Effective route planning for battery electric commercial vehicle (ECV) fleets has to take into account their limited autonomy and the possibility of visiting recharging stations during the course of a route. In this paper, we consider four variants of the electric vehicle-routing problem with time windows: (i) at most a single recharge per route is allowed, and batteries are fully recharged on visit of a recharging station; (ii) multiple recharges per route, full recharges only; (iii) at most a single recharge per route, and partial battery recharges are possible; and (iv) multiple, partial recharges. For each variant, we present exact branch-price-and-cut algorithms that rely on customized monodirectional and bidirectional labeling algorithms for generating feasible vehicle routes. In computational studies, we find that all four variants are solvable for instances with up to 100 customers and 21 recharging stations. This success can be attributed to the tailored resource extension functions (REFs) that e...

Exact Algorithms for Electric Vehicle-Routing Problems with Time Windows

The use of electric vehicles for goods distribution opens up a wide range of research problems. Battery electric vehicles (BEVs) operate on batteries that have a limited life, as well as specific charging and discharging patterns which need to be considered in the context of their use for goods distribution. While many transportation problems associated with the integration of freight electric vehicles in distribution management problems have been investigated, there is room for further research on specifically how to model battery degradation and behaviour in such problems. The aim of this paper is to provide tractable models for transportation scientists that will allow predicting the lifetime degradation and instantaneous charging and discharging behaviour of BEV batteries.

Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models

Electric vehicle routing problems (E-VRPs) extend classical routing problems to consider the limited driving range of electric vehicles. In general, this limitation is overcome by introducing planned detours to battery charging stations. Most existing E-VRP models assume that the battery-charge level is a linear function of the charging time, but in reality the function is nonlinear. In this paper we extend current E-VRP models to consider nonlinear charging functions. We propose a hybrid metaheuristic that combines simple components from the literature and components specifically designed for this problem. To assess the importance of nonlinear charging functions, we present a computational study comparing our assumptions with those commonly made in the literature. Our results suggest that neglecting nonlinear charging may lead to infeasible or overly expensive solutions. Furthermore, to test our hybrid metaheuristic we propose a new 120-instance testbed. The results show that our method performs well on these instances.

/pdf/the-electric-vehicle-routing-problem-with-nonlinear-charging-48uim4cq81.pdf

The electric vehicle routing problem with nonlinear charging function

Since the mid-2000s, electric vehicles have gained popularity in several countries even though their market share is still relatively low. However, most gains have been made in the area of passenger vehicles and most technical and scientific studies have been devoted to this case. By contrast, the potential of electric vehicular technology for goods distribution has received less attention. The issues related to the use of electric vehicles for goods distribution reveal a wide range of relevant research problems. The aims of this survey paper are to provide transportation researchers an overview of the technological and marketing background needed to conduct research in this area, to present a survey of the existing research in this field, and to offer perspectives for future research.

50th Anniversary Invited Article-Goods Distribution with Electric Vehicles: Review and Research Perspectives

The use of electric vehicles (EVs) in freight and passenger transportation gives birth to a new family of vehicle routing problems (VRPs), the so-called electric VRPs (e-VRPs). As their name suggests, e-VRPs extend classical VRPs to account (mainly) for two constraining EV features: the short driving range and the long battery charging time. As a matter of fact, routes performed by EVs usually need to include time-consuming detours to charging stations. Most of the existing literature on e-VRPs relies on one of the following assumptions: i) vehicles recharge to their battery to its maximum level every time they reach a charging station or ii) the amount of battery charge is a linear function of the charging time. In practical situations, however, the amount of charge (and thus the time spent at each charging point) is a decision variable and battery charge levels are a concave function of the charging times. In this research we introduce the electric vehicle routing problem with non-linear charging functions (e-VRP-NLCF). We propose a mixed-integer linear programming (MILP) formulation that, running on a commercial solver, is able to solve small instances of the problem. To tackle large-scale instances we propose a metaheuristic that uses a MILP formulation to find the optimal charging policy. We report on extensive computational experiments evaluating the performance of the proposed methods and analyzing the impact on the solutions of different charging policy assumptions.

