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The discrete facility location problem with balanced allocation of customers

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  • Marín, Alfredo

Abstract

We consider a discrete facility location problem where the difference between the maximum and minimum number of customers allocated to every plant has to be balanced. Two different Integer Programming formulations are built, and several families of valid inequalities for these formulations are developed. Preprocessing techniques which allow to reduce the size of the largest formulation, based on the upper bound obtained by means of an ad hoc heuristic solution, are also incorporated. Since the number of available valid inequalities for this formulation is exponential, a branch-and-cut algorithm is designed where the most violated inequalities are separated at every node of the branching tree. Both formulations, with and without the improvements, are tested in a computational framework in order to discriminate the most promising solution methods. Difficult instances with up to 50 potential plants and 100 customers, and largest easy instances, can be solved in one CPU hour.

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  • Marín, Alfredo, 2011. "The discrete facility location problem with balanced allocation of customers," European Journal of Operational Research, Elsevier, vol. 210(1), pages 27-38, April.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:1:p:27-38
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    References listed on IDEAS

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    1. Oded Berman & Edward H. Kaplan, 1990. "Equity Maximizing Facility Location Schemes," Transportation Science, INFORMS, vol. 24(2), pages 137-144, May.
    2. Berger, Paul D. & Bechwati, Nada Nasr, 2001. "The allocation of promotion budget to maximize customer equity," Omega, Elsevier, vol. 29(1), pages 49-61, February.
    3. Ivan Contreras & Elena Fernández & Alfredo Marín, 2010. "Lagrangean bounds for the optimum communication spanning tree problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 140-157, July.
    4. Jörg Kalcsics & Stefan Nickel & Justo Puerto & Antonio Rodríguez-Chía, 2010. "The ordered capacitated facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 203-222, July.
    5. Alfredo Marín & Stefan Nickel & Sebastian Velten, 2010. "An extended covering model for flexible discrete and equity location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 125-163, February.
    6. Emilio Carrizosa & Eduardo Conde & Manuel Muñoz-Márquez & Justo Puerto, 1997. "Simpson Points in Planar Problems with Locational Constraints. The Polyhedral-Gauge Case," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 291-300, May.
    7. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    8. Labbe, Martine, 1985. "Outcomes of voting and planning in single facility location problems," European Journal of Operational Research, Elsevier, vol. 20(3), pages 299-313, June.
    9. Oded Berman & Zvi Drezner & Arie Tamir & George Wesolowsky, 2009. "Optimal location with equitable loads," Annals of Operations Research, Springer, vol. 167(1), pages 307-325, March.
    10. Alfredo Marín, 2010. "Discrete location for bundled demand points," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 242-256, July.
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    Cited by:

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    3. Shahede Omidi & Jafar Fathali & Morteza Nazari, 2020. "Inverse and reverse balanced facility location problems with variable edge lengths on trees," OPSEARCH, Springer;Operational Research Society of India, vol. 57(2), pages 261-273, June.

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