Annals of Operations Research

, Volume 6, Issue 1, pp 1–19 | Cite as

Theoretical links between median and coverage location problems

  • R. L. Church
  • J. R. Weaver
Covering Problems


The relationship between the maximal covering problem and the P-median problem is reviewed. It is shown that two multiple coverage models, themaximumexpectedcoverageproblem (MECP) and thebackupcoverageproblem (BACOP), are special cases of thevectorassignmentP-medianproblem (VAPMP). This relationship is utilized to solve both MECP and BACOP on test sets from the literature. Computational experience is reported.

Keywords and phrases

Maximal covering P-median multiple coverage solution procedures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study, Mathematical Programming Study 12(1980)37.Google Scholar
  2. [2]
    G.N. Berlin, Facility location and vehicle allocation for the provision of an emergency service, Ph.D. Dissertation, The John Hopkins University, Baltimore, Maryland (1972).Google Scholar
  3. [3]
    O. Berman, Dynamic positioning of mobile servers on networks, TR-144, MIT, Operations Research Center, Cambridge, Massachusetts (1978).Google Scholar
  4. [4]
    A. Charnes and J. Storbeck, A goal programming model for the siting of multilevel EMS systems, Socio-Economic Planning Sciences 14(1980)155.CrossRefPubMedGoogle Scholar
  5. [5]
    K.R. Chelst and J. Anderson, An algorithm to convert the weightedp-median to the uncapacitated location problem, unpublished paper (1982).Google Scholar
  6. [6]
    R.L. Church, Solid waste wasteshead identification in the Tennessee Valley region utilizing multiobjective programming, Dept. of Civil Engineering, University of Tennessee, Knoxville (1979).Google Scholar
  7. [7]
    R.L. Church and T. Bell, Incorporating preferences in location-allocation models, Geographical Perspectives 48(1981)22.Google Scholar
  8. [8]
    R.L. Church and G. Bianchi, Recent developments in covering models for the location of emergency facilities, Paper presented at the ORSA/TIMS Meeting, Detroit, Michigan (1982).Google Scholar
  9. [9]
    R.L. Church and D. Eaton, Hierarchical location analysis utilizing covering objectives, Working paper, Dept. of Geography, University of California at Santa Barbara (1981).Google Scholar
  10. [10]
    R.L. Church and C.S. ReVelle, Maximal covering location problem, Papers of the Regional Science Association 32(1974)101.CrossRefGoogle Scholar
  11. [11]
    R.L. Church and C.S. ReVelle, Theoretical and computational links between thep-median, location set-covering, and maximal covering location problems, Geographical Analysis 8(1976)406.Google Scholar
  12. [12]
    R.L. Church and K.L. Roberts, Generalized coverage models and public facility location, Papers of the Regional Science Association 53(1983)117.CrossRefGoogle Scholar
  13. [13]
    G. Cornuejols, M.L. Fisher and G.L. Nemhauser, Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms, Management Science 23(1977)789.Google Scholar
  14. [14]
    M.S. Daskin, Application of an expected covering model to emergency medical service system design, Decision Sciences 13(1982)416.Google Scholar
  15. [15]
    M.S. Daskin, A maximum expected covering location model: Formulation, properties, and heuristic solution, Transportation Science 17(1983)48.Google Scholar
  16. [16]
    M.S. Daskin and E.H. Stern, A hierarchical objective set covering model for emergency medical service vehicle deployment, Transportation Science 15(1981)137.Google Scholar
  17. [17]
    D. Erlenkotter, A dual-based procedure for uncapacitated facility location, Oper. Res. 26(1978)992.Google Scholar
  18. [18]
    S.L. Hakimi, Optimum distribution of switching centers in a communication network and some related group theoretic problems, Oper. Res. 13(1965)562.Google Scholar
  19. [19]
    J. Halpern, The location of a center-median convex combination on an undirected tree, Journal of Regional Science 16(1976)237.Google Scholar
  20. [20]
    E.L. Hillsman, A system for location-allocation analysis, Ph.D. Dissertation, University of Iowa, Iowa City (1979).Google Scholar
  21. [21]
    K. Hogan and C.S. ReVelle, Backup coverage concepts in the location emergency service, Modeling and Simulation 14(1983)1423.Google Scholar
