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Optimum Locations on a Graph with Probabilistic Demands

Author

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  • H. Frank

    (University of California, Berkeley, California)

Abstract

The traffic demands at the stations of a communication network are usually not deterministic. Optimum locations found using deterministic techniques are poor when the random nature of the network traffic is considered. The concepts of absolute centers and medians are generalized to maximum probability absolute centers and medians. Minimum variance points are also considered. Techniques to locate these optimum points are discussed.

Suggested Citation

  • H. Frank, 1966. "Optimum Locations on a Graph with Probabilistic Demands," Operations Research, INFORMS, vol. 14(3), pages 409-421, June.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:3:p:409-421
    DOI: 10.1287/opre.14.3.409
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    Citations

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    Cited by:

    1. Jiamin Wang, 2007. "The (beta)-Reliable Median on a Network with Discrete Probabilistic Demand Weights," Operations Research, INFORMS, vol. 55(5), pages 966-975, October.
    2. Igor Averbakh, 2005. "The Minmax Relative Regret Median Problem on Networks," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 451-461, November.
    3. K Sörensen, 2008. "Investigation of practical, robust and flexible decisions for facility location problems using tabu search and simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 624-636, May.
    4. O Berman & J Wang, 2008. "The probabilistic 1-maximal covering problem on a network with discrete demand weights," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(10), pages 1398-1405, October.
    5. 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.
    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. 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.
    8. 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.
    9. Vladimir Marianov & Daniel Serra, 2009. "Median problems in networks," Economics Working Papers 1151, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    11. Berman, Oded & Sanajian, Nima & Wang, Jiamin, 2017. "Location choice and risk attitude of a decision maker," Omega, Elsevier, vol. 66(PA), pages 170-181.
    12. Kena Zhao & Tsan Sheng Adam Ng & Xiao Liu, 2020. "A guarantee rate optimization model for wastewater treatment system design under uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(6), pages 420-437, September.
    13. Alan Murray, 2010. "Advances in location modeling: GIS linkages and contributions," Journal of Geographical Systems, Springer, vol. 12(3), pages 335-354, September.

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