An efficient variable neighborhood search approach for the facility location problem with the limited choice rule

Abstract One of the most common problems in the expansion of a company consists of deciding the most appropriate locations for their facilities. This decision problem, known as the facility location problem, has been studied from different perspectives, considering a number of different constraints. Among these different versions of the problem, the facility location problem with the limited choice rule considers both the cost of opening facilities and the benefit of attracting customers under a deterministic utility approach. In this work, we propose a metaheuristic approach based on variable neighborhood search to tackle this problem. Our proposal is able to obtain the best results in 296 of the 309 instances studied, compared to state‐of‐the‐art algorithms. In addition, we propose an efficient local search that obtains a 91.5% average reduction in execution time compared to the version with the straightforward implementation. Therefore, this efficient proposal can be applied to larger instances that cannot be solved with previous approaches.