Abstract
We consider a generalization of the well-known capacitated facility location problem with single source constraints in which customer demand contains a flexible dimension. This work focuses on providing fast and practically implementable optimization-based heuristic solution methods for very large scale problem instances. We offer a unique approach that utilizes a high-quality efficient heuristic within a neighborhood search to address the combined assignment and fixed-charge structure of the underlying optimization problem. We also study the potential benefits of combining our approach with a so-called very large-scale neighborhood search (VLSN) method. As our computational test results indicate, our work offers an attractive solution approach that can be tailored to successfully solve a broad class of problem instances for facility location and similar fixed-charge problems.
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References
Adlakha, V., Kowalski, K.: A simple heuristic for solving small fixed-charge transportation problems. Omega 31(3), 205–211 (2003)
Ahuja, R.K., Orlin, J.B., Sharma, D.: Multi-exchange neighborhood search algorithms for the capacitated minimum spanning tree problem. Math. Program. 91, 71–97 (2001)
Ahuja, R.K., Olrin, J.B., Punnen, A.: A survey of very large scale neighborhood search techniques. Discrete Appl. Math. 123, 75–102 (2002)
Ahuja, R.K., Orlin, J.B., Pallottino, S., Scaparra, M.P., Scutella, M.G.: A multi-exchange heuristic for the single-source capacitated facility location problem. Manag. Sci. 50(6), 749–760 (2004)
Ahuja, R.K., Huang, W., Romeijn, H.E., Morales, D.R.: A heuristic approach to the multi-period single-sourcing problem with production and inventory capacities and perishability constraints. INFORMS J. Comput. 19, 14–26 (2007)
Balakrishnan, A., Geunes, J.: Production planning with flexible product specifications: an application to specialty steel manufacturing. Oper. Res. 51(1), 94–112 (2003)
Barcelo, J., Casanovas, J.: A heuristic Lagrangian algorithm for the capacitated plant location problem. Eur. J. Oper. Res. 15(2), 212–226 (1984)
Beasley, J.E.: Lagrangian heuristics for location problems. Eur. J. Oper. Res. 65, 383–399 (1993)
Delmaire, H., Diaz, J.A., Fernandez, E., Ortega, M.: Comparing new heuristics for the capacitated plant location problem. Technical Report DR97/10, Department of Statistics and Operations Research, Universitat Politecnica de Catalunya, Barcelona, Spain (1997)
Demaire, H., Diaz, J.A., Fernandez, E., Ortega, M.: Reactive grasp and tabu search based heuristics for the single source capacitated plant location problem. Inf. Syst. Oper. Res. 37(3), 194–225 (1999)
Erlenkotter, D.: A dual-based procedure for uncapacitated facility location. Oper. Res. 26(6), 992–1009 (1978)
Ford, L.R., Fulkerson, D.R.: Solving the transportation problem. Manag. Sci. 3(1), 24–32 (1956)
Freling, R., Romeijn, H.E., Romero Morales, D., Wagelmans, A.P.M.: A branch-and-price algorithm for the multi-period single-sourcing problem. Oper. Res. 51(6), 922–939 (2003)
Fukasawa, R., Longo, H., Lysgaard, J., de Aragao, M.P., Reis, M., Uchoa, E., Werneck, R.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math. Program. 106, 491–511 (2006)
Ghosh, D.: Neighborhood search heuristics for the uncapacitated facility location problem. Eur. J. Oper. Res. 150(1), 150–162 (2003)
Gray, P.: Exact solution of the fixed-charge transportation problem. Oper. Res. 19(6), 1529–1538 (1971)
Hindi, K.S., Pienkosz, K.: Efficient solution of large scale, single-source, capacitated plant location problems. J. Oper. Res. Soc. 50(3), 268–274 (1999)
Klincewicz, J.G., Luss, H.: A Lagrangian relaxation heuristic for capacitated facility location with single-source constraints. J. Oper. Res. Soc. 37(5), 495–500 (1986)
Lee, J.K., Kim, Y.D.: Search heuristics for resource constrained project scheduling. J. Risk 47(5), 678–689 (1996)
Lin, S., Kernighan, V.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)
Pigatti, A., Poggi de Aragao, M., Uchoa, E.: Stabilized branch-and-cut-and-price for the generalized assignment problem. Electr. Notes Discrete Math. 19, 389–395 (2005)
Rainwater, C., Geunes, J., Romeijn, H.E.: Capacitated facility location problem with single-source constraints and flexible demand. Technical report, Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, June (2008)
Rainwater, C., Geunes, J., Romeijn, H.E.: The generalized assignment problem with flexible jobs. Discrete Appl. Math. (2008). doi:10.1016/j.dam.2008.04.017
Ralphs, T.K., Kopman, L., Pulleybank, W.R., Trotter, L.E.: On the capacitated vehicle routing problem. Math. Program. 94, 343–359 (2003)
Reinelt, G.: TSPLIB-a traveling salesman problem library. ORSA J. Comput. 3, 376–384 (1991)
Savelsbergh, M.P.W.: A branch-and-price algorithm for the generalized assignment problem. Oper. Res. 45(6), 831–841 (1997)
Sun, M.: Solving the uncapacitated facility location problem using tabu search. Comput. Oper. Res. 33, 2563–2589 (2006)
Thompson, P., Orlin, J.B.: The theory of cyclic transfers. Technical Report 200-89, Operations Research Center, Massachusetts Institute of Technology, Cambridge MA (1989)
Thompson, P.M., Psaraftis, H.N.: Cycle transfer algorithms for multi-vehicle routing and scheduling problems. Oper. Res. 41, 935–946 (1993)
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This work was supported in part by the National Science Foundation under Grants No. DMI-0355533, CMMI-0926508, and CMMI-0927930.
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Rainwater, C., Geunes, J. & Romeijn, H.E. A facility neighborhood search heuristic for capacitated facility location with single-source constraints and flexible demand. J Heuristics 18, 297–315 (2012). https://doi.org/10.1007/s10732-011-9179-x
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DOI: https://doi.org/10.1007/s10732-011-9179-x