Heuristics for the dynamic facility location problem with modular capacities

This paper studies the Dynamic Facility Location Problem with Modular Capacities (DFLPM). It generalizes several facility location problems and consists in determining locations and sizes of facilities to minimize location and demand allocation costs with decisions taken periodically over a planning horizon. The DFLPM is solved using heuristics tailored for different scenarios and cost structures. We propose three linear relaxation based heuristics (LRH) and an evolutionary heuristic that hybridizes a genetic algorithm with a variable neighborhood descent (GA+VND). We adapt benchmark instances from the literature to yield several representations of scenarios and parameters structures. Experiments are reported comparing the heuristics to a state-of-the-art mixed integer programming (MIP) formulation for the problem. We show that the performance of the methods depends on the characteristics of the instance solved. For the benchmark instances, the LRH improved by VND finds solutions within 0.02% of the optimal ones in less than half of the time of the MIP. For the scenarios where construction costs are higher and module sizes are lower, the GA+VND proved to be effective to solve the problem, outperforming the LRH and the MIP. We also discuss the results from a practitioner point of view to identify situations where each method is preferable.