A combined multistart random constructive heuristic and set partitioning based formulation for the vehicle routing problem with time dependent travel times

Although the Vehicle Routing Problem (VRP) has been broadly addressed in the literature, most of the works consider constant travel times. This is a strong simplification that does not allow to correctly model real world applications. In fact, nowadays, travel times sensibly change, across the day, due to congestion phenomena. Therefore, to actually represent the reality, it is necessary to consider time dependent travel times. In this paper, the VRP with Time Dependent Travel Times, service times at nodes, and limit on the maximum route duration, is addressed. The objective function consists into minimizing the total travel time. A Multistart Random Constructive Heuristic, (MRCH), in which congestion level is considered, is proposed. The routes obtained by the MRCH are then used as columns in a Set Partitioning formulation. Computational results, carried out on instances derived by VRP instances taken from the literature, show the efficiency and effectiveness of the proposed approach.