Post on 19-Oct-2020
Review ArticleA Survey on the Electric Vehicle Routing Problem: Variants andSolution Approaches
Tomislav ErdeliT and TonIi CariT
Faculty of Transport and Traffic Sciences, University of Zagreb, Vukelićeva Street 4, Zagreb, Croatia
Correspondence should be addressed to Tomislav Erdelić; terdelic@fpz.hr
Received 14 December 2018; Revised 5 March 2019; Accepted 2 April 2019; Published 9 May 2019
Guest Editor: Eduardo Lalla-Ruiz
Copyright © 2019 Tomislav Erdelić and Tonči Carić. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.
In order to ensure high-quality and on-time delivery in logistic distribution processes, it is necessary to efficiently manage thedelivery fleet. Nowadays, due to the new policies and regulations related to greenhouse gas emission in the transport sector,logistic companies are paying higher penalties for each emission gram of CO2/km. With electric vehicle market penetration, manycompanies are evaluating the integration of electric vehicles in their fleet, as they do not have local greenhouse gas emissions,produce minimal noise, and are independent of the fluctuating oil price. The well-researched vehicle routing problem (VRP) isextended to the electric vehicle routing problem (E-VRP), which takes into account specific characteristics of electric vehicles.In this paper, a literature review on recent developments regarding the E-VRP is presented. The challenges that emerged with theintegration of electric vehicles in the delivery processes are described, together with electric vehicle characteristics and recent energyconsumption models. Several variants of the E-VRP and related problems are observed. To cope with the new routing challenges inE-VRP, efficient VRP heuristics and metaheuristics had to be adapted. An overview of the state-of-the-art procedures for solvingthe E-VRP and related problems is presented.
1. Introduction
The vehicle routing problem (VRP) is an NP-hard optimiza-tion problem that aims to determine a set of least-cost deliv-ery routes from a depot to a set of geographically scatteredcustomers, subject to side constraints [1]. The problem wasfirst defined by Dantzig and Ramser [2] as the Truck Dis-patching Problem. VRP is a generalization of the well-knowntraveling salesman problem (TSP), which aims to design oneleast-cost route to visit all the customers. The problem hasapplications in several real-life optimization problems, whichhas led to the definition of many problem variants over theyears: limited vehicle load capacity (capacitated VRP, CVRP),customer time windows (VRPwith time windows, VRPTW),multiple depots (multidepot VRP, MDVRP), pickup anddelivery (VRP with pickup and delivery, VRPPD), time-dependent travel time (time-dependent VRP, TD-VRP), het-erogeneous fleet (mixed fleet VRP, MFVRP), etc. [3, 4].Due to the complexity of the problem, exact procedures areonly capable of optimally solving small-sized problems: up
to 360 customers for CVRP [5] and 50-100 customers forVRPTW [6]. Over the years, a vast number of heuristics,metaheuristics, and hybrid procedures were proposed forsolving different VRP problems.
In the past decade, the European Union (EU) hasannounced many new actions and regulations related togreenhouse gas (GHG) emissions in the transport sector[7]. External factors and the rise of social and ecologicalawareness have prompted green initiatives in many com-panies. Conventional internal combustion engine vehicles(ICEVs), which are dependent on limited fossil fuels, severelypollute the environment, especially in congested urban areas.According to WEEA [8], the EU intends to decrease GHGemissions by 20% and 40% by 2020 and 2030, respectively.Sbihi and Eglese [9] introduced the research field of greenlogistics, which deals with the sustainability of deliveryprocesses by taking into account environmental and socialfactors. With the electric vehicle (EV) market penetration,many logistic companies evaluated the use of the EVs intheir vehicle fleet in order to decrease GHG emissions and,
HindawiJournal of Advanced TransportationVolume 2019, Article ID 5075671, 48 pageshttps://doi.org/10.1155/2019/5075671
http://orcid.org/0000-0002-8012-0090http://orcid.org/0000-0001-8564-4304https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2019/5075671
2 Journal of Advanced Transportation
therefore, reduce the charges for every emission gram ofCO2/km. EVs have several advantages compared to ICEVs:(i) they do not have local GHG emissions; (ii) they produceminimal noise; (iii) they can be powered from renewableenergy sources; and (iv) they are independent of the fluctu-ating oil price [10, 11]. There are two basic configurations ofEVs: the battery electric vehicle (BEV), which is exclusivelypowered from batteries mounted inside the vehicle, and thehybrid electric vehicle (HEV), which can be powered frombatteries inside the vehicle or by other energy sources, mostcommonly internal combustion engine. The plug-in HEV(PHEV) can be recharged by connecting the plug to theelectric power source. In this paper mostly BEVs for logisticpurposes are considered, where two main problems come tothe fore: limited driving range and the need for additionalrecharging infrastructure.
Due to the limited battery capacity, the range that deliveryBEVs can achieve with a fully charged battery is 160-240 km[12], which is much lower than the 480-650 km range ofICEVs [13]. To achieve a similar driving range as ICEVs, BEVshave to visit charging stations (CSs) more frequently. Today,there is still a lack of CSs in the road network infrastructure,and their locations and energy demand should be plannedin future infrastructural plans. For an empty BEV to becomeoperable again, battery energy has to be renewed at a CS.This can be performed in two ways: (i) by swapping emptybatteries with fully charged ones at Battery Swapping Station(BSS) or (ii) by charging at CS [14, 15]. The former processcan be performed in a time comparable to the refueling timeof ICEVs. In the latter process BEVs recharge their batteries atCSs by plugging into the electric power source. The rechargetime depends on the state of charge (SoC) when entering theCS, the desired SoC level when leaving CS, and the chargingfunction.
1.1. Recent Literature Reviews and Scientific Contribution.Here we present, to our knowledge, the most recent literaturereviews on the E-VRP and related problems.
