Bi-level Multi-capacitated Facility location Problem

Facility location problems can be considered as a century-old science. Studies on this subject began in the 1950s and are still relevant today. In 2016, a new variant of the location problems, called “budget constraint multi-capacitated location problem” (BMCLP), is published to generalize the p-median one. In this work, we propose a generalization of the BMCLP into a bilevel location problem (plants-depots and depots-customers) in order to consider, the modern supply chain constraints. We therefore established a mathematical formulation for the new problem, named “bi-level multi-capacitated facility location problem” and we created data instances adapted to this new formulation based on semi-random factors and certain generation methods available in the literature. In order to validate the latter formulation, we proposed Branch & Cut solving method used by CPLEX solver. Finally, we present the obtained computational results, which prove the efficiency of the new formulation for the tested instances.