  22. [22]
    T.D. Klastorin, On the maximal covering location problem and the generalized assignment problem, Management Science 25(1979)107.Google Scholar
  23. [23]
    P.B. Mirchandani, Locational decisions on stochastic networks, Geographical Analysis 12(1980)172.Google Scholar
  24. [24]
    P.B. Michandani, A. Oudjit and R.T. Wong, Multi-dimensional extensions and a nested dual approach for theM-median problem, Eur. J. Oper. Res. submitted.Google Scholar
  25. [25]
    G.C. Moore and C.S. ReVelle, The hierarchical service location problem, Management Science 28(1982)775.CrossRefGoogle Scholar
  26. [26]
    J.M. Mulvey and H.P. Crowder, Cluster analysis: An application of Lagrangian relaxation, Management Science 25(1979)329.Google Scholar
  27. [27]
    S.C. Narula, U.I. Ogbu and H.M. Samuelsson, An algorithm for thep-median problem, Oper Res. 25(1977)709.CrossRefGoogle Scholar
  28. [28]
    A.W. Neebe, A branch and bound algorithm for thep-median transportation problem, J. Oper. Res. Soc. 29(1978)989.Google Scholar
  29. [29]
    J. Penalba, Incorporating preference objectives into facility location models, Masters Paper, University of Tennessee, Knoxville (1980).Google Scholar
  30. [30]
    D.R. Plane and T.E. Hendrick, Mathematical programming and the location of fire companies for the Denver fire department, Oper. Res. 25(1977)563.Google Scholar
  31. [31]
    C.S. ReVelle and R.W. Swain, Central facilities location, Geographical Analysis 2(1970)30.Google Scholar
  32. [32]
    P. Rojeski and C.S. ReVelle, Central facilities location under an investment constraint, Geographical Analysis 2(1970)343.Google Scholar
  33. [33]
    G.T. Ross and R.M. Soland, Modeling facility location problems as generalized assignment problems, Management Science 24(1977)345.Google Scholar
  34. [34]
    T.W. Ruefli and J.E. Storbeck, Behaviorally linked hierarchies, Environment and Planning 9(1982)257.Google Scholar
  35. [35]
    D.A. Schilling, Dynamic location modeling for public-sector facilities: A multicriteria approach, Decision Sciences 11(1980)714.Google Scholar
  36. [36]
    D.A. Schilling, D.J. Elizinga, J. Cohon, R.L. Church and C.S. ReVelle, The team fleet models for simultaneous facility equipment siting, Transportation Science 13(1979)163.Google Scholar
  37. [37]
    D.E. Shobrys, A model for the selection of shipping routes and storage locations for hazardous substances, Ph.D. Dissertation, The John Hopkins University, Baltimore, Maryland (1981).Google Scholar
  38. [38]
    J. Storbeck, Slack, natural slack, and location covering, Socio Economic Planning Sciences 16(1982)99.CrossRefPubMedGoogle Scholar
  39. [39]
    R. Swain, A decomposition algorithm for a class of facility location problems, Ph.D. Dissertation, Cornell University, Itaca, New York (1971).Google Scholar
  40. [40]
    C. Swoveland, D. Uyeno, I. Vertinsky and R. Vickson, Ambulance location: A probabilistic enumeration approach, Management Science 20(1973)686.Google Scholar
  41. [41]
    M.B. Teitz and P. Bart, Heuristic methods for estimating the generalized vertex median of a weighted graph, Oper. Res. 16(1968)995.Google Scholar
  42. [42]
    C. Toregas and C.S. ReVelle, Optimal location under time or distance constraints, Papers of the Regional Science Association 28(1972)133.CrossRefGoogle Scholar
  43. [43]
    F.J. Vasko and G.R. Wilson, An efficient heuristic for large set covering problems, Naval Research Logistics Quarterly 31(1984)163.Google Scholar
  44. [44]
    J.R. Weaver and R.L. Church, Computational procedures for location problems on stochastic networks, Transportation Science 17(1983)168.CrossRefGoogle Scholar
  45. [45]
    J.R. Weaver and R.L. Church, A median location model with nonclosest facility service, Transportation Science 19(1985)58.Google Scholar
  46. [46]
    J.R. Weaver and R.L. Church, A comparison of solution procedures for covering location problems, Modeling and Simulation 14(1983)1417.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1986

Authors and Affiliations

  • R. L. Church
    • 1
  • J. R. Weaver
    • 2
  1. 1.Department of GeographyUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Management Science and StatisticsUniversity of AlabamaAlabamaUSA

Personalised recommendations