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Probabilistic Weights in the One-Dimensional Facility Location Problem

Author

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  • George O. Wesolowsky

    (McMaster University, Canada)

Abstract

This note deals with the one-dimensional facility location model in which the weights, which can represent either demand volumes or demands and costs combined, are known only probabilistically. The demand points themselves, or at least the "feeder" routes to the demand points, for the facility are located on a straight line which represents a road or some other transportation route. It is assumed that the weights of the demand points have a multivariate normal distribution. The probability of the facility being optimally located at any point on the route is derived; it is shown that only the demand points have non-zero probabilities. In addition, the expected value of perfect information (EVPI) is found. In this problem, the EVPI is the expected difference in costs between the actual best location and the optimum location obtained by using expected weights. The EVPI, therefore, is the maximum amount the decision maker should pay for information about weights if expected values are acceptable as a decision criterion.

Suggested Citation

  • George O. Wesolowsky, 1977. "Probabilistic Weights in the One-Dimensional Facility Location Problem," Management Science, INFORMS, vol. 24(2), pages 224-229, October.
    • Handle: RePEc:inm:ormnsc:v:24:y:1977:i:2:p:224-229
    DOI: 10.1287/mnsc.24.2.224
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    Cited by:

    1. Badri, Masood A., 1999. "Combining the analytic hierarchy process and goal programming for global facility location-allocation problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 237-248, September.
    2. 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.
    3. Dongyan Chen & Chan He & Senlin Wu, 2016. "Single facility collection depots location problem with random weights," Operational Research, Springer, vol. 16(2), pages 287-299, July.
    4. 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.
    5. Berman, Oded & Drezner, Zvi, 2008. "The p-median problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 189(1), pages 19-30, August.
    6. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    7. Averbakh, Igor & Berman, Oded, 2000. "Algorithms for the robust 1-center problem on a tree," European Journal of Operational Research, Elsevier, vol. 123(2), pages 292-302, June.
    8. 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.
    9. Igor Averbakh, 2005. "The Minmax Relative Regret Median Problem on Networks," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 451-461, November.
    10. 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.
    11. 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.
    12. George L. Vairaktarakis & Panagiotis Kouvelis, 1999. "Incorporation dynamic aspects and uncertainty in 1‐median location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 147-168, March.

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