Multi-level multi-capacitated facility location problem: formulation and resolution.

Facility location problem is one of the most problems studied since the 1950 years; many variants have been introduced in order to deal with real-world problems. In 2016, a new variant was developed to generalize the p-median problem, called “budget constraint multi-capacitated location problem” (BMCLP). This paper aims to generalize the BMCLP onto the multi-level, a problem that arises in many scopes as telecommunication, freight transportation, etc. Therefore, we proposed a mathematical formulation as mixed integer, called “Multi-level multi-capacitated facility location problem” (MLMCLP) and generated an artificial set of instances in order to validate the new formulation. Finally, we apply the Branch and Cut solving method using the CPLEX solver. The results obtained from the numerical study show the robustness of the proposed formulation.