Dynamic Multi-Level Multi-capacitated Facility Location Problem: Formulation and Resolution

Since the 1950s, the facility location problem (FLP) has been extensively studied, leading to the introduction of various variants aimed at addressing real-world challenges. One such variant emerged in 2020 as the "Multilevel Multi-capacitated facility location problem" (MLMCLP). This paper seeks to further generalize the MLMCLP to accommodate the dynamic scenarios encountered in diverse fields like telecommunication and freight transportation. To achieve this, we introduce a mathematical model named "Dynamic Multi-level multi-capacitated facility location problem" (DMLMCLP). To validate our new approach, we create a set of artificial instances. The model demonstrates robustness through the application of the Branch and Cut solving method, employing the CPLEX solver. The numerical study results affirm the effectiveness of our model.