Juan et al. [16] presented a review regarding the envi-ronmental, strategic, and operational challenges of EV inte-gration in logistics and transportation activities. The authorsperformed a comprehensive analysis of environmental chal-lenges including the transportation impact on the pollutionand EVs’ possible contribution to the reduction of carbonemissions. Regarding the strategic challenges, the authorspresented issues related to CSs: battery swap technology,different charging technologies, CS location problem, limitednumber of charges, and charging network; issues related tothe EVs: mixed fleet of ICEVs and EVs, economic challengeswhen integrating EVs in a fleet, and routing constraints.The solution approaches for the E-VRP were presented ingeneral, as a class of VRP solving procedures. Similarly,Margaritis et al. [17] presented practical and research chal-lenges of EVs focusing on battery development, lack ofcharger compatibility, systematic energy management, thelack of optimization procedures that could minimize theEV routing and scheduling decisions, cooling/heating usage,financial sources, novel policies,measures for EVdeploymentin transport services, etc.
Montoya [18] researched several variants of the E-VRP:green VRP (GVRP), E-VRP with partial recharging andnonlinear charging functions, and the technician routingproblem with a mixed fleet of ICEVs and EVs. For eachproblem, effective solving procedures were proposed: multi-space sampling heuristic, iterated local search enhanced withheuristic concentration, and two-phase parallel metaheuris-tic based on solving a set of subproblems and extended set-covering formulation. The authors also formulated a fixedroute vehicle charging problem (FRVCP) with and withouttime windows to optimize the charging decisions for a routewith a fixed customer sequence. The authors did not focus asmuch on reviewing the E-VRP literature, especially not on theprocedures for solving the problem. Compared to Montoya[18], this paper did not focus as much on the FRVCP andtechnician routing problem or on detailed procedures usedto solve those problems.
The most recent survey on the E-VRP is presented byPelletier et al. [19] and it includes technical backgroundon EV types and batteries, EV market penetration, EVcompetitiveness and incentives, and an overview of theexisting research regarding EVs in transportation science.The authors provided a comprehensive review on, at the time,the latest solving procedures for the E-VRP with mixed fleetand optimal paths and covered several key papers regardingpartial recharges, hybrid vehicles, and different chargingtechnologies.
In this paper, a survey on the E-VRP is presented,which includes approaches for solving the E-VRP and relatedproblems that emerged with BEVs integration in the logisticprocesses.The focus is not on the economic and environmen-tal challenges related to BEVs. Most of the latest literaturereviews were published in 2016; hence, to the best of ourknowledge, there is no published research that summarizesthe state-of-the-art research in the E-VRP field. In this paperwe outline the following contributions:
(i) a review of the recent energy consumption modelsthat could be used in BEV routing models;
(ii) an updated literature review and a concise tablesummary of already reviewed E-VRP variants suchas GVRP, mixed fleet, BSSs, partial recharges, anddifferent charging technologies;
(iii) a review of the additional emerged E-VRP variants,which include hybrid vehicles, CS siting, nonlinearcharging function, dynamic traffic conditions andcharging schedule optimization;
(iv) a comprehensive analysis of operation research proce-dures in the E-VRP, which includes an overview of theprocedures employed for solving various E-VRP vari-ants, highlighting state-of-the-art procedures, and aconcise table summary of the applied procedures.
1.2. Organization of This Paper. The remainder of this paperis organized as follows. In Section 2, the E-VRP is describedand the literature review of the basic problem formulationis presented. In Section 3, basic characteristics and recentenergy consumption models of BEVs are described together
Journal of Advanced Transportation 3
with the BEV’s application and evaluation in the deliveryprocesses. In Section 4, variants of the E-VRP are presentedwith some related problems from the literature. In Section 5,approaches for solving E-VRP are presented, which includestate-of-the-art exact, heuristic, metaheuristic, and hybridprocedures.The conclusion and future research directions aregiven in Section 6.
2. Electric Vehicle Routing Problem
With BEV penetration in logistic distribution processes, aproblem of routing a fleet of BEVs has emerged: the E-VRP. The E-VRP aims to design least-cost BEV routes inorder to serve a set of customers by taking into accountoften used constraints: vehicle load capacity, customer timewindows, working hours, etc. [3, 20]. Additionally, BEVshave the limited driving range which directly corresponds tomore frequent recharging events at CSs. CSs can be built atseparate locations as public CSs or mounted at customers’locations as private CSs. The time needed to travel to a CSand the recharging time are important aspects of fleet routing,especially if customer time windows are taken into account.
