The location routing problem with facility sizing decisions

The location routing problem (LRP) integrates operational decisions on vehicle routing operations with strategic decisions on the location of the facilities or depots from which the distribution will take place. In other words, it combines the well-known vehicle routing problem (VRP) with the facility location problem (FLP). Hence, the LRP is an NP-hard combinatorial optimization problem, which justifies the use of metaheuristic approaches whenever large-scale instances need to be solved. In this paper, we explore a realistic version of the LRP in which facilities of different capacities are considered, i.e., the manager has to consider not only the location but also the size of the facilities to open. In order to tackle this optimization problem, three mixed-integer linear formulations are proposed and compared. As expected, they have been proved to be cost- and time- inefficient. Hence, a biased-randomized iterated local search algorithm is proposed. Classical instances for the LRP with homogeneous facilities are naturally extended to test the performance of our approach.