Journal of the Operational Research Society

, Volume 54, Issue 8, pp 871–877 | Cite as

A probabilistic one-centre location problem on a network

Theoretical Paper


In this paper we consider the one-centre problem on a network when the speeds on links are stochastic rather than deterministic. Given a desirable time to reach customers residing at the nodes, the objective is to find the location for a facility such that the probability that all nodes are reached within this time threshold is maximized. The problem is formulated, analyzed and solved by using multivariate normal probabilities. The procedure is demonstrated on an example problem.


location computational analysis networks and graphs stochastic optimization 


  1. Sylvester JJ (1857). A question in the geometry of situation. Quart J Pure Appl Math 1: 79.Google Scholar
  2. Elzinga DJ and Hearn DW (1972). The minimum covering sphere problem. Mngt Sci 19: 96–104.CrossRefGoogle Scholar
  3. Drezner Z and Shelah S (1987). On the complexity of the Elzinga–Hearn algorithm for the 1-centre problem. Math Opns Res 12: 255–261.CrossRefGoogle Scholar
  4. Shamos MI and Hoey D (1975). Closest point problems. Proceedings of the 16th Annual Symposium on Foundations of Computer Science pp 151–162.Google Scholar
  5. Okabe A, Boots B and Sugihara K (1992). Spatial Tesselations. Concepts and Applications of Voronoi Diagrams, Wiley: Chichester.Google Scholar
  6. Hearn DW and Vijay J (1982). Efficient algorithms for the (weighted) minimum circle problem. Opns Res 30: 777–795.CrossRefGoogle Scholar
  7. Dyer ME (1983). On the complexity of vertex enumeration methods. Math Opns Res 8: 381–402.CrossRefGoogle Scholar
  8. Hakimi SL (1964). Optimal location of switching centres and the absolute centres and median of a graph. Opns Res 12: 450–459.CrossRefGoogle Scholar
  9. Handler GY (1973). Minimax location of a facility in an undirected tree graph. Transport Sci 7: 287–293.CrossRefGoogle Scholar
  10. Kariv O and Hakimi SL (1979). An algorithm approach to network location problems. Part 1. The p centres. SIAM J Appl Math 37: 539–560.CrossRefGoogle Scholar
  11. Mirchandani PB and Francis RL (eds.) (1990). Discrete Location Theory, Wiley: New York.Google Scholar
  12. Frank H (1966). Optimum locations on graphs with correlated normal demands. Opns Res 15: 552–557.CrossRefGoogle Scholar
  13. Frank H (1967). A note on a graph theoretic game of Hakimi's. Opns Res 15: 567–570.CrossRefGoogle Scholar
  14. Berman O and Wang J (2000). The 1-median and 1-antimedian problems with uniform distributed demands. Working Paper, Rotman School of Management, University of Toronto.Google Scholar
  15. Berman O, Wang J, Drezner Z and Wesolowsky G (2003). The minimax and maximin location problems with uniform distributed weights. IIE Trans, in press.Google Scholar
  16. Berman O, Wang J, Drezner Z and Wesolowsky G (2001). Probabilistic minimax location problems on the plane Working Paper, Rotman School of Management, University of Toronto.Google Scholar
  17. Mirchandani PB and Odoni AR (1979). Location of medians on stochastic networks. Transport Sci 13: 85–97.CrossRefGoogle Scholar
  18. Wesolowsky GO (1977). Probabilistic weights in the one-dimensional facility location problem. Mngt Sci 24: 224–229.CrossRefGoogle Scholar
  19. Drezner Z and Wesolowsky GO (1981). Optimum location probabilities in the l p distance weber problem. Transport Sci 15: 85–97.CrossRefGoogle Scholar
  20. Drezner Z (1992). On the computation of the multivariate normal integral. ACM Trans Math Software 18: 470–480.CrossRefGoogle Scholar
  21. Drezner Z (1993). Algorithm 725: computation of the multivariate normal integral. ACM Trans Math Software 19: 546.CrossRefGoogle Scholar
  22. Johnson NL and Kotz S (1972). Distributions in Statistics: Continuous Multivariate Distributions, Wiley: New York.Google Scholar

Copyright information

© Palgrave Macmillan Ltd 2003

Authors and Affiliations

  1. 1.University of TorontoTorontoCanada
  2. 2.California State University-FullertonFullertonUSA

Personalised recommendations