Review Article

A Survey on the Electric Vehicle Routing Problem: Variants and Solution Approaches

Table 1

Overview of the E-VRP variants and related problems.

Reference Problem nameChargingOtherObjective
CTWMIXLRPFLNLPRDFCBSTDH

Bektaş and Laporte [40]PRPXXEmission model, speed limitationTotal costs: labor, fuel and emission as a function of load and speed

Conrad and Figliozzi [22]Recharging VRPXXXVehicle number and total traveling costs: distance, service time, recharging time

Gonçalves et al. [21]VRPPD with mixed fleetXXXNo CS location, time constraintTotal traveling costs: fixed and variable

Demir et al. [32]PRPXXEmission modelTotal traveling costs: labor, fuel and emission as a function of load and speed; speed optimization

Erdoğan and Miller-Hooks [23]GVRPXAFVs, limited route durationVehicle number and total traveled distance

Omidvar and Tavakkoli-Moghaddam [24]GVRPXXXXAFVs, limited fuel capacity and route duration, congestion managementTotal costs: vehicle fixed costs, distance, time and emission

Abdallah [41]PHEVRPTWXXXXXElectric charge cost is neglectedRouting costs: time run on the fossil oil

Barco et al. [34, 42]E-VRP and charge schedulingXXXXXEnergy consumption and battery degradation model, private and public CS, time-dependent energy ratesEnergy consumption

Davis and Figliozzi [10]XXEnergy consumption model with speed profiles, limit route duration and energy consumption (battery capacity), no recharging during the routeTotal costs: vehicle purchase, energy, maintenance, tax incentive, battery replacement, routing

Van Duin et al. [43]FSMVRPTW, EVFSMVRPTWXXXNo recharge, range constrained by battery, relaxed time window constraints, emissionTotal costs: vehicle fixed costs, time and distance

Adler and Mirchandani [44]Online routing of BEVsXBattery reservations, waiting for fully charged batteryThe average vehicle delay time

Alesiani and Maslekar [45]BEV routingXWaiting time cost at CS is proportional to the number of EVs in CS, limiting the number of CSs in route and number of vehicles in CS, energy consumption modelTraveling, charging and energy consumption costs

Demir et al. [37]PRPXXFuel consumption and emission modelBi-objective minimization of fuel consumption and total driving time

Felipe et al. [46]GVRP-MTPRXXXXTotal recharging costs: fixed and variable

Preis et al. [35]Energy-optimized routing of BEVsXXXEnergy consumption modelEnergy consumption

Sassi et al. [47]
Sassi et al. [48]
Sassi et al. [49]
HEVRP-TDMF VRP-HFCC VRP-MFHEVXXXXXTime-dependent charging costs, operating windows and power limitation of CS, compatibility of BEVs with chargers, electricity grid capacity [47, 49]Vehicle number and total costs: fixed, routing, charging and waiting costs

Schneider et al. [25]E-VRPTWXXXVehicle number and total traveled distance

Zündorf [50]EVRCXXXXBattery constrained SPP, different CS types: regular, superchargers and BSS, energy consumption modelTravel time

Bruglieri et al. [29, 51]E-VRPTWXXXXVehicle number and total travel, recharging and waiting time

Goeke and Schneider [30]E-VRPTWMFXXXXEnergy consumption model: varying BEV load, road slopeVehicle number and different objectives: (i) distance, (ii) costs: labor, driver wage, vehicle propulsion - electric energy and diesel costs, (iii) (ii) + battery replacement cost

Lebeau et al. [52]FSMVRPTW-EVXXXXEnergy consumption model based on the collected data, recharge only at the depotTotal costs: vehicles fixed and operating costs, labor costs

Moghaddam [53]E-VRPTWPRXXXXCapacitated CSsVehicle number and number of CSs

Pourazarm et al. [54]Single/Multi BEV routingXXXHomogeneous and in-homogeneous CSsTotal time

Schneider et al. [55]VRPIS (EVRPRF)XXTotal travel and fixed vehicle costs

Yang and Sun [56]BSS-EV-LRPXXXTotal routing and construction costs

Desaulniers et al. [57]E-VRPTW -SF/MF/SP/MPXXXXVehicle number and total routing costs