To the best of our knowledge, the first research regardingthe routing of an electric fleet was published by Gonçalveset al. [21], with the authors observing VRPPD using a mixedfleet of EVs and ICEVs. Refueling of the vehicle is performedat the location where the need for the refueling occurred andthe total refuel time is computed, based on the total distancetraveled by the EV. Conrad and Figliozzi [22] formulatedrecharging VRP in which vehicles with limited driving rangeare allowed to refuel at customers’ locations during the routeto up to 80% of the vehicle’s battery capacity. The authorsdescribed an application of the model and analyzed theimpact of different driving ranges, fixed charging times, andtime windows on EV routes and solution quality. The resultsindicated that customer time windows greatly limit routedistance when recharging time is long and vehicle rangeis constrained. Erdoğan and Miller-Hooks [23] formulatedGVRP in which a fleet of vehicles is powered by alterna-tive fuels (alternative fuel vehicle, AFV): biodiesel, ethanol,hydrogen, methanol, natural gas, electricity, etc. AFVs canrefuel at separately located stations, with fixed refuelingtime. The authors did not consider customer time windowsand vehicle load capacity constraints. New problem-specificinstances were developed and two heuristics for solving theproblem were applied. The results showed that the limitationof driving range severely increased the number of refuelingstations and the total traveled distance in the solution. Asimilar problem was researched by Omidvar and Tavakkoli-Moghaddam [24], in which the authors added vehicle loadconstraint, customer time windows, and congestion manage-ment, as the vehicle can stay at the customer’s location duringthe congestion hours. The authors minimized emission andpollution costs by applying commercial software for solvingsmall instances and two metaheuristics for solving largerinstances. Schneider et al. [25] published the first researchon routing a BEV fleet by taking into account possiblevisits to CSs and charging time dependent on the SoC levelwhen entering a CS. The problem was formulated as E-VRP
with time windows (E-VRPTW) as they took into accountload, battery, and time window constraints. The authorsformulated E-VRPTW as the mixed integer linear program(MILP) on the complete directed graph 𝐺, where customersare modeled as graph vertices and paths between customersare modeled as graph arcs. Here, the basic model formulationis given. Let 𝑉 = {1, . . . , 𝑁} be a set of geographicallyscattered customers who need to be served, and let 𝐹 be a setof CSs for BEVs. In order to allow multiple visits to the sameCS, a virtual set of CSs 𝐹 is defined. Vertices 0 and 𝑁 + 1denote the depot, and every route begins with vertex 0 andends with vertex 𝑁 + 1 (𝑉0,𝑁+1 = 𝑉 ∪ {0} ∪ {𝑁 + 1}). Graph𝐺 is defined as 𝐺 = (𝑉0,𝑁+1 ∪ 𝐹, 𝐴), where 𝐴 is set of arcs,𝐴 = {(𝑖, 𝑗) | 𝑖, 𝑗 ∈ 𝑉0,𝑁+1 ∪ 𝐹, 𝑖 ̸= 𝑗}. Depending on the real-life constraints, different (𝑖, 𝑗) arc values can be interpretedas distance 𝑑𝑖𝑗, travel time 𝑡𝑖𝑗, energy consumption 𝑒𝑖𝑗, speedV𝑖𝑗, cost 𝑐𝑖𝑗, etc. The binary variable 𝑥𝑖𝑗 = {0, 1} is equal to 1if arc (𝑖, 𝑗) is traversed in the solution, and 0 otherwise. Thewhole MILP program for the E-VRPTW with equations forload, battery, time windows, flow, and subtour constraints ispresented by Schneider et al. [25].
In the VRP, it is customary for the primary objectiveto minimize the total number of vehicles used (1) and thento minimize the total distance traveled (2) or some otherobjective functions [26]. Total vehicle number is a primaryobjective as generally greater savings can be achieved withfewer vehicles (vehicle fixed costs, labor cost, etc.). Such anobjective is contradictory as with fewer vehicles total traveleddistance increases and vice versa. By taking into account thehigh purchase cost of BEVs, such a hierarchical objectiveseems justifiable in BEV routing applications [25, 27].
min ∑𝑗∈𝑉∪𝐹
𝑥0𝑗 (1)min ∑
𝑖∈𝑉0∪𝐹,𝑗∈𝑉𝑁+1∪𝐹
,𝑖 ̸=𝑗
𝑑𝑖𝑗𝑥𝑖𝑗 (2)Objective functions can be complex with simultaneous mini-mization of vehicle number, total traveled distance [28], totaltravel times [29], total routing cost and planning horizon [11,27, 30, 31], GHG emission [32, 33], energy consumption [34–36], etc. Total routing costs of BEVs usually consist of BEVacquisition cost, circulation tax, maintenance, costs relatedto the energy consumption (electric energy price), cost ofbattery pack renewal after its lifetime, labor costs, etc. Insteadof a single-objective function, some authors use multiobjec-tive function, i.e., fuel consumption and total driving time[37], fuel consumption and route cost [38], battery swappingand charge scheduling [39], etc. An overview of differentobjectives in E-VRP is presented in Table 1 in the columnObjective.
3. Battery Electric Vehicles inDelivery Processes
