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Optimum Location Probabilities in the l p Distance Weber Problem

Author

Listed:
  • Z. Drezner

    (University of Michigan, Dearborn, Michigan)

  • G. O. Wesolowsky

    (McMaster University, Hamilton, Ontario)

Abstract

In this paper it is assumed that the weights which summarize cost and volume parameters in the Weber problem are known only probabilistically. In general, the object is to find the probability that the facility will be optimally located at any given point or in any region. We assume that the weights have a truncated (no negative values) multivariate normal distribution with known means, variances and covariances. An efficient computational procedure is given in the p = 1 case (rectangular distances) for finding the desired probabilities approximately. An efficient method is also given for finding the approximate probability that a facility will be optimally located at any given demand point in the general l p case.

Suggested Citation

  • Z. Drezner & G. O. Wesolowsky, 1981. "Optimum Location Probabilities in the l p Distance Weber Problem," Transportation Science, INFORMS, vol. 15(2), pages 85-97, May.
    • Handle: RePEc:inm:ortrsc:v:15:y:1981:i:2:p:85-97
    DOI: 10.1287/trsc.15.2.85
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    Citations

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    Cited by:

    1. Zvi Drezner & Mozart B. C. Menezes, 2016. "The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution," Annals of Operations Research, Springer, vol. 246(1), pages 205-226, November.
    2. Zhang, Bo & Li, Hui & Li, Shengguo & Peng, Jin, 2018. "Sustainable multi-depot emergency facilities location-routing problem with uncertain information," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 506-520.
    3. 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.
    4. Drezner, Zvi & Scott, Carlton H., 1999. "On the feasible set for the squared Euclidean Weber problem and applications," European Journal of Operational Research, Elsevier, vol. 118(3), pages 620-630, November.
    5. Drezner, Zvi & Shiode, Shogo, 2007. "A distribution map for the one-median location problem on a network," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1266-1273, June.
    6. O Berman & Z Drezner, 2003. "A probabilistic one-centre location problem on a network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 871-877, August.
    7. Berman, Oded & Drezner, Zvi, 2008. "The p-median problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 189(1), pages 19-30, August.

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