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. © 2020 IEEE.