A theoretical and computational study of green vehicle routing problems

This work investigates green vehicle routing problems (G-VRPs). GVRPs are NP-hard problems embodying the motivation, concepts, and advances of green logistics in the vehicle routing problem (VRP) domain. To address the shorter autonomy of electric vehicles, the G-VRP considers Alternative Fuel Stations (AFSs) that can be used to refuel vehicles in travel. Originally, the G-VRP prohibits consecutive AFS visits, i.e., a solution cannot have an edge between two AFSs. Here, besides the original G-VRP, we also consider the variant in which consecutive AFS visits are allowed. This research proposes combinatorial properties, concerning the number of visits to the AFSs, bounds on fuel consumption, and bounds on the number of routes and their cost. Furthermore, this research proposes valid inequalities, MILP formulations, preprocessing conditions, and lower bounds which strengthen the mathematical formulations for both G-VRP versions, thus improving their exact solution. The proposed methodologies were evaluated with extensive computational experiments. The results are analyzed and discussed, and conclusions on the benefits of the contributions are presented.