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A New Chance-Constrained Maximum Capture Location Problem

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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.

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References

  • Balakrishnan, P. and tJ. Storbeck. (1991). “McTRESH: Modeling Maximum Coverage with Threshold Constraint.” Environment & Planning B 18, 459–472.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Current, J. and tJ. Storbeck. (1994). “A Multiobjective Approach to Design Franchise Outlet Networks.” Journal of Operational Research Society 45, 71–81.

    Google Scholar 

  • 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 

  • Drezner, T. (1994). “Locating a Single New Facility among Existing Unequally Attractive Facilities.” Journal of Regional Science 34, 237–252.

    Google Scholar 

  • 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 

  • Drezner, T., tZ. Drezner, and S. Shiode. (2002). “A Threshold Satisfying Competitive Location Model.” Journal of Regional Science 42(2), 287–299.

    Google Scholar 

  • 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 

  • 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 

  • Glover, F. (1989). “Tabu Search. Part I.” ORSA Journal of Computing 1, 190–206.

    Google Scholar 

  • Glover, F. (1990). “Tabu Search. Part II.” ORSA Journal of Computing 2, 4–32.

    Google Scholar 

  • Hotelling, H. (1929). “Stability in Competition.” Economic Journal 39, 41–57.

    Google Scholar 

  • Huff, D. (1964). “Defining and Estimating a Trading Area.” Journal of Marketing 28, 34–38.

    Google Scholar 

  • Jobson, J.D. (1991). AppliedMultivariate Data Analysis. Vol. 1: Regression and Experimental Design. New York: Springer.

    Google Scholar 

  • 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 

  • 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 

  • 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.

  • 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 

  • Osman, I. (1995). “Heuristics for the Generalized Assignment Problem: Simulated Annealing and Tabu Search Approaches.” OR Spektrum 17, 211–225.

    Google Scholar 

  • 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 

  • Reilly, W.J. (1929). The Law of Retail Gravitation. New York: Knickerbocker Press.

    Google Scholar 

  • ReVelle, C. (1986). “The Maximum Capture or “Sphere of Influence” Location Problem: Hotelling Revisited on a Network.” Journal of Regional Science 26(2).

  • 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 

  • 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.

  • 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 

  • Serra, D., tV. Marianov, and C. ReVelle (1992). “The Hierarchical Maximum Capture Problem.” European Journal of Operational Research 62(3), 34–56.

    Google Scholar 

  • Serra, D., tS. Ratick, and C. ReVelle (1996). “The Maximum Capture Problem with Uncertainty.” Environment and Planning B 62, 49–59.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Shonkwiler, J. and tT. Harris. (1996). “Rural Retail Business Thresholds and Interdependencies.” Journal of Regional Science 36, 617–630.

    Google Scholar 

  • Stüzle, T. (1997). “Max-Min Ant System for the Quadratic Assignment Problem.” Technical Report AIDA–97–4, FG Intellektik, TU Darmstadt, Germany.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Swain, R. (1974). “A Parametric Decomposition Algorithm for the Solution of Uncapacited Location Problems.” Management Science 21, 189–198.

    Google Scholar 

  • 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 

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Authors and Affiliations

  1. Department of Economics and Business, Universitat Oberta de Catalunya, Avda. Tibidabo, 39-43, 08035, Barcelona, Spain

    Rosa Colomé

  2. Department of Economics and Business and GREL-IET, Universitat Pompeu Fabra, Ramon Trias Fargas, 25-27, 08005, Barcelona, Spain

    Helena R. Lourenço & Daniel Serra

Authors
  1. Rosa Colomé
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  2. Helena R. Lourenço
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  3. Daniel Serra
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Colomé, R., Lourenço, H.R. & Serra, D. A New Chance-Constrained Maximum Capture Location Problem. Annals of Operations Research 122, 121–139 (2003). https://doi.org/10.1023/A:1026194423072

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