The major problem that BEVs in delivery processes arefacing is the limited driving range. Grunditz and Thiringer[101] analyzed over 40 globally available BEVs, which can
4 Journal of Advanced Transportation
Table1:Overviewof
theE
-VRP
varia
ntsa
ndrelatedprob
lems.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Bektaş
andLapo
rte
[40]
PRP
XX
Emissionmod
el,speed
limitatio
n
Totalcosts:
labo
r,fueland
emissionas
afun
ctionof
load
andspeed
Con
radandFigliozzi
[22]
Recharging
VRP
XX
XVe
hiclen
umbera
ndtotal
travelingcosts
:distance,service
time,recharging
time
Gon
çalves
etal.[21]
VRP
PDwith
mixed
fleet
XX
XNoCS
locatio
n,tim
econstraint
Totaltravelin
gcosts
:fixedand
varia
ble
Dem
iretal.[32]
PRP
XX
Emissionmod
el
Totaltravelin
gcosts
:labor,fuel
andem
issionas
afun
ctionof
load
andspeed;speed
optim
ization
Erdo
ğanand
Miller-H
ooks
[23]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Omidvara
ndTavakkoli-
Moghadd
am[24]
GVRP
XX
XX
AFV
s,lim
itedfuel
capacityandroute
duratio
n,congestio
nmanagem
ent
Totalcosts:
vehiclefi
xedcosts
,dista
nce,tim
eand
emission
Abdallah[41]
PHEV
RPTW
XX
XX
XElectriccharge
costis
neglected
Routingcosts
:tim
erun
onthe
fossiloil
Barcoetal.[34,42]
E-VRP
and
charge
schedu
ling
XX
XX
X
Energy
consum
ption
andbatte
rydegradation
mod
el,priv
atea
ndpu
blicCS
,tim
e-depend
entenergy
rates
Energy
consum
ption
DavisandFigliozzi
[10]
XX
Energy
consum
ption
mod
elwith
speed
profi
les,lim
itroute
duratio
nandenergy
consum
ption(battery
capacity),no
recharging
durin
gther
oute
Totalcosts:
vehiclep
urchase,
energy,m
aintenance,tax
incentive,batte
ryreplacem
ent,
routing
VanDuinetal.[43]
FSMVRP
TW,
EVFSMVRP
TWX
XX
Norecharge,range
constrainedby
batte
ry,
relaxedtim
ewindo
wconstraints,em
ission
Totalcosts:
vehiclefi
xedcosts
,tim
eand
dista
nce
Journal of Advanced Transportation 5
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Adlera
ndMirc
hand
ani[44
]Onliner
outin
gof
BEVs
XBa
ttery
reservations,
waitin
gforfullycharged
batte
ryTh
eaverage
vehicled
elay
time
Alesia
niandMaslekar
[45]
BEVrouting
X
Waitin
gtim
ecostatC
Sisprop
ortio
naltothe
numbero
fEVsinCS
,lim
iting
then
umbero
fCS
sinroutea
ndnu
mber
ofvehiclesin
CS,energy
consum
ptionmod
el
Traveling,charging
andenergy
consum
ptioncosts
Dem
iretal.[37]
PRP
XX
Fuelconsum
ptionand
emissionmod
el
Bi-objectiv
eminim
izationof(1)
fuelconsum
ptionand(2)tot
aldrivingtim
e
Felip
eetal.[46]
GVRP
-MTP
RX
XX
XTo
talrechargingcosts
:fixedand
varia
ble
Preise
tal.[35]
Energy-
optim
ized
routingof
BEVs
XX
XEn
ergy
consum
ption
mod
elEn
ergy
consum
ption
Sassietal.[47]
Sassietal.[48]
Sassietal.[49]
HEV
RP-TDMF
VRP
-HFC
CVRP
-MFH
EVX
XX
XX
Time-depend
ent
charging
costs
,operatin
gwindo
wsa
ndpo
wer
limitatio
nof
CS,
compatib
ilityof
BEVs
with
chargers,electric
itygrid
capacity[47,49]
Vehiclen
umbera
ndtotalcosts:
fixed,rou
ting,charging
and
waitin
gcosts
Schn
eidere
tal.[25]
E-VRP
TWX
XX
Vehiclen
umbera
ndtotal
traveled
dista
nce
Zünd
orf[50]
EVRC
XX
XX
Batte
ryconstrainedSP
P,different
CStypes:
regu
lar,superchargers
andBS
S,energy
consum
ptionmod
el
Traveltim
e
Brug
lierietal.[29,51]
E-VRP
TWX
XX
XVe
hiclen
umbera
ndtotaltravel,
recharging
andwaitin
gtim
e
Goeke
andSchn
eider
[30]
E-VRP
TWMF
XX
XX
Energy
consum
ption
mod
el:varying
BEV
load,roadslo
pe
Vehiclen
umbera
nddifferent
objectives:(i)dista
nce,(ii)c
osts:
labo
r,driver
wage,vehicle
prop
ulsio
n-e
lectric
energy
and
dieselcosts
,(iii)(ii)
+batte
ryreplacem
entcost
6 Journal of Advanced Transportation
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Lebeau
etal.[52]
FSMVRP
TW-
EVX
XX
X
Energy
consum
ption
mod
elbasedon
the
collected
data,recharge
onlyatthed
epot
Totalcosts:
vehiclesfixed
and
operatingcosts
,labor
costs
Moghadd
am[53]
E-VRP
TWPR
XX
XX
CapacitatedCS
sVe
hiclen
umbera
ndnu
mbero
fCS
s
Pourazarm
etal.[54]
Sing
le/M
ulti
BEVrouting
XX
XHom
ogeneous
and
in-hom
ogeneous
CSs
Totaltim
e
Schn
eidere
tal.[55]
VRP
IS(EVRP
RF)
XX
Totaltraveland
fixed
vehicle
costs
Yang
andSun[56]
BSS-EV
-LRP
XX
XTo
talrou
tingandconstructio
ncosts
Desaulniersetal.[57]
E-VRP
TW-SF/MF/SP
/MP
XX
XX
Vehiclen
umbera
ndtotalrou
ting
costs
Dop
pstadt
etal.[58]
HEV
-TSP
XX
Four
mod
esof
travel:
combu
stion
,electric
,charging
andbo
ost
mod
e,no
CSsv
isits
Totalcostsas
long
asmaxim
alrouted
urationisno
toverrun
Hierm
annetal.[31]
E-FSMFT
WX
XX
XVe
hiclen
umbera
ndtotalcosts:
vehiclefi
xedandroutingcosts
Keskin
andÇa
tay[
28]
E-VRP
TWPR
XX
XX
Vehiclen
umbera
ndtotal
traveled
dista
nce
Koça
ndKa
raoglan
[59]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Linetal.[60
]E-VRP
XX
Energy
consum
ption
mod
elandload
effect
Totalcosts:
batte
rycharging
,traveltim
eand
waitin
gcosts
Masliakova
[61]
Routingand
charging
ofelectricbu
ses
XX
X
Energy
consum
ption
mod
el,two
typeso
fbu
sesd
epending
onthe
charging
event:en-rou
teor
atdepo
t,ho
mogeneous
and
in-hom
ogeneous
CSs
Investm
entand
operations
costs
,atraveltim
eofp
assengers
Mirm
oham
madietal.
