Uma abordagem de decomposição de Benders com aproximação externa para a localização de instalações com regra de escolha limitada

Abstract

In this study, a new exact approach for competitive facility location problems with limited choice rule is proposed. The approach involves the development of a hybrid method based on Benders decomposition with outer approximation, where the outer approximation master problem is solved using a Benders decomposition algorithm. Given the decomposition structure of the problem, it is possible to generate a Benders feasibility cut for each customer at a time. However, instead of adding them all at once to the master problem, these cuts were grouped following a clustering of customers into small groups. To further optimize the solution process, the Benders feasibility cuts were separated through inspection. Medium and large-scale instances were used to evaluate the computational performance of the proposed approach in comparison to existing methods in the literature. The results demonstrate the superiority of the proposed method over existing methods in the literature, particularly when evaluated on medium and large-scale instances.