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, Volume 50, Issue 1, pp 60–74 | Cite as

An effective heuristic for the P-median problem with application to ambulance location

Application Article

Abstract

We consider the p-median problem which is to find the location of p-facilities so as to minimize the average weighted distance or time between demand points and service centers. Many heuristic algorithms have been proposed for this problem. In this paper we present a simple new heuristic which is effective for moderately size problem. The heuristic uses a reduction and an exchange procedure. Our methodology is tested on 400 randomly generated problems with 10 to 50 customer locations as well as 6 well known literature test problems. We also compare our method with the Branch and Bound method in terms of quality and computational time using a larger problem size of 150 customer locations. For the random problems the generated solutions were on average within 0.61 % of the optimum. A similar result was achieved for the literature test problems. A comparative analysis with literature heuristics supports the superiority of our method. The computational time of our heuristic is 0.75 % of the Branch and Bound Method. We also apply our heuristic to a case study involving the location of emergency vehicles (ambulances) in Perth City (Australia).

Keywords

Heuristics Facilities Location P-median problem 

References

  1. 1.
    Savas, E.: Simulation and cost-effectiveness analysis of New York’s emergency ambulance service. Manag. Sci. 15, 608–627 (1969)CrossRefGoogle Scholar
  2. 2.
    Fitzsimmons, J.A.: A methodology for emergency ambulance deployment. Manag. Sci. 19, 627–636 (1973)CrossRefGoogle Scholar
  3. 3.
    Swoveland, C., Uyeno, D., Vertinsky, I., Vickson, R.: Ambulance location: a probabilistic enumeration approach. Manag. Sci. 20, 687–697 (1973)CrossRefGoogle Scholar
  4. 4.
    Gendreau, M., Laporte, G., Semet, F.: Solving an ambulance location model by Tabu Search. Locat. Sci. 5, 75–88 (1998)CrossRefGoogle Scholar
  5. 5.
    Repede, J.F., Bernando, J.J.: Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky. Eur. J. Oper. Res. 75, 567–581 (1994)CrossRefGoogle Scholar
  6. 6.
    McAleer, W.E., Naqvi, I.A.: The relocation of ambulance stations: a successful case study. Eur. J. Oper. Res. 75, 582–588 (1994)CrossRefGoogle Scholar
  7. 7.
    Goldberg, J.R., Dietrich, R., Cheng, J.M., Mitwasi, M.G., Valenzuela, T., Criss, E.: Validating and applying a model for locating emergency medical vehicles in Tucson, AZ (case study). Eur. J. Oper. Res. 49, 308–324 (1990)CrossRefGoogle Scholar
  8. 8.
    Fujiwara, O., Makjamroen, T., Gruta, K.K.: Ambulance deployment analysis: a case study of Bangkok. Eur. J. Oper. Res. 31, 9–18 (1987)CrossRefGoogle Scholar
  9. 9.
    Calvo, A., Marks, H.: Location of health care facilities: an analytical approach. Socio Econ. Plan. Sci. 7, 407–422 (1973)CrossRefGoogle Scholar
  10. 10.
    Berlin, G., Revelle, C., Elzinga, J.: Determining ambulance-hospital locations for on-scene and hospital services. Environ. Plan. A 8, 553–561 (1976)CrossRefGoogle Scholar
  11. 11.
    Mirchandani, P.B.: Locational decisions on stochastic networks. Geogr. Anal. 12, 172–183 (1980)CrossRefGoogle Scholar
  12. 12.
    Carson, Y., Batta, R.: Locating an ambulance on Amherst campus of State University of New York at Buffalo. Interfaces 20, 43–49 (1990)CrossRefGoogle Scholar
  13. 13.
    Serra, D., Marianov, V.: The p-median problem in a changing network: the case of Barcelona. Locat. Sci. 6, 383–394 (1998)CrossRefGoogle Scholar
  14. 14.
    Paluzzi, M.: Testing a Heuristic p-Median Location Allocation Model for Siting Emergency Service Facilities. Paper presented at annual meeting of association of American Geographers, Philadelphia, PA (2004)Google Scholar
  15. 15.
    Caccetta, L., Dzator, M.: Models for the location of emergency facilities. In: Proceedings Modsim 2001. (2001)Google Scholar
  16. 16.
    Caccetta, L., Dzator, M.: Heuristics methods for locating emergency facilities. In: Proceedings Modsim 2005. (2005)Google Scholar
  17. 17.
    Dzator, M.: Facility Location in Cities: the Optimal Location of Emergency Unit Within Cities. VDM Verlag (2008)Google Scholar
  18. 18.
    Uyeno, D.H., Seeberg, C.: A practical methodology for ambulance location. Simul. 79–87 (1984)Google Scholar
  19. 19.
    Maranzana, F.E.: On the location of supply points to minimize transport costs. Oper. Res. Q. 15, 261–270 (1964)CrossRefGoogle Scholar
  20. 20.
    Teitz, M.B., Bart, P.: Heuristic methods for estimating generalized vertex median of a weighted graph. Oper. Res. 16, 955–961 (1968)CrossRefGoogle Scholar
  21. 21.
    Hakimi, S.L.: Optimisation locations of switching centres and the absolute centres and medians of a graph. Oper. Res. 12, 450–459 (1964)CrossRefGoogle Scholar
