alberto Ceselli & Federico Liberatore & Giovanni Righini, 2009. "A computational evaluation of a general branch-and-price framework for capacitated network location problems," Annals of Operations Research, Springer, vol. 167(1), pages 209-251, March.
    13. Righini, Giovanni, 1995. "A double annealing algorithm for discrete location/allocation problems," European Journal of Operational Research, Elsevier, vol. 86(3), pages 452-468, November.
    14. Zohreh Hosseini Nodeh & Ali Babapour Azar & Rashed Khanjani Shiraz & Salman Khodayifar & Panos M. Pardalos, 2020. "Joint chance constrained shortest path problem with Copula theory," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 110-140, July.
    15. Joshua Q. Hale & Enlu Zhou & Jiming Peng, 2017. "A Lagrangian search method for the P-median problem," Journal of Global Optimization, Springer, vol. 69(1), pages 137-156, September.
    16. Hauser, John R. & Urban, Glen L. & Weinberg, Bruce D., 1992. "Time flies when you're having fun : how consumers allocate their time when evaluating products," Working papers 3439-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    17. Sharma, R.R.K. & Berry, V., 2007. "Developing new formulations and relaxations of single stage capacitated warehouse location problem (SSCWLP): Empirical investigation for assessing relative strengths and computational effort," European Journal of Operational Research, Elsevier, vol. 177(2), pages 803-812, March.
    18. A.A. Ageev & M.I. Sviridenko, 2004. "Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 307-328, September.
    19. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envira:v:14:y:1982:i:7:p:917-932. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.