An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows

The need to reduce pollution and traffic in city centers requires the use of small vans, electric vehicles, and drones to distribute goods. Because of autonomy and capacity issues, these vehicles need to perform multiple trips from/to the depot during the day. The category of decision-making problems modeling such distribution problems are known as multitrip vehicle-routing problems (MTVRPs), which generalize the well-known vehicle-routing problem by allowing vehicles to perform multiple trips per day. Several MTVRPs are solved in the literature with different mathematical models and algorithms. In “An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows,” R. Paradiso, R. Roberti, D. Laganà, and W. Dullaert propose a single algorithm that can solve, to optimality, the MTVRP with capacity and time windows constraints and four variants of this problem featuring additional operational constraints. The proposed framework significantly outperforms the state-of-the-art algorithms from the literature. Multitrip vehicle - routing problems (MTVRPs) generalize the well-known VRP by allowing vehicles to perform multiple trips per day. MTVRPs have received a lot of attention lately because of their relevance in real-life applications—for example, in city logistics and last-mile delivery. Several variants of the MTVRP have been investigated in the literature, and a number of exact methods have been proposed. Nevertheless, the computational results currently available suggest that MTVRPs with different side constraints require ad hoc formulations and solution methods to be solved. Moreover, solving instances with just 25 customers can be out of reach for such solution methods. In this paper, we proposed an exact solution framework to address four different MTVRPs proposed in the literature. The exact solution framework is based on a novel formulation that has an exponential number of variables and constraints. It relies on column generation, column enumeration, and cutting plane. We show that this solution framework can solve instances with up to 50 customers of four MTVRP variants and outperforms the state-of-the-art methods from the literature.