[62]
Perio
dicg
reen
VRP
XX
XX
Perio
dicr
outin
g,prim
aryandsecond
ary
timew
indo
ws,sta
tictraffi
ccon
ditio
nswith
inap
eriod
Totalemissions,totalservice
timea
ndpenalties
Journal of Advanced Transportation 7
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Mon
toya
etal.[63]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Robertiand
Wen
[64]
E-TS
PTW
XX
XTo
taltraveleddista
nce
Schiffere
tal.[11,27]
E-LR
PTWPR
XX
XX
X
CSsa
tcustomers’
locatio
ns,picku
pand
delivery,multip
ledriver
shiftsa
ndmultip
leplanning
perio
ds,
emissions
Totalcostsdu
ringthep
lann
ing
perio
d:CS
andBE
Vinvestm
ent
costs
,fixedcosts
(tax,
maintenance),dista
nce
depend
entcosts(energy)
Wen
etal.[65]
E-VSP
XX
Timetablebu
strip
s,multip
ledepo
ts,tim
ewindo
wso
fdepotsa
ndCS
s
Totalcost:vehicles
andtraveling
costs
And
elmin
and
Bartolini[66]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtraveled
dista
nce
ÇatayandKe
skin
[67]
E-VRP
TWPR
XX
XX
XNormalandfastcharger
atCS
sVe
hiclen
umbera
ndtotal
recharging
costs
Froger
etal.[68]
E-VRP
-NL-C
XX
XCapacitatedCS
sTo
taltravel,s
ervice,charginga
ndwaitin
gtim
e
Hof
etal.[69]
BSS-EV
-LRP
XX
XTo
talrou
tingandconstructio
ncosts
LeggieriandHaouari
[70]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Mancini
[71]
HVRP
XFu
llinsta
ntrecharge
Totaltraveleddista
ncew
ithpenalties
foru
singinternal
combu
stion
engine
Mon
toya
etal.[72]
E-VRP
-NL
XX
XCS
types:slo
w,mod
erate
andrapid
Totaltraveland
recharging
time
Schiffera
ndWalther
[73]
E-LR
PTWPR
XX
XX
X
Totald
istance,num
bero
fvehiclesandCS
sused,totalcosts:
investm
entcostsof
BEVsa
ndCS
s,andop
erationalcosts
Shao
etal.[74]
EVRP
-CTV
TTX
XX
XTo
talcosts:
travel,charging,
penalty,and
fixed
vehiclec
osts
8 Journal of Advanced Transportation
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Swedaetal.[75]
Adaptiv
eroutingand
recharging
policieso
fEVs
XX
Heterogeneous
CSs-
the
prob
ability
ofbeing
availablea
ndexpected
waitin
gtim
e,origin-destin
ationpairs
Traveling,waitin
gand
recharging
costs
Vincentetal.[76]
HVRP
XX
Vertex
demandin
CVRP
isassociated
with
travel
timefor
each
arcin
HVRP
Totalcosts
Amiri
etal.[39]
BSSlocatio
n&
schedu
ling
XX
Multi-ob
jective-
minim
ization
of(1)ba
ttery
charging
and
powe
rlossc
osts;(2)de
viation
from
nominalvoltage;and(3)
networkcapacityreleasing
Brug
lierietal.[77]
E-VRe
PX
X
One
way
carsharin
gservice,wo
rkersw
ithbicycles
goto
theE
Vs
locatio
nsandrelocate
them
,battery
level
demandrequ
est
Multi-ob
jective:(1)
minim
izationof
thew
orkers
employed;(2)m
inim
izationof
thed
urationof
thelon
gestroute;
and(3)ma
ximizationof
the
numbero
fservedrelocatio
nrequ
ests
JooandLim
[78]
EVrouting
Energy
SPP,no
recharging
,energy
consum
ptionmod
el
Minim
izee
nergyconsum
ption
andaveragespeed
onthep
ath
Keskin
andÇa
tay[
79]
E-VRP
TW-FC
XX
XX
XVe
hiclen
umbera
ndtotal
recharging
costs
Keskin
etal.[80]
E-VRP
TW-FC
XX
XX
M/M
/1qu
euingsyste
matcapacitatedCS
s,batte
rycapacity
restr
ictio
n,four
planning
intervalsina
day,partialrechargen
otevidentinpaper
Totalcost:energy
cost,
routing,
labo
rand
penalties
forlate
arriv
als
Kullm
anetal.[81]
E-VRP
-PP
XX
X
PublicandprivateC
Ss,
capacitatedCS
,single
charging
techno
logy
per
CS
Expected
timetovisit
allthe
custo
mers
Lietal.[82]
MBF
M&
recharging
prob
lem
XX
Electric,diesel,
compressednaturalgas
andhybrid-dieselbuses
Totaln
etwo
rkbenefit
ofreplacingoldvehicles
with
new
ones
with
inthep
lann
ingho
rizon
andbu
dgetconstraints
Journal of Advanced Transportation 9
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Luetal.[83]
MTF
SPX
XX
X
Travelrequ
estarekn
own
aprio
riin
time-varying
origin-destin
ationtables,
servicea
nddeadheaded
tripsw
ithdifferent
consum
ptionrate,B
EVs
have
high
erprioritythan
ICEV
s
Totaloperatin
gcostof
ataxi
company
Masmou
dietal.[84]
DARP
-EV
XX
XX
Energy
consum
ption
mod
elof
Genikom
sakis
andMitrentsis[85]w
ithconstant
speed,
acceleratio
nandroad
slope;differentvehicle
resources:
accompanyingperson
seat,handicapp
edperson
seat,stre
tcher
and/or
