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Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem

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  • Mohammad Nezhad, Ali
  • Manzour, Hasan
  • Salhi, Said

Abstract

Facility location problem is one of the strategic logistical drivers within the supply chain which is a hard to solve optimization problem. In this study, we focus on the uncapacitated single-source multi-product production/distribution facility location problem with the presence of set-up cost. To efficiently tackle this decision problem, two Lagrangian-based heuristics are proposed one of which incorporates integer cuts to strengthen the formulation. Local search operators are also embedded within these methods to improve the upper bounds as the search progresses. Three sets of instances with various characteristics are generated and used to evaluate the performance of the proposed algorithms. Encouraging results are obtained when assessed against an ILP formulation using CPLEX. The latter is used for generating optimal solutions for small size instances and also as a means for producing upper and lower bounds for larger ones when restricted by a limited amount of execution time.

Suggested Citation

  • Mohammad Nezhad, Ali & Manzour, Hasan & Salhi, Said, 2013. "Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem," International Journal of Production Economics, Elsevier, vol. 145(2), pages 713-723.
    • Handle: RePEc:eee:proeco:v:145:y:2013:i:2:p:713-723
    DOI: 10.1016/j.ijpe.2013.06.001
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    1. Holmberg, Kaj & Ronnqvist, Mikael & Yuan, Di, 1999. "An exact algorithm for the capacitated facility location problems with single sourcing," European Journal of Operational Research, Elsevier, vol. 113(3), pages 544-559, March.
    2. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    3. Gzara, Fatma & Erkut, Erhan, 2009. "A Lagrangian relaxation approach to large-scale flow interception problems," European Journal of Operational Research, Elsevier, vol. 198(2), pages 405-411, October.
    4. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    5. Klose, Andreas, 2000. "A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 126(2), pages 408-421, October.
    6. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    7. Barreto, Sergio & Ferreira, Carlos & Paixao, Jose & Santos, Beatriz Sousa, 2007. "Using clustering analysis in a capacitated location-routing problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 968-977, June.
    8. Cortinhal, Maria Joao & Captivo, Maria Eugenia, 2003. "Upper and lower bounds for the single source capacitated location problem," European Journal of Operational Research, Elsevier, vol. 151(2), pages 333-351, December.
    9. Tragantalerngsak, Suda & Holt, John & Ronnqvist, Mikael, 1997. "Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 102(3), pages 611-625, November.
    10. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    11. R. K. Ahuja & J. B. Orlin & S. Pallottino & M. P. Scaparra & M. G. Scutellà, 2004. "A Multi-Exchange Heuristic for the Single-Source Capacitated Facility Location Problem," Management Science, INFORMS, vol. 50(6), pages 749-760, June.
    12. Barcelo, J. & Casanovas, J., 1984. "A heuristic lagrangean algorithm for the capacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 15(2), pages 212-226, February.
    13. Chen, Chia-Ho & Ting, Ching-Jung, 2008. "Combining Lagrangian heuristic and Ant Colony System to solve the Single Source Capacitated Facility Location Problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(6), pages 1099-1122, November.
    14. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 383-399, March.
    15. Lin, C.K.Y., 2009. "Stochastic single-source capacitated facility location model with service level requirements," International Journal of Production Economics, Elsevier, vol. 117(2), pages 439-451, February.
    16. Sridharan, R., 1993. "A Lagrangian heuristic for the capacitated plant location problem with single source constraints," European Journal of Operational Research, Elsevier, vol. 66(3), pages 305-312, May.
    17. Ronnqvist, Mikael & Tragantalerngsak, Suda & Holt, John, 1999. "A repeated matching heuristic for the single-source capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 51-68, July.
    18. Tragantalerngsak, Suda & Holt, John & Ronnqvist, Mikael, 2000. "An exact method for the two-echelon, single-source, capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 123(3), pages 473-489, June.
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