The authors propose a model for locating a fixed number of multiple-server service centers or facilities that may become congested. Customers arriving at these centers must wait in line until served. The locations of the facilities and the allocations of customers to them are chosen by the planner, so to minimize both travel costs and system-wide congestion (or queuing) at centers. All the customers arriving at the facilities must be served, up to a certain maximum line length. The travel cost in which customers incur is a function of the length of the trip to the facility, while the congestion cost at a facility is a general function of the number of customers waiting on line or being served at the facility. The resulting model is a nonlinear p-median formulation. A solution method for this nonlinear model is proposed, and computational experience is presented.
Batta, R.1988. ‘‘Single Server Queuing-Location Models With Rejection’’Transportation Science22:209-16.
2.
Batta, R.1989. ‘‘A Queuing-Location Model With Expected Service Time Dependent Queuing Disciplines’’European Journal of Operational Research39:192-205.
3.
Batta, R., J. Dolan, and N. Krishnamurthy .1989. ‘‘The Maximal Expected Covering Location Problem: Revisited’’Transportation Science23:277-87.
4.
Batta, R., R. Larson, and A. Odoni.1988. ‘‘A Single-Server Priority Queuing-Location Model’’Networks8:87-103.
5.
Benati, S., and G. Laporte.1994. ‘‘Tabu Search Algorithms for the (r | Xp)-Medianoid and (r | p)-Centroid Problems’’Location Science2:193-204.
6.
Berman, O., and D. Krass.2002. ‘‘Facility Location Problems With Stochastic Demand and Congestion.’’ In Facility Location: Applications and Theory, Ch. 11, edited by Z. Drezner and H. Hamacher.Berlin: Springer-Verlag, 329-371.
7.
Berman, O., D. Krass, and J. Wang.2006. ‘‘Locating Service Facilities to Reduce Loss Demand’’IIE Transactions38:933-46.
8.
Berman, O., R. Larson, and S. Chiu.1985. ‘‘Optimal Server Location on a Network Operating as a M/G/1 Queue’’Operations Research12:746-71.
9.
Berman, O., R. Larson, and C. Parkan.1987. ‘‘The Stochastic Queue P-Median Location Problem’’Transportation Science21:207-16.
10.
Berman, O., and R. Mandowsky.1986. ‘‘Location-Allocation on Congested Networks’’European Journal of Operational Research26:238-50.
11.
Boffey, B., R. Galvão, and L. Espejo.2007. ‘‘A Review of Congestion Models in the Location of Facilities With Immobile Servers. ’’ European Journal of Operational Research178:643-62.
12.
Colorni, A., M. Dorigo, and V. Maniezzo.1991a. ‘‘Distributed Optimisation by Ant Colonies.’’Proceeding of ECAL91 - European Conference on Artificial Life, Paris, France, Elsevier, 134-42.
13.
Colorni, A., M. Dorigo, and V. Maniezzo.1991b. ‘‘The Ant System: Optimisation by a Colony of Cooperating Agents’’ IEEE Transactions on Systems , Man and Cybernetics - Part B26:29-41.
14.
Dorigo, D., and G. DiCaro.1999. ‘‘The Ant Colony Optimization Meta-Heuristic.’’ In News Ideas in Optimisation , edited by D. Corne, M. Dorigo, and F. Glover.McGraw-Hill, New York, 11-32.
15.
Dorigo, M., V. Maniezzo, and A. Colorni.1996. ‘‘The Ant System: Optimization by a Colony of Cooperating Agents’’. IEEE Transactions on Systems, Man, and Cybernetics-Part B26:29-41.
16.
Gendreau, M., Z. Hertz, and G. Laporte.1994. ‘‘A Tabu Search Heuristic for the Vehicle Routing Problem’’Management Science40:1276-89.
17.
Glover, F.1989. ‘‘Tabu Search, Part I’’. ORSA Journal of Computing1:190-206.
18.
Glover, F.1990. ‘‘Tabu Search, Part II’’. ORSA Journal of Computing2:4-32.
19.
Hillier, F.S., and G.J. Lieberman.2004. Introduction to Operations Research, Eight Edition, McGraw-Hill Higher Education, Boston, MA.
20.