Doppstadt et al. [58]HEV-TSPXXFour modes of travel: combustion, electric, charging and boost mode, no CSs visitsTotal costs as long as maximal route duration is not overrun

Hiermann et al. [31]E-FSMFTWXXXXVehicle number and total costs: vehicle fixed and routing costs

Keskin and Çatay [28]E-VRPTWPRXXXXVehicle number and total traveled distance

Koç and Karaoglan [59]GVRPXAFVs, limited route durationVehicle number and total traveled distance

Lin et al. [60]E-VRPXXEnergy consumption model and load effectTotal costs: battery charging, travel time and waiting costs

Masliakova [61]Routing and charging of electric busesXXXEnergy consumption model, two types of buses depending on the charging event: en-route or at depot, homogeneous and in-homogeneous CSsInvestment and operations costs, a travel time of passengers

Mirmohammadi et al. [62]Periodic green VRPXXXXPeriodic routing, primary and secondary time windows, static traffic conditions within a periodTotal emissions, total service time and penalties

Montoya et al. [63]GVRPXAFVs, limited route durationVehicle number and total traveled distance

Roberti and Wen [64]E-TSPTWXXXTotal traveled distance

Schiffer et al. [11, 27]E-LRPTWPRXXXXXCSs at customers’ locations, pickup and delivery, multiple driver shifts and multiple planning periods, emissionsTotal costs during the planning period: CS and BEV investment costs, fixed costs (tax, maintenance), distance dependent costs (energy)

Wen et al. [65]E-VSPXXTimetable bus trips, multiple depots, time windows of depots and CSsTotal cost: vehicles and traveling costs

Andelmin and Bartolini [66]GVRPXAFVs, limited route durationVehicle number and traveled distance

Çatay and Keskin [67]E-VRPTWPRXXXXXNormal and fast charger at CSsVehicle number and total recharging costs

Froger et al. [68]E-VRP-NL-CXXXCapacitated CSsTotal travel, service, charging and waiting time

Hof et al. [69]BSS-EV-LRPXXXTotal routing and construction costs

Leggieri and Haouari [70]GVRPXAFVs, limited route durationVehicle number and total traveled distance

Mancini [71]HVRPXFull instant rechargeTotal traveled distance with penalties for using internal combustion engine

Montoya et al. [72]E-VRP-NLXXXCS types: slow, moderate and rapidTotal travel and recharging time

Schiffer and Walther [73]E-LRPTWPRXXXXXTotal distance, number of vehicles and CSs used, total costs: investment costs of BEVs and CSs, and operational costs

Shao et al. [74]EVRP-CTVTTXXXXTotal costs: travel, charging, penalty, and fixed vehicle costs

Sweda et al. [75]Adaptive routing and recharging policies of EVsXXHeterogeneous CSs - the probability of being available and expected waiting time, origin-destination pairsTraveling, waiting and recharging costs

Vincent et al. [76]HVRPXXVertex demand in CVRP is associated with travel time for each arc in HVRPTotal costs

Amiri et al. [39]BSS location & schedulingXXMulti-objective - minimization of battery charging and power loss costs; deviation from nominal voltage; and network capacity releasing

Bruglieri et al. [77]E-VRePXXOne way car sharing service, workers with bicycles go to the EVs locations and relocate them, battery level demand requestMulti-objective: minimization of the workers employed; minimization of the duration of the longest route; and maximization of the number of served relocation requests

Joo and Lim [78]EV routingEnergy SPP, no recharging, energy consumption modelMinimize energy consumption and average speed on the path

Keskin and Çatay [79]E-VRPTW-FCXXXXXVehicle number and total recharging costs

Keskin et al. [80]E-VRPTW-FCXXXXM/M/1 queuing system at capacitated CSs, battery capacity restriction, four planning intervals in a day, partial recharge not evident in paperTotal cost: energy cost, routing, labor and penalties for late arrivals

Kullman et al. [81]E-VRP-PPXXXPublic and private CSs, capacitated CS, single charging technology per CSExpected time to visit all the customers

Li et al. [82]MBFM & recharging problemXXElectric, diesel, compressed natural gas and hybrid-diesel busesTotal network benefit of replacing old vehicles with new ones within the planning horizon and budget constraints