awheelchair,
limiteduser
ridetim
e
Totalrou
tingcosts
(distance)
Paze
tal.[86]
MDEV
LRPT
W-B
S/PR
/BSP
RX
XX
XX
XTh
reeM
IPmod
els
depend
ingon
thep
artia
lrecharge
andBS
STo
taltraveleddista
nce
Pelletie
retal.[87]
EFV-
CSP
XX
X
Preemptivec
harging
with
alim
itednu
mbero
fchargersandcharging
eventsatthed
epot,
time-depend
entenergy
costs
,FRD
charge,grid
restr
ictio
n,cyclicand
calend
arbatte
rydegradation
Totalchargingcosts
Poon
thalirand
Nadarajan
[38]
F-GVRP
X
Fuelconsum
ption
mod
el,varying
speed,
AFV
s,lim
itedroute
duratio
n
Bi-objectiv
e:(1)rou
tingcosts
;and(2)fue
lcon
sumption
Schiffera
ndWalther
[88]
LRPIF
XX
XX
XLo
adingandrefueling
facilities
Totalcosts:
investm
entcostsof
vehiclesandfacilities,routing
costs
10 Journal of Advanced Transportation
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
Schiffera
ndWalther
[89]
RELR
PTWPR
XX
XX
X
Uncertain
custo
mer
patte
rnscenarioso
ver
workingdays
regarding
thes
patia
lcustomer
distr
ibution,
demand
andservicetim
ewindo
ws
Totalcosts:
investm
entcostsof
vehiclesandfacilities,routing
costs
Shao
etal.[90]
E-VRP
XX
Energy
consum
ption
mod
el:cargo
load,
uncertaintravelspeed
Totalcosts:
travel,chargingand
fixed
vehiclec
osts
Wangetal.[91]
BEVrouting
XParkingfee,capacitated
CSs-
queuingtim
e
Multi-ob
jectivem
inim
izationof
(1)traveltim
e:driving,qu
euing
andcharging
time;(2)ch
arging
costs
:electric
ity,service
and
parkingfee;(3)en
ergy
consum
ption
Zhangetal.[36]
E-VRP
X
Energy
consum
ption
mod
el,emissions,static
speed,charging
time
unkn
own
Energy
consum
ption
Bassoetal.[92]
2sEV
RPX
XX
X
Each
CSsc
anhave
different
charging
rate,
energy
consum
ption
mod
elforroad
segm
ents:
speedprofi
le,
road
slope,acceleration
Totalenergyconsum
ption
Breunigetal.[93]
E2EV
RPX
Twoechelons
-first
ICEV
sand
second
BEVs,
fullrecharge
when
visitingCS
s,charging
timeu
nkno
wn
Totalrou
tingcosts
Brug
lierietal.[94]
GVRP
XAFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Froger
etal.[95]
E-VRP
-NL
XX
XTo
taltraveland
charging
time
Hierm
annetal.[96]
H2E-FT
WX
XX
XX
XProp
ulsio
nmod
edecisio
nTo
talcosts:
fixed
andvaria
ble
Jieetal.[97]
2E-EVRP
-BSS
XX
Routingin
twoechelons,
sensitivity
analysisof
batte
rydrivingrange
andvehiclee
missions
Totalrou
tingcosts
,the
batte
rysw
apping
costs
andtheh
andling
costs
atthes
atellites
Journal of Advanced Transportation 11
Table1:Con
tinued.
Reference
Prob
lem
name
Charging
Other
Objectiv
eC
TWMIX
LRP
FL
NL
PRDFC
BSTD
H
KoyuncuandYavuz
[98]
MGVRP
XX
XX
XX
ICEV
s(fixed
recharge
time)
andAFV
s,no
de-
and-arc
MILP
form
ulation,
single
recharge
techno
logy
per
CS,add
ition
almod
eling:
custo
merdemands,
custo
mervehicle
restr
ictio
ns,sub
scrip
tion
orpay-as-you
-go
refuelingcosts
,completely
heterogeneou
sfleet,
last-
mile
deliveryand
closed
timew
indo
ws
Totaltravelin
gcost
Macrin
aetal.[99]
GMFV
RP-
PRTW
XX
XX
XX
X
Sing
lerecharge
techno
logy
perC
S,bu
tdifferent
charging
techno
logies
between
CSs,energy
consum
ptionmod
elfor
road
segm
entswith
time-depend
entspeeds
Costo
fenergyr
echarged
durin
gther
outeandatthed
epot,fuel
costs
,and
costrelatedto
traveled
dista
nce
Macrin
aetal.[33]
GMFV
RP-
PRTW
XX
XX
XX
Sing
lerecharge
techno
logy
perC
S,bu
tdifferent
charging
techno
logies
between
CSs
Recharging
,rou
tingand
activ
ationcosts
,lim
item
issions
Normasarietal.[100]
CGVRP
XX
AFV
s,lim
itedroute
duratio
nVe
hiclen
umbera
ndtotal
traveled
dista
nce
Refer
ence:referencedpaper;Problem
name:thenameof
theanalyzed
prob
lem;13columns
representin
gcharacteris
ticso
fthe
prob
lem
inthefollo
wingorder:C:
vehicleload
(cargo)c
apacity,T
W:customer
time
windo
ws,MIX
:heterogeneous
(mixed)fl
eet,LR
P:locatio
nroutingprob
lem,F:fixed(con
stant)refuel(recharge)tim
e,L:lin
earc
hargingprocess,NL:no
nlinearc
hargingprocess,PR
:partia
lrecharges
trategy,DFC
:different
charging
techno
logies,BS:batte
rysw
apstr
ategy,TD
:tim
e-depend
enttraveltim
es,H
:hybrid
vehicles,O
ther:som
especialcharacteris
ticofthep
roblem
;Objective:theo
bjectiv
efun
ctionforthe
optim
ization.