Jamil, M., A. Baveja, and R. Batta.1999. ‘‘The Stochastic Queue Center Problem’’Computers and Operations Research26:1423-36.
21.
Kariv, O., and S. Hakimi.1979. ‘‘An Algorithmic Approach to Network Location Problems I: The P-Centers’’Siam Journal of Applied Mathematics37:513-38.
22.
Klincewicz, J.G.1992. ‘‘Avoiding Local Optima in the P-Hub Location Problem Using Tabu Search and GRASP’’Annals of Operations Research40:283-302.
23.
Lourenço, H., and D. Serra.2002. ‘‘Meta-Heuristics for the Generalized Assignment Problem’’ In Mathware & Soft Computing9(2-3):209-34.
24.
Marianov, V., and C. ReVelle.1994. ‘‘The Queuing Probabilistic Location Set Covering Problem and Some Extensions’’Socio-Economic Planning Sciences28:167-78.
25.
Marianov, V., and C. ReVelle.1995. ‘‘Siting of Emergency Services.’’ In Facility Location: A Survey of Applications and Methods , edited by Zvi Drezner, 199-223. New York, NY: Springer Verlag.
26.
Marianov, V., and C. ReVelle.1996. ‘‘The Queuing Maximal Availability Location Problem: A Model for the Siting of Emergency Vehicles’’European Journal of Operational Research93:110-20.
27.
Marianov, V., M. Ríos, and F.J. Barros.2005. ‘‘Allocating Servers to Facilities, When Demand is Elastic to Travel and Waiting Times’’RAIRO Operations Research39:143-62.
28.
Marianov, V., and D. Serra.1998. ‘‘Probabilistic Maximal Covering Location-Allocation for Congested Systems’’Journal of Regional Science38:401-24.
29.
Marianov, V., and D. Serra.2001. ‘‘Hierarchical Location-Allocation Models for Congested Systems’’European Journal of Operational Research135:196-209.
30.
Marianov, V., and D. Serra.2002. ‘‘Location-Allocation of Single and Multiple-Server Service Centers With Constrained Queues or Waiting Times’’Annals of Operations Research111:33-48.
31.
Marianov, V., and D. Serra.2003. ‘‘Location of Hubs Behaving as M/D/c Queues’’Computers and Operations Research30:983-1003.
32.
Marianov, V., D. Serra, and C. ReVelle.1999. ‘‘Location of Hubs in a Competitive Environment’’European Journal of Operational Research114:363-71.
33.
ReVelle, C., and S. Swain.1970. ‘‘Central Facilities Location’’Geographical Analysis2:30-42.
34.
Rolland, E., D.A. Schilling, and J.R. Current.1997. ‘‘An Efficient Tabu Search Procedure for the P-Median Problem’’European Journal of Operational Research96:329-42.
35.
Serra, D., H. Eiselt, G. Laporte, and C. ReVelle.1999. ‘‘Market Capture Models Under Various Customer Choice Rules’’Environment and Planning B26:141-50.
36.
Stützle, T.1997. Max Min Ant System for the quadratic assignment problem . Technical Report AIDA -97 -4, FG Intellektik, TU Darmstadt, Germany, July 1997.
37.
Stützle, T.1998a. ‘‘An Ant Approach for the Flow Shop Problem’’ . Proceedings of the 6th European Congress on Intelligent Techniques & Soft Computing (EUFIT’98), 3, Verlag Mainz, Aachen, Germany, 1560-1564.
38.
Stützle, T.1998b. ‘‘Local Search Algorithms for Combinatorial Problems-Analysis, Improvements, and New Applications.’’ PhD Thesis, Department of Computer Science, Darmstadt University of Technology, Germany.
39.
Stützle, T., and H. Hoos.1999. ‘‘Max-Min Ant System and Local Search for Combinatorial Optimisation’’. In Meta-Heuristics: Trends in Local Search Paradigms for Optimisation, edited by S. Vos, S. Martello, I. H. Osman, and C. Roucairol, Kluwer Academic Publishers, Boston, 313-29.
40.
Sun, J., and Y. Gu.2002. ‘‘A Parametric Approach for a Non-Linear Discrete Location Problem’’Journal of Combinatorial Optimization6:119-32.