https://hal.archives-ouvertes.fr/hal-01179356/document

The electric vehicle routing problem with non-linear charging functions

The green vehicle routing problem (Green VRP) is an extension of the VRP in which routes are performed using alternative fuel vehicles (AFVs). AFVs have limited tank capacity, so routes may visit alternative fuel stations (AFSs) en-route. We propose a simple yet effective two-phase heuristic to tackle the Green VRP. In the first phase our heuristic builds a pool of routes via a set of randomized route-first cluster-second heuristics with an optimal AFSs insertion procedure. In the second phase our approach assembles a Green VRP solution by solving a set partitioning formulation over the columns (routes) stored in the pool. To test our approach, we performed experiments on a set of 52 instances from the literature. The results show that our heuristic is competitive with state-of-the-art methods. Our heuristic unveiled 8 new best-known solutions, matched another 40, and delivered solutions with an average gap of 0.14% for the 4 remaining instances.

A multi-space sampling heuristic for the green vehicle routing problem

Motivated by stricter environmental regulations, government incentives, branding opportunities, and potential cost reductions, companies are replacing their conventional vehicles (CVs) with electric vehicles (EVs). However, due to financial and operational restrictions, these fleet transitions usually occur in several stages. This introduces new operational challenges, because most existing fleet management and routing tools are not designed to handle hybrid fleets of CVs and EVs. In this paper, we study a problem arising in the daily operations of telecommunication companies, public utilities, home healthcare providers, and other businesses: the technician routing and scheduling problem with conventional and electric vehicles (TRSP-CEV). To solve this problem we propose a two-phase parallel matheuristic. In the first phase the matheuristic decomposes the problem into several vehicle routing problems with time windows, and it solves these problems (in parallel) using a greedy randomized adaptive search procedure (GRASP). At the end of each GRASP iteration, the routes making up the local optimum are stored in long-term memory. In the second phase, the method uses the stored routes to find a TRSP-CEV solution. We discuss computational experiments on industrial instances provided by a French utility. We provide managerial insight into the impact of the proportion of EVs in the fleet on metrics such as the number of routes, the total operational cost, and the CO2 emissions. Additionally, we present state-of-the-art results for the closely related electric fleet size and mix vehicle routing problem with time windows and recharging stations.

https://hal.archives-ouvertes.fr/hal-01813887/document

The technician routing and scheduling problem with conventional and electric vehicle

Electric vehicle routing problems (eVRPs) extend classical routing problems to consider the limited driving range of electric vehicles. In general, this limitation is overcome by introducing planned detours to battery charging stations. Most existing eVRP models rely on one (or both) of the following assumptions: (i) the vehicles fully charge their batteries every time they reach a charging station, and (ii) the battery charge level is a linear function of the charging time. In practical situations, however, the amount of charge is a decision variable, and the battery charge level is a concave function of the charging time.In this paper we extend current eVRP models to consider partial charging and nonlinear charging functions. We present a computational study comparing our assumptions with those commonly made in the literature. Our results suggest that neglecting partial and nonlinear charging may lead to infeasible or overly expensive solutions.

/pdf/the-electric-vehicle-routing-problem-with-partial-charging-1iik0iy9hy.pdf

The electric vehicle routing problem with partial charging and nonlinear charging function

This research introduces the multi-product capacitated facility location problem with general production and building costs (MP-CFLPGC). The MP-CFLPGC extends previous problems found in the literature by including multiple products and general production and building cost functions that allow the modeling of different behaviors like economies of scale and congestion. The MP-CFLPGC is formulated as a mixed integer linear program (MILP). To evaluate the performance of the proposed formulation we analyze the results of a commercial optimizer on a set of 288 randomly generated test instances that resemble the Colombian cement industry supply chain. After one hour the optimizer achieved an optimality gap of 1.0 % or less in 55 % out of the 288 test instances. On average the optimality gap was 3.57 %. Additionally, we propose a randomized mathematical-programming-based heuristic for the test instances where the MILP formulation presents significantly high optimality gaps.

Alejandro Montoya

Papers

The electric vehicle routing problem with nonlinear charging function

A multi-space sampling heuristic for the green vehicle routing problem

The technician routing and scheduling problem with conventional and electric vehicle

The electric vehicle routing problem with partial charging and nonlinear charging function

Multi-product capacitated facility location problem with general production and building costs