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.
Bibliographical noteCopyright © 2014 Jos´e-Fernando Camacho-Vallejo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Bi-level approaches
- Bi-level models