A mathematical model for the time-dependent vehicle routing problem

In this study, the Time-Dependent Vehicle Routing Problem (TDVRP) is considered which is a generalized version of the classical Vehicle Routing Problem (VRP). Unlike the VRP, the TDVRP can be defined as the routing a fleet of vehicle in which vehicle speeds are variable between the nodes. For the first time in literature, a new mathematical model, based on linear function, is developed for the TDVRP which considers the time-dependent speed function that satisfies the first-in-first-out (FIFO) property and differs from the existing models in literature. Computational results on a large set of instances, generated from literature, are presented and the performance of the model evaluated in terms of computation time and percentage deviations to optimal solution. Three scenario analyses are conducted to assess the effect of changing several parameters on the model performance.