Annals of Operations Research

, Volume 167, Issue 1, pp 337–352 | Cite as

The multiple server center location problem

  • Robert AboolianEmail author
  • Oded Berman
  • Zvi Drezner


In this paper, we introduce the multiple server center location problem. p servers are to be located at nodes of a network. Demand for services of these servers is located at each node, and a subset of nodes are to be chosen to locate one or more servers in each. Each customer selects the closest server. The objective is to minimize the maximum time spent by any customer, including travel time and waiting time at the server sites. The problem is formulated and analyzed. Results for heuristic solution approaches are reported.


Genetic Algorithm Feasible Solution Arrival Rate Service Rate Berman 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Batta, R., & Berman, O. (1989). A location model for a facility operating M/G/K queue. Networks, 19, 717–728. CrossRefGoogle Scholar
  2. Beasley, J. E. (1990). OR-library—distributing test problems by electronic mail. Journal of the Operational Research Society, 41, 1069–1072. Also available at CrossRefGoogle Scholar
  3. Berman, O., & Drezner, Z. (2007). The multiple server location problem. Journal of the Operational Research Society, 58, 91–99. CrossRefGoogle Scholar
  4. Berman, O., & Krass, D. (2002a). Facility location problems with stochastic demands and congestion. In Z. Drezner & H. W. Hamacher (Eds.), Location analysis: applications and theory (pp. 329–371). New York: Springer. Chap. 11. Google Scholar
  5. Berman, O., & Krass, D. (2002b). Recent developments in the theory and applications of location models, Part II. Annals of Operations Research, 111, 15–16. CrossRefGoogle Scholar
  6. Berman, O., & Mandowsky, R. (1986). Location-allocation on congested networks. European Journal of Operations Research, 26, 238–250. CrossRefGoogle Scholar
  7. Berman, O., Larson, R. C., & Chiu, S. (1985). Optimal server location on a network operating as an M/G/1 queue. Operations Research, 33, 746–771. CrossRefGoogle Scholar
  8. Berman, O., Larson, R. C., & Parkan, C. (1987). The stochastic queue p-median problem. Transportation Science, 21, 207–216. CrossRefGoogle Scholar
  9. Berman, O., Krass, D., & Wang, J. (2006). Locating service facilities to reduce lost demand. IIE Transactions, 38, 933–946. CrossRefGoogle Scholar
  10. Castillo, I., Ingolfsson, A., & Sim, T. (2002). Socially optimal location of facilities with fixed servers, stochastic demand and congestion (Management Science Working Paper 02-4). University of Alberta School of Business, Edmonton, Canada. Google Scholar
  11. Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers and Operations Research, 13, 533–549. CrossRefGoogle Scholar
  12. Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic. Google Scholar
  13. Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley. Google Scholar
  14. Holland, J. H. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press. Google Scholar
  15. Kirkpatrick, S., Gelat, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680. CrossRefGoogle Scholar
  16. Klienrock, L. (1975). Queueing systems. New York: Wiley. Google Scholar
  17. Marianov, V., & Rios, M. (2000). A probabilistic quality of service constraint for a location model of switches in ATM communications networks. Annals of Operations Research, 96, 237–243. CrossRefGoogle Scholar
  18. Marianov, V., & Serra, D. (1998). Probabilistic maximal covering location-allocation for congested systems. Journal of Regional Science, 38, 401–424. CrossRefGoogle Scholar
  19. Pasternack, B. A., & Drezner, Z. (1998). A note on calculating steady state results for an M/M/k queuing system when the ratio of the arrival rate to the service rate is large. Journal of Applied Mathematics and Decision Sciences, 2, 133–135. CrossRefGoogle Scholar
  20. Teitz, M. B., & Bart, P. (1968). Heuristic methods for estimating the generalized vertex median of a weighted graph. Operations Research, 16, 955–961. CrossRefGoogle Scholar
  21. Wang, Q., Batta, R., & Rump, C. M. (2002). Algorithms for a facility location problem with stochastic customer demand and immobile servers. Annals of Operations Research, 111, 17–34. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.College of Business AdministrationCalifornia State University San MarcosSan MarcosUSA
  2. 2.Joseph L. Rotman School of ManagementUniversity of TorontoTorontoCanada
  3. 3.College of Business and EconomicsCalifornia State University FullertonFullertonUSA

Personalised recommendations