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Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

Author

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  • José-Fernando Camacho-Vallejo
  • Álvaro Eduardo Cordero-Franco
  • Rosa G. González-Ramírez

Abstract

This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg’s game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time.

Suggested Citation

  • José-Fernando Camacho-Vallejo & Álvaro Eduardo Cordero-Franco & Rosa G. González-Ramírez, 2014. "Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, February.
    • Handle: RePEc:hin:jnlmpe:430243
    DOI: 10.1155/2014/430243
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    Cited by:

    1. Kailash Lachhwani, 2021. "Solving the general fully neutrosophic multi-level multiobjective linear programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1192-1216, December.
    2. Herminia I. Calvete & Carmen Galé & Aitor Hernández & José A. Iranzo, 2024. "A Bilevel Approach to the Facility Location Problem with Customer Preferences Under a Mill Pricing Policy," Mathematics, MDPI, vol. 12(22), pages 1-26, November.
    3. Lazar Mrkela & Zorica Stanimirović, 2022. "A variable neighborhood search for the budget-constrained maximal covering location problem with customer preference ordering," Operational Research, Springer, vol. 22(5), pages 5913-5951, November.

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