The multi-depot vrp with vehicle interchanges

Résumé

In real-world logistic operations there are a lot of situations that can be exploited to get better operational strategies. It is important to study these new alternatives, because they can represent significant cost reductions to the companies working with physical distribution. This thesis defines the Multi-Depot Vehicle Routing Problem with Vehicle Interchanges (MDVRPVI). In this problem, both vehicle capacities and duration limits on the routes of the drivers are imposed. To favor a better utilization of the available capacities and working times, it is allowed to combine pairs of routes at predefined interchange locations. The objective of this thesis is to analyze and solve the Multi-Depot Vehicle Routing Problem adding the possibility to interchange vehicles at predefined points. With this strategy, it is possible to reduce the total costs and the number of used routes with respect to the classical approach: The Multi-Depot Vehicle Routing Problem (MDVRP). It should be noted that the MDVRP is more challenging and sophisticated than the single-depot Vehicle Routing Problem (VRP). Besides, most exact algorithms for solving the classical VRP are difficult to adapt in order to solve the MDVRP (Montoya-Torres et al., 2015). From the complexity point of view, the MDVRPVI is NP-Hard, since it is an extension of the classical problem, which is already NP-Hard. We present a tight bound on the costs savings that can be attained allowing interchanges. Three integer programming formulations are proposed based on the classical vehicle-flow formulations of the MDVRP. One of these formulations was solved with a branch-and-bound algorithm, and the other two formulations, with branch-and-cut algorithms. Due to its great symmetry, the first formulation is only able to solve small instances. To increase the dimension of the instances used, we proposed two additional formulations that require one or more families of constraints of exponential size. In order to solve these formulations, we had to design and implement specific branch-and-cut algorithms. For these algorithms we implemented specific separation methods for constraints that had not previously been used in other routing problems. The computational experience performed evidences the routing savings compared with the solutions obtained with the classical approach and allows to compare the efficacy of the three solution methods proposed.