Lu et al. [83]MTFSPXXXXTravel request are known a priori in time-varying origin-destination tables, service and deadheaded trips with different consumption rate, BEVs have higher priority than ICEVsTotal operating cost of a taxi company

Masmoudi et al. [84]DARP-EVXXXXEnergy consumption model of Genikomsakis and Mitrentsis [85] with constant speed, acceleration and road slope; different vehicle resources: accompanying person seat, handicapped person seat, stretcher and/or a wheelchair, limited user ride timeTotal routing costs (distance)

Paz et al. [86]MDEVLRPTW - BS/PR/BSPRXXXXXXThree MIP models depending on the partial recharge and BSSTotal traveled distance

Pelletier et al. [87]EFV-CSPXXXPreemptive charging with a limited number of chargers and charging events at the depot, time-dependent energy costs, FRD charge, grid restriction, cyclic and calendar battery degradationTotal charging costs

Poonthalir and Nadarajan [38]F-GVRPXFuel consumption model, varying speed, AFVs, limited route durationBi-objective: routing costs; and fuel consumption

Schiffer and Walther [88]LRPIFXXXXXLoading and refueling facilitiesTotal costs: investment costs of vehicles and facilities, routing costs

Schiffer and Walther [89]RELRPTWPRXXXXXUncertain customer pattern scenarios over working days regarding the spatial customer distribution, demand and service time windowsTotal costs: investment costs of vehicles and facilities, routing costs

Shao et al. [90]E-VRPXXEnergy consumption model: cargo load, uncertain travel speedTotal costs: travel, charging and fixed vehicle costs

Wang et al. [91]BEV routingXParking fee, capacitated CSs - queuing timeMulti-objective minimization of travel time: driving, queuing and charging time; charging costs: electricity, service and parking fee; energy consumption

Zhang et al. [36]E-VRPXEnergy consumption model, emissions, static speed, charging time unknownEnergy consumption

Basso et al. [92]2sEVRPXXXXEach CSs can have different charging rate, energy consumption model for road segments: speed profile, road slope, accelerationTotal energy consumption

Breunig et al. [93]E2EVRPXTwo echelons - first ICEVs and second BEVs, full recharge when visiting CSs, charging time unknownTotal routing costs

Bruglieri et al. [94]GVRPXAFVs, limited route durationVehicle number and total traveled distance

Froger et al. [95]E-VRP-NLXXXTotal travel and charging time

Hiermann et al. [96]E-FTWXXXXXXPropulsion mode decisionTotal costs: fixed and variable

Jie et al. [97]2E-EVRP-BSSXXRouting in two echelons, sensitivity analysis of battery driving range and vehicle emissionsTotal routing costs, the battery swapping costs and the handling costs at the satellites

Koyuncu and Yavuz [98]MGVRPXXXXXXICEVs (fixed recharge time) and AFVs, node- and -arc MILP formulation, single recharge technology per CS, additional modeling: customer demands, customer vehicle restrictions, subscription or pay-as-you-go refueling costs, completely heterogeneous fleet, last-mile delivery and closed time windowsTotal traveling cost

Macrina et al. [99]GMFVRP-PRTWXXXXXXXSingle recharge technology per CS, but different charging technologies between CSs, energy consumption model for road segments with time-dependent speedsCost of energy recharged during the route and at the depot, fuel costs, and cost related to traveled distance

Macrina et al. [33]GMFVRP-PRTWXXXXXXSingle recharge technology per CS, but different charging technologies between CSsRecharging, routing and activation costs, limit emissions

Normasari et al. [100]CGVRPXXAFVs, limited route durationVehicle number and total traveled distance

Reference: referenced paper; Problem name: the name of the analyzed problem; 13 columns representing characteristics of the problem in the following order: C: vehicle load (cargo) capacity, TW: customer time windows, MIX: heterogeneous (mixed) fleet, LRP: location routing problem, F: fixed (constant) refuel (recharge) time, L: linear charging process, NL: nonlinear charging process, PR: partial recharge strategy, DFC: different charging technologies, BS: battery swap strategy, TD: time-dependent travel times, H: hybrid vehicles, Other: some special characteristic of the problem; Objective: the objective function for the optimization.