A pick-up and delivery problem with time windows by electric vehicles (original) (raw)

Abstract

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). Purpose What are the reason(s) for writing the paper or the aims of the research? The main goal of this research is to address a problem that presents many significant and relevant impacts, among the others : a reduction of the polluting emissions thanks to the use of EVs (environmental sustainability); an optimized delivery of door-to-door transportation services to the citizens and, in particular, to the elderly and disabled people (social sustainability) and finally, significant reductions in the use of fossil-fuel and considerable energy savings (economic sustainability). Design/methodology/approach How are the objectives achieved? Include the main method(s) used for the research. What is the approach to the topic and what is the theoretical or subject scope of the paper? Starting from the state-of-art, a multi-objective mixed integer linear formulation of the E-PDPTW is proposed with the aim to minimize the total travel distance, the total cost due to the used electric vehicles and due to the penalties for the delayed services. From a methodological point of view, the WSM is adopted in order to have a unique objective function, expressed as weighted sum of the above cited terms. In addition, in order to properly set the weights, a method, derived from the AHP, is proposed. Beyond the classical PDPTW constraints, additional conditions are imposed with reference to the use of EVs such as an upper bound on the total distance of each route. The final solution is then expressed in terms of both the optimal routes and the charging stations used in each of them. Originality/value What is new in the paper? State the value of the paper and to whom. The originality of the work consists in introducing the use of the EVs in the context of the multi-objective PDPTW. Moreover, the paper analyzes the routing problem of the EVs taking into consideration also the recharging stations, topic recently investigated in literature by very few researchers.

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