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An effective heuristic for large-scale capacitated facility location problems


The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for large-scale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of “promising” variables forming the core problem and on a Branch-and-Cut algorithm that solves the core problem. Computational results on very large scale instances (up to 4 million variables) are reported.

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  1. Aardal, K.: On the solution of one and two-level capacitated facility location problems by the cutting plane approach. Ph.D. Thesis, CORE, Louvain-la-Neuve (1992)

  2. Aardal, K.: Capacitated facility location: separation algorithms and computational experience. Math. Program. 81, 149–175 (1998)

  3. Aardal, K., Pochet, Y., Wolsey, L.A.: Capacitated facility location: valid inequalities and facets. Math. Oper. Res. 20, 562–582 (1995)

  4. Anbil, R., Barahona, F.: The volume algorithm: producing primal solutions with a subgradient method. Math. Program. 87(3), 385–399 (2000)

  5. Balas, E., Zemel, E.: An algorithm for the zero-one knapsack problems. Oper. Res. 28, 1130–1154 (1980)

  6. Barahona, F., Chudak, F.A.: Near-optimal solution to large scale facility location problems. Internal Report, IBM Research Division, T.J. Watson Research Center, RC 21606 (1999)

  7. Beasley, J.E.: An algorithm for solving large capacitated warehouse location problems. Eur. J. Oper. Res. 33, 314–325 (1988)

  8. Beasley, J.E.: Lagrangean heuristics for location problems. Eur. J. Oper. Res. 33, 383–399 (1993)

  9. Camerini, P.M., Fratta, L., Maffioli, F.: On improving relaxation methods by modified gradient techniques. Math. Program. Study 3, 26–34 (1975)

  10. Caprara, A., Fischetti, M., Toth, P., Vigo, D., Guida, P.L.: Algorithms for railway crew management. Math. Program. 79, 125–141 (1997)

  11. Chudak, F.A., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. In: Proceedings of the 7th International IPCO Conference, June 1999 (1999)

  12. Cornuejols, G., Sridharan, R., Thizy, J.M.: A comparison of heuristics and relaxations for the capacitated plant location problem. Eur. J. Oper. Res. 50, 280–297 (1991)

  13. Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. DIMACS Technical Report, 98–30 (1998)

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Correspondence to Antonio Sforza.

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Avella, P., Boccia, M., Sforza, A. et al. An effective heuristic for large-scale capacitated facility location problems. J Heuristics 15, 597 (2009).

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  • Capacitated facility location problem
  • Lagrangean relaxation
  • Branch-and-cut