Pickup and delivery with electric vehicles under stochastic battery depletion

Highlights

• A pickup and delivery problem with electric vehicles under stochastic battery depletion is addressed.

• A chance-constrained mixed integer non-linear programming model is presented.

• A linear approximation for energy requirement estimation is proposed.

• Respecting stochastic battery depletion alleviates the range anxiety of drivers.

• The added value of the study is shown by means of several numerical experiments.

Abstract

The use of electric vehicles in passenger and freight transportation has been increasing especially in developed countries. Stochastic battery depletion is one of the concerns that needs to be addressed in electric vehicle routing. This paper accordingly proposes a chance-constrained mixed integer non-linear programming model and a linear approximation for the pickup and delivery problem with electric vehicles under stochastic battery depletion assumption. The ability to respect stochastic battery depletion could also help to alleviate the range anxiety of drivers. We have showed the added value of respecting stochasticity in battery depletion and applicability of the proposed approximation by means of several numerical experiments.

Introduction

Prominent goals stated in the 2011 European White Paper to achieve a competitive and resource efficient transport system are to “halve the use of ‘conventionally-fuelled’ cars in urban transport by 2030; phase them out in cities by 2050; achieve essentially CO₂-free city logistics in major urban centres by 2030.” (EU White Paper, 2011). The term ‘conventionally-fuelled’ refers to vehicles that use non-hybrid, internal combustion engines. One of the alternative transportation options to conventional ones is Battery-Electric Freight Vehicles (BEV). They are currently regarded as a viable solution to achieve a sustainable logistic system (Savelsbergh & Van Woensel, 2016).

BEV offer several benefits in urban applications. The main benefits that could be attained by the use of BEV for transportation can be summarized as follows: (i) reduction or elimination of tailpipe emissions contributing to air quality, (ii) ensuring relatively higher energy efficiency especially in lower speeds, and (iii) reduction of road traffic noise nuisance by the help of quieter engines for drivers and people in residential areas (Afroditi et al., 2014, Pelletier et al., 2016).

At the moment the current practice is to use conventional gasoline and diesel vehicles for the vast majority of freight deliveries in urban environments.¹ However, fleet proportion of electric vehicles for both passenger and freight transportation especially in the developed countries continually increases by means of academic research, technological developments, aggressive boost of authorities and applied projects in real life distribution networks. For instance, a research conducted in Urban System Laboratory at Imperial College London demonstrates that switching ten percent of London’s current truck and van fleets from diesel to electrical by 2021 could enable to save the capital close to £1 billion and contribute to the correction of London’s air pollution problems.² One of the projects on the topic named FREVUE³ funded by the European Union’s Seventh Framework Programme provided evidence on how the use of BEV can contribute to emission free city logistics and how these vehicles can be used as a viable alternative for conventional ones.

For urban applications, one of the main weaknesses in BEV is range anxiety, which is a feeling that your electric vehicle cannot complete your planned trip (Jing, Yan, Kim, & Sarvi, 2016). That anxiety may arise due to various reasons such as optimistic vehicle range limit indication or uncertain traffic conditions. Improving the accuracy of range-prediction technology is listed as one of the main strategies used to alleviate range anxiety among BEV users (Eisel et al., 2016, Guo et al., 2018). Road and traffic conditions are the prominent factors that affect the rate of battery depletion. Accordingly, for decision makers in logistics management, it is key to plan the most efficient drive route that takes road and traffic conditions into account, which are often uncertain in real life urban problems.

In operational-level urban logistics management, thousands of companies and organizations engaged in delivery and/or collection of goods (or people) are confronted with the vehicle routing problem (VRP) every day (Toth and Vigo, 2014, Braekers et al., 2016). The classical VRP deals with a problem of finding the least cost tours for visiting a number of scattered customers. Our focus here is on a variant of the VRP called one-to-one pickup and delivery problem (PDP) that aims to satisfy paired pickup and delivery requests, i.e., each of the pickup request is associated with a single delivery destination (Cordeau et al., 2008, Şahin et al., 2013). Fig. 1 presents a generic representation of the one-to-one PDP with electric vehicles containing a depot, two battery swap stations, three vehicles (routes) and 14 requests. For each request $i,i^{+}$ on the upper part of each node refers a pickup point and $i^{-}$ refers the corresponding delivery point. Values on the lower part of each node show the remaining battery level of vehicles.

As distinct from the vast of the literature, in line with recent developments in the field we address the one-to-one PDP when BEV are used for delivery operations. Such an attempt requires to consider the following specific features of the problem. First, the maximum range of electric vehicles might restrict to complete some delivery tours and the used batteries might have to be replaced with fully charged ones in the battery swap locations (Yang and Sun, 2015, Koç and Karaoglan, 2016). Second, energy consumption of vehicles along the route might be subject to uncertainty, especially in urban distribution that escalates range anxiety of drivers (Liu, Wang, Yamamoto, & Morikawa, 2018), and several potential costs including vehicle rescue service and penalty costs of not being able to complete delivery plans on-time. To the best of our knowledge, the aforementioned issues have not been tackled in the literature before.

From this point of view, this paper aims to provide a model for the pickup and delivery problem with electric vehicles and stochastic battery depletion. The use of the model could ensure to have applicable delivery plans for logistics decision makers. Note that the provided plans could be regarded as worthwhile in terms of triple bottom line of sustainable development: economic (logistics costs), environmental (energy usage) and social (range anxiety of drivers). The ability to respect stochastic battery depletion could help to alleviate the range anxiety of drivers. Here, exact energy consumption amounts between location pairs are not known in advance. For each arc and vehicle, the uncertain energy consumption is represented by a normally distributed random variable with a certain mean and standard deviation. The uncertainty is thereby quantified.

The rest of the paper is structured as follows. Section 2 presents a brief literature review on the topic to demonstrate the contribution to the field. Section 3 presents a formal description of the studied problem. Section 4 presents the proposed decision support model. Section 5 provides computational analyses. The last section presents conclusions and future research directions.