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An LP-based heuristic for two-stage capacitated facility location problems

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  • A Klose

    (Universität St. Gallen)

Abstract

In this paper, a linear programming based heuristic is considered for a two-stage capacitated facility location problem with single source constraints. The problem is to find the optimal locations of depots from a set of possible depot sites in order to serve customers with a given demand, the optimal assignments of customers to depots and the optimal product flow from plants to depots. Good lower and upper bounds can be obtained for this problem in short computation times by adopting a linear programming approach. To this end, the LP formulation is iteratively refined using valid inequalities and facets which have been described in the literature for various relaxations of the problem. After each reoptimisation step, that is the recalculation of the LP solution after the addition of valid inequalities, feasible solutions are obtained from the current LP solution by applying simple heuristics. The results of extensive computational experiments are given.

Suggested Citation

  • A Klose, 1999. "An LP-based heuristic for two-stage capacitated facility location problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(2), pages 157-166, February.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:2:d:10.1057_palgrave.jors.2600675
    DOI: 10.1057/palgrave.jors.2600675
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    Citations

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    Cited by:

    1. Kim, Youngjin & Lee, Youngho & Han, Junghee, 2011. "A splitter location-allocation problem in designing fiber optic access networks," European Journal of Operational Research, Elsevier, vol. 210(2), pages 425-435, April.
    2. Eskigun, Erdem & Uzsoy, Reha & Preckel, Paul V. & Beaujon, George & Krishnan, Subramanian & Tew, Jeffrey D., 2005. "Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers," European Journal of Operational Research, Elsevier, vol. 165(1), pages 182-206, August.
    3. Chandra Ade Irawan & Dylan Jones, 2019. "Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities," Annals of Operations Research, Springer, vol. 272(1), pages 41-67, January.
    4. 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.
    5. Yang, Zhen & Chen, Haoxun & Chu, Feng & Wang, Nengmin, 2019. "An effective hybrid approach to the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 467-480.
    6. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    8. Li, Jinfeng & Chu, Feng & Prins, Christian & Zhu, Zhanguo, 2014. "Lower and upper bounds for a two-stage capacitated facility location problem with handling costs," European Journal of Operational Research, Elsevier, vol. 236(3), pages 957-967.
    9. Andreas Klose & Andreas Drexl, 2005. "Lower Bounds for the Capacitated Facility Location Problem Based on Column Generation," Management Science, INFORMS, vol. 51(11), pages 1689-1705, November.
    10. Romeijn, H.E. & Romero Morales, D., 2000. "A Greedy Heuristic for a Three-Level Multi-Period Single-Sourcing Problem," ERIM Report Series Research in Management ERS-2000-04-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    11. Keskin, Burcu B. & Uster, Halit, 2007. "Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 663-682, October.
    12. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    13. Liu, Zhimin & Wu, Zhong & Ji, Ying & Qu, Shaojian & Raza, Hassan, 2021. "Two-stage distributionally robust mixed-integer optimization model for three-level location–allocation problems under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    14. Raghavan, S. & Sahin, Mustafa & Salman, F. Sibel, 2019. "The capacitated mobile facility location problem," European Journal of Operational Research, Elsevier, vol. 277(2), pages 507-520.

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