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Annals of Operations Research

, Volume 122, Issue 1–4, pp 121–139 | Cite as

A New Chance-Constrained Maximum Capture Location Problem

  • Rosa Colomé
  • Helena R. Lourenço
  • Daniel Serra
Article

Abstract

The paper presents a new model based on the basic Maximum Capture model, MAXCAP. The new Chance-Constrained Maximum Capture model introduces a stochastic threshold constraint, which recognises the fact that a facility can be open only if a minimum level of demand is captured. A metaheuristic based on Max-Min Ant System and Tabu Search procedure is presented to solve the model. This is the first time that the Max-Min Ant system is adapted to solve a location problem. Computational experience and an application to 55-node network are also presented.

stochastic location capture models 

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References

  1. Balakrishnan, P. and tJ. Storbeck. (1991). “McTRESH: Modeling Maximum Coverage with Threshold Constraint.” Environment & Planning B 18, 459–472.Google Scholar
  2. Benati, S. and tG. Laporte. (1994). “Tabu Search Algorithms for the (r|Xp)-Medianoid and (r|p)-Centroid Problems.” Location Science 2(4), 193–204.Google Scholar
  3. Berry, B.J. and tW. Garrison. (1958). “Recent Developments of Central Place Theory.” Papers and Proceedings of the Regional Science Association 4, 107–120.Google Scholar
  4. Colomé, R. and tD. Serra. (2000). “Supermarket Key Attributes and Location Decisions: A Comparative Study between British and Spanish Consumers.” Economic and Business Working Paper No. 469, Pompeu Fabra University, Barcelona, Spain.Google Scholar
  5. Colorni, A., tM. Dorigo, and V. Maniezzo. (1991a). “Distributed Optimisation by Ant Colonies,“ In Proceedings of ECAL91 –European Conference on Artificial Life. Paris: Elsevier, pp. 134–142.Google Scholar
  6. Colorni, A., tM. Dorigo, and V. Maniezzo. (1991b). “The Ant System: Optimisation by a Colony of Cooperating Agents. Part B.” IEEE Transactions on Systems, Man and Cybernetics 26(1), 29–41.Google Scholar
  7. Current, J. and tJ. Storbeck. (1994). “A Multiobjective Approach to Design Franchise Outlet Networks.” Journal of Operational Research Society 45, 71–81.Google Scholar
  8. Dorigo, D. and tG. DiCaro. (1999). “The Ant Colony OptimizationMeta-Heuristic.” In D. Corne, M. Dorigo, and F. Glover (eds.), News Ideas in Optimisation. New York: McGraw-Hill.Google Scholar
  9. Drezner, T. (1994). “Locating a Single New Facility among Existing Unequally Attractive Facilities.” Journal of Regional Science 34, 237–252.Google Scholar
  10. Drezner T. (1995). “Competitive Facility Location in the Plane.” In Z. Drezner (ed.), Facility Location: A Survey of Applications and Methods. New York: Springer, pp. 285–300.Google Scholar
  11. Drezner, T., tZ. Drezner, and S. Shiode. (2002). “A Threshold Satisfying Competitive Location Model.” Journal of Regional Science 42(2), 287–299.Google Scholar
  12. Eiselt, H.A. and tG. Laporte. (1989). “The Maximum Capture Problem in a Weighted Network.” Journal of Regional Science 29(3), 433–439.Google Scholar
  13. Gendreau, M., tZ. Hertz, and G. Laporte. (1994). “A Tabu Search Heuristic for the Vehicle Routing Problem.” Management Science 40(10), 1276–1289.Google Scholar
  14. Glover, F. (1989). “Tabu Search. Part I.” ORSA Journal of Computing 1, 190–206.Google Scholar
  15. Glover, F. (1990). “Tabu Search. Part II.” ORSA Journal of Computing 2, 4–32.Google Scholar
  16. Hotelling, H. (1929). “Stability in Competition.” Economic Journal 39, 41–57.Google Scholar
  17. Huff, D. (1964). “Defining and Estimating a Trading Area.” Journal of Marketing 28, 34–38.Google Scholar
  18. Jobson, J.D. (1991). AppliedMultivariate Data Analysis. Vol. 1: Regression and Experimental Design. New York: Springer.Google Scholar
  19. Kariv, O. and tS. Hakimi. (1979). “An Algorithmic Approach to Network Location Problems 2: The p-Medians.” SIAM Journal on Applied Mathematics 37, 539–560.Google Scholar
  20. Klincewicz, J.G. (1992). “Avoiding Local Optima in the p-Hub Location Problem Using Tabu Search and GRASP.” Annals of Operations Research 40, 283–302.Google Scholar
