A MILP model and heuristic approach for facility location under multiple operational constraints

• We study a multi-period facility location problem featuring many realistic constraints.
• We use a 2-phase solution approach: clustering of customers then facility location.
• Clustering aims at evaluating the average transport costs form facilities to customers.
• Exact and heuristic solution methods are tested using real life data.
• Insights related to multi-period modeling are discussed using the numerical results.

In the present work, we study a multi-period facility location problem featuring many realistic constraints. In order to take into account vehicle routing from distribution centers to customers while maintaining a manageable size of the optimization problem, we develop a two-phase solution approach. In the first phase, the average distances and costs of transport from distribution centers to customers are evaluated using an exact clustering procedure based on a set-partitioning formulation. These costs serve as input to the facility location problem in the second phase, which is formulated as a mixed integer linear program and solved using a state-of-the art commercial solver. Many numerical experiments using real life data from the automotive industry are carried out in order to derive some insights related to multi-period modeling. We first show that in our case study, using static assignment decisions is better for the company as the corresponding operational benefit outweighs the additional cost to be incurred. We then compare the outputs of the multi-period model with those of its single-period counterpart. Finally, to cope with the computational difficulties encountered during the numerical experiments, we propose a linear relaxation based heuristic to solve larger instances of the problem. The heuristic method provides good quality solutions while significantly improving computation times.