  22. 22.
    Kariv, O., Hakimi, S.L.: An algorithmic approach to network location problems II: the p-medians. SIAM J. Appl. Math. 37, 539–560 (1979)CrossRefGoogle Scholar
  23. 23.
    Daskin, M.S.: Network and discrete location: models, algorithms and applications, p. 498. Wiley, New York (1995)CrossRefGoogle Scholar
  24. 24.
    Eaton, D.J., Daskin, M.S., Simmons, D., Bulloch, B., Jansma, G.: Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces 15, 96–108 (1985)CrossRefGoogle Scholar
  25. 25.
    Toregas, C., Swain, R., ReVelle, C., Bergman, L.: The location of emergency service facilities. Oper. Res. 19, 1363–1373 (1971)CrossRefGoogle Scholar
  26. 26.
    Plane, D.R., Hendrick, T.E.: Mathematical programming and the location of fire companies for Denver fire department. Oper. Res. 25, 563–578 (1977)CrossRefGoogle Scholar
  27. 27.
    Densham, P.J., Rushton, G.: A more efficient heuristic for solving large p-median problems. Pap. Reg. Sci. 71, 307–329 (1992)CrossRefGoogle Scholar
  28. 28.
    Ashayeri, J., Heuts, R., Tammel, B.: A modified simple heuristic for the p-median problem, with facilities design applications. Robot Comput. Integ. Manuf. 21(4), 451–464 (2005)CrossRefGoogle Scholar
  29. 29.
    Chiyoshi, F., Galvao, R.D.: A statistical analysis of simulated annealing applied to the p-median problem. Ann. Oper. Res. 96, 61–74 (2000)CrossRefGoogle Scholar
  30. 30.
    Righini, G.: A double annealing algorithm for discrete location/allocation problems. Eur. J. Oper. Res. 86, 452–468 (1995)CrossRefGoogle Scholar
  31. 31.
    Alp, O., Erkut, E., Drezner, Z.: An efficient genetic algorithm for the p-median problem. Ann. Oper. Res. 122, 21–42 (2003)CrossRefGoogle Scholar
  32. 32.
    Bozkaya, B., Zhang, J., Erkut, E.: An efficient genetic algorithm for the p-median problem. In: Drezner, Z., Hamacher, H. (eds.) Facility Location: Applications and Theory, pp. 179–205 (2002)Google Scholar
  33. 33.
    Chiou, Y., Lan, L.W.: Genetic clustering algorithms. Eur. J. Oper. Res. 135(2), 413–427 (2001)CrossRefGoogle Scholar
  34. 34.
    Dvorett, J.: Compatibility-Based Genetic Algorithm. A New Approach to the p-Median Problem. Technical Report, Department of Industrial Engineering and Management, Northwestern University, Evanston, IL (1999)Google Scholar
  35. 35.
    Salhi, S.: Defining Tabu list size and aspiration criterion within Tabu search methods. Comput. Oper. Res. 29, 67–86 (2002)CrossRefGoogle Scholar
  36. 36.
    Rolland, E., Schilling, D.A., Current, J.R.: An efficient Tabu search procedure for the p-median problem. Eur. J. Oper. Res. 96, 75–86 (1996)Google Scholar
  37. 37.
    Voss, S.: A reverse elimination approach for the p-median problem. Stud. Locat. Anal. 8, 49–58 (1996)Google Scholar
  38. 38.
    Swain, R.: A Decomposition Algorithm for a Class of Facility Location Problems. Unpublished Ph. D. dissertation, Cornell University, Ithaca, NY (1971)Google Scholar
  39. 39.
    Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: Solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)CrossRefGoogle Scholar
  40. 40.
    Karg, R.L., Thompson, G.L.: A heuristic approach to solving traveling salesman problem. Manag. Sci. 10, 225–248 (1964)CrossRefGoogle Scholar
  41. 41.
    Hribar, M., Daskin, M.S.: A dynamic programming heuristic for the p-median problem. Eur. J. Oper. Res. 101, 499–508 (1997)CrossRefGoogle Scholar
  42. 42.
    Khumawala, B.M.: An efficient algorithm for the p-median problem with maximum distance constraints. Geogr. Anal. 5, 309–321 (1973)CrossRefGoogle Scholar
  43. 43.
    Hillman, E.L., Rushton, G.: The p-median problem with maximum distance constraints: a comment. Geogr. Anal. 7, 85–89 (1975)CrossRefGoogle Scholar
  44. 44.
    Church, R.L., Meadows, M.E.: Location modeling utilizing maximum distance criteria. Geogr. Anal. 11, 358–373 (1979)CrossRefGoogle Scholar
  45. 45.
    Neebe, A.W.: A procedure for locating emergency service facilities for all possible response distances. J. Oper. Res. Soc. 39, 743–748 (1988)Google Scholar
  46. 46.
    Rahman, S., Smith, D.K.: A comparison of two heuristic methods for the p-median problem with and without maximum distance constraints. Int. J. Oper. Prod. Manag. 11, 76–84 (1991)CrossRefGoogle Scholar
  47. 47.
    Government of Western Australia Department of Health Annual Report 2009/10. Available at http://www.health.wa.gov.au/publication annual report 2010 DOH.cfm
  48. 48.
    Ahern, T.: St John ambulance annual report 2009/10. Available at http://www.ambulance.net.au/content.asp?id.176. (2010)
  49. 49.

Copyright information

© Operational Research Society of India 2012

Authors and Affiliations

  1. 1.Department of MathematicsThe University of NewcastleCallaghanAustralia
  2. 2.School of BusinessThe University of NewcastleCallaghanAustralia

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