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Global optimization algorithm for capacitated multi-facility continuous location-allocation problems

Author

Listed:
  • Cristiana L. Lara

    (Carnegie Mellon University)

  • Francisco Trespalacios

    (ExxonMobil Research and Engineering Company)

  • Ignacio E. Grossmann

    (Carnegie Mellon University)

Abstract

In this paper we propose a nonlinear Generalized Disjunctive Programming model to optimize the 2-dimensional continuous location and allocation of the potential facilities based on their maximum capacity and the given coordinates of the suppliers and customers. The model belongs to the class of Capacitated Multi-facility Weber Problem. We propose a bilevel decomposition algorithm that iteratively solves a discretized MILP version of the model, and its nonconvex NLP for a fixed selection of discrete variables. Based on the bounding properties of the subproblems, $$\epsilon $$ ϵ -convergence is proved for this algorithm. We apply the proposed method to random instances varying from 2 suppliers and 2 customers to 40 suppliers and 40 customers, from one type of facility to 3 different types, and from 2 to 32 potential facilities. The results show that the algorithm is more effective at finding global optimal solutions than general purpose global optimization solvers tested.

Suggested Citation

  • Cristiana L. Lara & Francisco Trespalacios & Ignacio E. Grossmann, 2018. "Global optimization algorithm for capacitated multi-facility continuous location-allocation problems," Journal of Global Optimization, Springer, vol. 71(4), pages 871-889, August.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:4:d:10.1007_s10898-018-0621-6
    DOI: 10.1007/s10898-018-0621-6
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    References listed on IDEAS

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    1. Hanif D. Sherali & Intesar Al-Loughani & Shivaram Subramanian, 2002. "Global Optimization Procedures for the Capacitated Euclidean and l p Distance Multifacility Location-Allocation Problems," Operations Research, INFORMS, vol. 50(3), pages 433-448, June.
    2. Necati Aras & İ. Kuban Altınel & Metin Orbay, 2007. "New heuristic methods for the capacitated multi‐facility Weber problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 21-32, February.
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    4. Jein-Shan Chen & Shaohua Pan & Chun-Hsu Ko, 2011. "A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation," Journal of Global Optimization, Springer, vol. 50(4), pages 713-728, August.
    5. Hanif D. Sherali & Frederick L. Nordai, 1988. "NP-Hard, Capacitated, Balanced p -Median Problems on a Chain Graph with a Continuum of Link Demands," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 32-49, February.
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    Cited by:

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