12 Journal of Advanced Transportation
be categorized into small, medium-large, high-performing,and sports cars. All of the BEV models utilize lithium-basedbatteries, especially lithium-ion [102] with battery capacityand distance varying within the ranges 12-90 kWh and 85-528 km, respectively. An averagemedium-sized personal BEVhas a battery capacity of 30 kWh, which is enough to travel250 km. In the delivery process, mostly light vans and freightBEVs are used, which have a shorter driving range (160-240 km) compared to the driving range of ICEVs (480-650km) [13, 43, 103]. The reason is that the battery has lowerspecific energy (130 Wh/kg) than the fossil oil (1233Wh/kg),and the amount of energy that can be stored in the batteryis much lower than in the fossil oil. Batteries mounted inBEVs are mostly the main cause of high acquisition costsand technical limitations as the battery degrades over time,resulting in decreased maximal capacity. Pelletier et al. [104]concluded that the battery should be replaced after fiveto ten years or after 1,000 to 2,000 cycles with large SoCvariations. The authors also described factors that influencesuch battery degradation: overcharging, overdischarging,high and low temperatures, high SoC during storage, largedepth of discharge, etc., and they presented battery degra-dation models that can be used in goods distribution withBEVs.
3.1. BEV Application. BEVs are more likely to be used onshort distances and/or in urban areas where they are moreeffective than ICEVs due to the low driving speed, lownoise production, frequent stops, and financial incentives.In cases when the average route length is short, such as theaverage FedEx route length in the USA, which is 68 km[12], BEVs can be applied directly and recharging can beperformed on return to the depot. BEVs are already beingapplied in such occasions: DHL, UPS, FedEx, and Coca-Cola [105, 106] use BEVs mostly for last-mile deliveriesas distances are shorter and vehicle loads are lower. Manycompanies are performing case studies of integrating BEVsin their delivery fleet. Lin et al. [60] were debating the useof BEVs in time-precise deliveries as the long rechargingtime at CS causes hard completion of an on-time delivery,which then significantly increases the overall routing costs.Davis and Figliozzi [10] and van Duin et al. [43] evaluateda wide range of scenarios to compare the routing costs ofICEVs and BEVs. Van Duin et al. [43] concluded that BEVshave the ability to efficiently perform urban freight transportand meanwhile to reduce the GHG emissions and noisenuisance. Davis and Figliozzi [10] reported that BEVs are notcompetitive if the solution to the same problem results in ahigher number of BEVs than the number of ICEVs. For BEVsto be competitive, the authors pointed out a combinationof several key elements: high daily distance (as much asmaximum BEV driving range), low speeds and congestions,frequent customer stops, the reduction of a BEV’s purchasecost by tax incentives or technology development, and longplanning horizon. On the other hand, Schiffer et al. [27]conducted a case study using freight BEVs for deliveries witha planning horizon of five years and compared the resultsto the delivery done by conventional freight trucks. Severalcharacteristics of the performed case study are important:
(i) delivery radius up to 190 km from the depot; (ii) CSslocated at customers’ locations, which allows simultaneouscharging while unloading goods; (iii) already existing strongcurrent at CSs; and (iv) vehicles returning to the depot at leastonce a day. Overall, the authors concluded that there is nooperational limitation when using BEVs compared to ICEVs,as the used number of vehicles and total traveled distance arecompetitive, and at the same time, the overall costs are lowerwith almost 25% less CO2 emission. A year later, Schiffer etal. [11] repeated the case study with more realistic costs whena strong current at the CS is not available and concludedthat, with the higher CS investment costs, BEVs are nolonger competitive. To fully assess the integration of BEVs inlogistic processes, the authors pointed out three key elements:different network structures, future CO2 emission policies,and future technology development (battery capacity andcharging infrastructure).
3.2. Energy Consumption. Due to the low specific energy,energy consumption should be precisely estimated in orderto achieve a BEV’s maximal driving range and to reducethe overall routing costs. The energy consumption can beestimated by simulation models but due to the complexity ofthe E-VRP and unknown driving cycles in advance, mostlymacroscopic models with several real-world approximationsare applied in the BEV routing models. In the availableliterature, energy consumption is often estimated using lon-gitudinal dynamics model (LDM). Here, the LDM of Asameret al. [107] is presented. Force 𝐹 needed to accelerate and toovercome resistances (grade, rolling, and air) is given by (3),where 𝑚 is vehicle mass (mostly empty vehicle), 𝑎 accelera-tion, V vehicle speed, 𝑔 gravitational constant, 𝑓 the inertiaforce of vehicle rotating parts (up to 5% of the total vehiclemass), 𝛼 road slope, 𝑐𝑟 rolling friction coefficient, 𝑐𝑑 air dragcoefficient, 𝜌 air density, and 𝐴 vehicle frontal air surface. If𝐹 ≥ 0, the vehicle is accelerating and power is needed forthe movement of BEV (motor mode); otherwise, if 𝐹 < 0,deceleration (braking) or driving downhill is occurring andenergy is returned into theBEV’s battery as the electric enginehas the ability to return the energy (recuperating mode).By process of recuperation, up to 15% of totally consumedenergy can be returned [51, 108]. Electric power that comesfrom the battery is divided into the auxiliary power 𝑃0 andmechanical power 𝑃𝑚 = 𝐹V. Auxiliary power is spent onthe electronic devices in the vehicle: heating, ventilation,light, etc., which can shorten the BEV’s range up to 30%[109]. Battery power 𝑃𝑏 can be computed by (4), where 𝜇𝑚 isthe transmission coefficient between the electric motor anddrivetrain, 𝜇𝑒 is the conversion ratio from chemical energyin the battery to electric energy, and 𝜇𝑔 is the conversionratio from mechanical energy on wheels to chemical energystored in the battery. Energy is returned into the batteryonly if the force 𝐹 is lower than zero and speed is higherthan the experimentally determined value V𝑚𝑖𝑛 [107]. Energyconsumption can be computed by the time integration of(4).
𝐹 = 𝑚𝑔 sin 𝛼⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟Grade
+ 𝑐𝑟𝑚𝑔 cos 𝛼⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟Rolling
+ 0.5𝑐𝑑𝜌𝐴V2⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟Air
+ 𝑓𝑚𝑎⏟⏟⏟⏟⏟⏟⏟Acc.