  21. Lourenço, H. and tD. Serra, “Meta-Heuristics for the Generalized Assignment Problem.” In Mathware & Soft Computing, Special Issue on Ant Colony Optimization: Models and Applications, forthcoming.Google Scholar
  22. Marianov, V., tD. Serra, and C. ReVelle. (1999). “Location of Hubs in a Competitive Environment.” European Journal of Operational Research 114, 363–371.Google Scholar
  23. Osman, I. (1995). “Heuristics for the Generalized Assignment Problem: Simulated Annealing and Tabu Search Approaches.” OR Spektrum 17, 211–225.Google Scholar
  24. Pirlot, M. (1992). “General Local Search Heuristics in Combinatorial Optimisation: A Tutorial.” JORBEL, Belgian Journal of Operations Research, Statistics and Computer Science 32(1–2), 7–67.Google Scholar
  25. Reilly, W.J. (1929). The Law of Retail Gravitation. New York: Knickerbocker Press.Google Scholar
  26. ReVelle, C. (1986). “The Maximum Capture or “Sphere of Influence” Location Problem: Hotelling Revisited on a Network.” Journal of Regional Science 26(2).Google Scholar
  27. Rolland, E., tD. Schilling, and J. Current. (1997). “An Efficient Tabu Search Procedure for the p-Median Problem.” European Journal of Operation Research 96(2), 329–342.Google Scholar
  28. Santos-Peñate, D., tR. Suárez-Vega, and P. Dorta-González. (1997). “Localización competitiva con criterios basados en funciones de atracción.” In XXIII Congreso Nacional de Estadística e Investigación Operativa, Valencia, 11–14 de marzo.Google Scholar
  29. Serra, D. and tV. Marianov. (1999). “The p-Median Problem in a Changing Network: The Case of Barcelona.” Location Science 6(4), 383–394.Google Scholar
  30. Serra, D., tV. Marianov, and C. ReVelle (1992). “The Hierarchical Maximum Capture Problem.” European Journal of Operational Research 62(3), 34–56.Google Scholar
  31. Serra, D., tS. Ratick, and C. ReVelle (1996). “The Maximum Capture Problem with Uncertainty.” Environment and Planning B 62, 49–59.Google Scholar
  32. Serra, D. and tC. ReVelle. (1994). “Market Capture by Two Competitors: The Preemptive Location Problem.” Journal of Regional Science 34(4), 549–561.Google Scholar
  33. Serra, D. and tC. ReVelle. (1996). “Competitive Location on Networks.” In Z. Drezner (ed.), Facility Location. A Survey of Applications and Methods. Berlin: Springer.Google Scholar
  34. Serra, D., tC. ReVelle, and K. Rosing (1999). “Surviving in a Competitive Spatial Market: The Threshold Capture Model.” Journal of Regional Science 39(4), 637–652.Google Scholar
  35. Shonkwiler, J. and tT. Harris. (1996). “Rural Retail Business Thresholds and Interdependencies.” Journal of Regional Science 36, 617–630.Google Scholar
  36. Stüzle, T. (1997). “Max-Min Ant System for the Quadratic Assignment Problem.” Technical Report AIDA–97–4, FG Intellektik, TU Darmstadt, Germany.Google Scholar
  37. Stüzle, T. (1998a). “An Ant Approach for the Flow Shop Problem.” In Proceedings of the 6th European Congress on Intelligent Techniques & Soft Computing (EUFIT'98), Vol. 3, pp. 1560–1564.Google Scholar
  38. Stüzle, T. (1998b). “Local Search Algorithms for Combinatorial Problems –Analysis, Improvements, and New Applications.” Ph.D. Thesis, Department of Computer Science, Darmstadt University of Technology, Germany.Google Scholar
  39. Stüzle, T. and tH. Hoos. (1999). “Max-Min Ant System and Local Search for Combinatorial Optimisation.” In S. Voß, S. Martello, I.H. Osman, and C. Roucairol (eds.), Meta-Heuristics: Trends in Local Search Paradigms for Optimisation. Dordrecht: Kluwer Academic, pp. 313–329.Google Scholar
  40. Swain, R. (1974). “A Parametric Decomposition Algorithm for the Solution of Uncapacited Location Problems.” Management Science 21, 189–198.Google Scholar
  41. Teitz, M.B. and tP. Bart. (1986). “Heuristic Methods for Extracting the Generalized Vertex Median of a Weighted Graph.” Operations Research 16, 955–965.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Rosa Colomé
    • 1
  • Helena R. Lourenço
    • 2
  • Daniel Serra
    • 2
  1. 1.Department of Economics and BusinessUniversitat Oberta de CatalunyaBarcelonaSpain
  2. 2.Department of Economics and Business and GREL-IETUniversitat Pompeu FabraBarcelonaSpain

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