A Pickup and Delivery Problem with Time Windows by Electric Vehicles

The Pickup and Delivery Problem with Time Windows (PDPTW) is a Vehicle Routing Problem with Time Windows (VRPTW) in which each customer, together with a demand and a time window for the service, specifies also an origin (pickup) and a destination (delivery). Our work manly extends the PDPTW to the case in which the fleet consists of electric vehicles (E-PDPTW), in order to exploit their significant advantages in terms of energy saving and sustainability. The E-PDPTW is then modeled as a multi-objective optimization problem in order to minimize the total travel distance, the total cost due to the used electric vehicles and the penalties due to the delayed services. In addition, beyond the classical vehicle routing constraints, in order to consider the practical difficulties due to the limited battery life of the electric vehicles (EVs) and to the poor availability of the recharging stations, some additional constraints are also imposed. The problem is then formulated as a multiobjective mathematical programming model and solved by applying the Weighted Sum Method (WSM) with weights determined by an approach derived from the Analytical Hierarchical Process (AHP).