A pick-up and delivery problem with time windows by electric vehicles

In the pick-up and delivery problem with time windows (PDPTW), each transportation service is delivered, from an origin to a destination, satisfying both the time windows and the precedence constraints. This paper addresses the related vehicle routing problem by using only electric vehicles (EVs) and by introducing the recharging stations (RSs). The problem is formulated as a multi-objective mixed integer linear model for minimising the total travel distance, the total cost for the EVs used and the total penalty cost for the unsatisfied time windows. In addition, length constraints on the routes are imposed in order to include several aspects such as the limited availability of the RSs. The weighted sum method is adopted and, to properly set the weights, three methods, derived from the analytical hierarchical process, are compared. Computational experiments on some instances are carried out, in order to assess the behaviour of our approach in terms of solution quality.