Annals of Operations Research

, Volume 111, Issue 1–4, pp 35–50 | Cite as

Location–Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times

  • Vladimir Marianov
  • Daniel Serra


Recently, the authors have formulated new models for the location of congested facilities, so to maximize population covered by service with short queues or waiting time. In this paper, we present an extension of these models, which seeks to cover all population and includes server allocation to the facilities. This new model is intended for the design of service networks, including health and EMS services, banking or distributed ticket-selling services. As opposed to the previous Maximal Covering model, the model presented here is a Set Covering formulation, which locates the least number of facilities and allocates the minimum number of servers (clerks, tellers, machines) to them, so to minimize queuing effects. For a better understanding, a first model is presented, in which the number of servers allocated to each facility is fixed. We then formulate a Location Set Covering model with a variable (optimal) number of servers per service center (or facility). A new heuristic, with good performance on a 55-node network, is developed and tested.

queuing heuristics location 


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  1. [1]
    R. Batta, Single server queueing-location models with rejection, Transportation Science 22 (1988) 209-216.Google Scholar
  2. [2]
    R. Batta, A queueing-location model with expected service time dependent queueing disciplines, European Journal of Operational Research 39 (1989) 192-205.Google Scholar
  3. [3]
    R. Batta, R. Larson and A. Odoni, A single-server priority queueing-location model, Networks 8 (1988) 87-103.Google Scholar
  4. [4]
    O. Berman and R. Larson, Optimal 2-facility network districting in the presence of queueing, Transportation Science 19 (1985) 261-277.Google Scholar
  5. [5]
    O. Berman, R. Larson and S. Chiu, Optimal server location on a network operating as a M/G/1 Queue, Operations Research 12 (1985) 746-771.Google Scholar
  6. [6]
    O. Berman, R. Larson and C. Parkan, The stochastic queue p-median location problem, Transportation Science 21 (1987) 207-216.Google Scholar
  7. [7]
    O. Berman and R. Mandowsky, Location-allocation on congested networks, European Journal of Operational Research 26 (1986) 238-250.Google Scholar
  8. [8]
    R. Church and C. ReVelle, The Maximal Covering Location Problem, Papers of the Regional Science Association 32 (1974) 101-118.Google Scholar
  9. [9]
    G. Cornuejols, R. Sridharan and J. Thizy, A comparison of heuristics and relaxations for the capacitated plant location problem, European Journal of Operational Research 50 (1991) 280-297.Google Scholar
  10. [10]
    J. Current and J. Storbeck, Capacitated covering models, Environment and Planning B 15 (1988) 153-164.Google Scholar
  11. [11]
    M.S. Daskin, A maximum expected covering location model: Formulation, properties and heuristic solution, Transportation Science 17 (1983) 48-70.Google Scholar
  12. [12]
    P. Davis and T. Ray, A branch and bound algorithm for the Capacitated Facilities Location Problem, Naval Research Logistics Quarterly 16 (1969) 331-334.Google Scholar
  13. [13]
    P. Densham and G. Rushton, Strategies for solving large location-allocation problems by heuristic methods, Environment and Planning A 24 (1992) 289-304.Google Scholar
  14. [14]
    R. Galvão, The use of Lagrangean relaxation in the solution of unicapacitated facility location problems, Location Science 1(1) (1993) 57-70.Google Scholar
  15. [15]
    A. Geoffrion, Lagrangean relaxation for integer programming, Mathematical Programming Study 2 (1974) 82-114.Google Scholar
  16. [16]
    R. Gerrard and R. Church, Closest assignment constraints and location models: Properties and structure, Location Science 4 (1996) 251-270.Google Scholar
  17. [17]
    S.L. Hakimi, Optimal locations of switching centers and the absolute centers and medians of a graph, Operations Research 12 (1964) 450-459.Google Scholar
  18. [18]
    R.C. Larson, A hypercube queueing model for facility location and redistricting in urban emergency services, Computers and Operations Research 1 (1974) 67-95.Google Scholar
  19. [19]
    V. Marianov and C. ReVelle, The Queueing Probabilistic Location Set Covering Problem and some extensions, Socio-Economic Planning Sciences 28 (1994) 167-178.Google Scholar
  20. [20]
    V.Marianov and C. ReVelle, The QueueingMaximum Availability Location Problem, European Journal of Operational Research 93 (1996) 110-120.Google Scholar
  21. [21]
    V. Marianov and D. Serra, Probabilistic, maximal covering location-allocation models for congested systems, Journal of Regional Science 38 (1998) 401-424.Google Scholar
  22. [22]
    H. Pirkul and D. Schilling, The maximal covering location problem with capacities on total workload, Management Science 37 (1991) 233-248.Google Scholar
  23. [23]
    C. ReVelle, Facility siting and integer-friendly programming, European Journal of Operational Research 65 (1993) 147-158.Google Scholar
  24. [24]
    C. ReVelle and K. Hogan, A reliability-constrained siting model with local estimates of busy fractions, Environment and Planning B: Planning and Design 15 (1988) 143-152.Google Scholar
  25. [25]
    C. ReVelle and K. Hogan, TheMaximum Reliability Location Problemand ?-Reliable p-Center Problem: Derivatives of the Probabilistic Location Set Covering Problem, Annals of Operations Research 18 (1989) 155-174.Google Scholar
  26. [26]
    C. ReVelle and S. Swain, Central facilities location, Geographical Analysis 2 (1970) 30-42.Google Scholar
  27. [27]
    G. Rogeski and C. ReVelle, Central facilities location under an investment constraint, Geographical Analysis 2 (1975) 343-353.Google Scholar
  28. [28]
    K. Rosing, An empirical investigation of the effectiveness of a vertex substitution heuristic, Environment and Planning B 24 (1997) 59-67.Google Scholar
  29. [29]
    K. Rosing and C. ReVelle, Heuristic concentration: Two stage solution construction, European Journal of Operational Research 97 (1997) 75-86.Google Scholar
  30. [30]
    K. Rosing, C. ReVelle and H. Rosing-Vogelaar, The p-median model and its linear programming relaxation: An approach to large problems, Journal of the Operational Research Society 30 (1979) 815-823.Google Scholar
  31. [31]
    R. Swain, A parametric decomposition algorithm for the solution of uncapacitated location problems, Management Science 21 (1974) 189-198.Google Scholar
  32. [32]
    M. Tietz and P. Bart, Heuristic methods for estimating the generalized vertex median of a weigthed graph, Operations Research 16 (1968) 955-965.Google Scholar
  33. [33]
    C. Toregas, R. Swain, C. ReVelle and L. Bergman, The location of emergency service facilities, Operations Research 19 (1971) 1363-1373.Google Scholar
  34. [34]
    C.Wagner and F. Falkston, The optimal nodal location of public facilities with price sensitive demand, Geographical Analysis 7 (1975) 69-79.Google Scholar
  35. [35]
    R.Wolff, Stochastic Modeling and the Theory of Queues (Prentice-Hall, Englewood Cliffs, NJ, 1989).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Vladimir Marianov
    • 1
  • Daniel Serra
    • 2
  1. 1.Department of Electrical EngineeringPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Department of Economics and BusinessUniversitat Pompeu FabraBarcelonaSpain

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