(3)
Journal of Advanced Transportation 13
𝑃𝑏 = {{{{{{{{{𝜇𝑒 (𝜇𝑚𝐹V + 𝑃0) , if 𝐹 ≥ 0{{{0, if V ≤ V𝑚𝑖𝑛𝜇𝑔𝐹V + 𝑃0, else, if 𝐹 < 0 (4)
Goeke and Schneider [30] extended the energy consump-tion model by taking into account variable vehicle load masswhen delivering goods without acceleration and brakingprocesses. In the CVRP variants, as customers are beingserved, vehicle load is decreasing. The authors concluded thatactual load strongly improves the solution quality, as a largenumber of solutions generated without taking into accountload distribution tend to be infeasible due to the violation ofbattery capacity or time windows.
Genikomsakis and Mitrentsis [85] presented a morerealistic electric engine model: the load-efficiency curve isapproximated by piecewise function and the normalizationfactor is added to take into account the motor size. Theauthors used the recuperation energy factor dependent onthe vehicle speed as follows: below V𝑚𝑖𝑛 there is no energyrecuperation, beyond V𝑚𝑎𝑥 maximum energy is recuperated,and in between linear interpolation of energy recuperationis assumed. Therefore, regarding the energy recuperation theauthors observed two cases: (i) when recuperated energyexceeds the consumption of the auxiliary devices and theexcess of energy is stored into the battery; (ii) when recu-perated energy is not sufficient to cover the consumptionof the auxiliary devices and thus the energy is drawn fromthe battery. The authors compared their model on nine char-acteristic driving cycles (short/long, congested/uncongested,highway, etc.) to the FASTSim simulation tool [110], and thisresulted in a relative energy consumption error of up to 4%.The developed energy consumption model was used to createa database of coefficients for several key characteristics:motortype, motor power, battery type, road type, road slope, roadspeed limit, etc.
Macrina et al. [99] developed an energy model formixed GVRP with partial recharging and time windows.The authors modeled vehicle speed on arc (𝑖, 𝑗) with threephases ℎ: acceleration (ℎ = 1), constant speed (ℎ = 2),and deceleration (ℎ = 3), resulting with either triangularfunction (1 → 3) or trapezoidal function (1 → 2 →3). The fuel consumption of ICEV is based on the similarLDM model, presented by (5) and (6), where 𝑢𝑖 is the load(cargo) weight, 𝜁 fuel-to-air mass ratio, 𝜅 heating value oftypical diesel fuel, 𝜓 conversion factor, 𝑘 engine frictioncoefficient, 𝑁𝑒 radial engine speed, 𝐷𝑒 engine displacement,𝜇𝑑 diesel engine efficiency, 𝜇𝑑𝑡 drivetrain efficiency, and 𝑡ℎtravel spent in phase ℎ [40, 111]. For the consumption of BEV,the authors proposed a similar model to that presented by(7), where 𝜂+ℎ and 𝜂−ℎ are the efficiency of the electric enginein motor and recuperating mode. The authors compared theproposed energy consumption model to the basic model,where energy consumed is proportional to the distancetraveled, and the energy consumption model of Goeke andSchneider [30], where acceleration and braking processes arenot taken into account. The results showed that, comparedto the proposed energy consumption model, basic energyconsumption model and the model of Goeke and Schneider
[30] produce an average relative error of 70% and 4%,respectively.𝐹𝑖𝑗ℎ (𝑢𝑖)= (𝑔 sin 𝛼 + 𝑐𝑟𝑔 cos 𝛼 + 𝑎 (𝑡𝑖𝑗ℎ)) (𝑚 + 𝑢𝑖) + 0.5𝑐𝑑𝜌𝐴V (𝑡𝑖𝑗ℎ)2 (5)𝐹𝑀𝑖𝑗 (𝑢𝑖) = ∑
ℎ=1,2,3
( 𝜁𝜅𝜓)(𝑘𝑁𝑒𝐷𝑒 + 𝐹𝑖𝑗ℎ (𝑢𝑖) V (𝑡𝑖𝑗ℎ)⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟𝑃𝑀𝑖𝑗ℎ
(𝑢𝑖)
/𝜇𝑑𝜇𝑑𝑡)𝑡ℎ (6)𝐸𝐸𝑖𝑗 (𝑢𝑖) = ∑
ℎ=1,2,3
(𝐹𝑖𝑗ℎ (𝑢𝑖) V (𝑡𝑖𝑗ℎ) /𝜂ℎ) 𝑡ℎ⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟𝐸𝐸𝑖𝑗ℎ
(𝑢𝑖)
,𝜂ℎ= {{{
𝜂+ℎ ≤ 1, 𝐸𝐸𝑖𝑗ℎ (𝑢𝑖) > 0 & 0 ≤ 𝑃𝑀𝑖𝑗ℎ (𝑢𝑖) ≤ 100 kW (ℎ = 1, 2)𝜂−ℎ ≥ 1, 𝐸𝐸𝑖𝑗ℎ (𝑢𝑖) < 0 & − 100 ≤ 𝑃𝑀𝑖𝑗ℎ (𝑢𝑖) ≤ 0 kW (ℎ = 3)(7)
Basso et al. [92] developed an energy consumption modelfor two-stage E-VRP (2sEVRP) that includes detailed topog-raphy and speed profiles. The similar LDMmodel of Asameret al. [107] is applied for computing the energy consumptionon a road segment (link), but with time-dependent speed,varying mass, constant slope, and link distance. For each link,similar to Macrina et al. [99], the three or two characteristicphases of speed curve can be distinguished. In such a way,acceleration and breaking processes before and after theintersection are taken into account. As mass changes duringthe delivery, the energy consumption is expressed as a linearfunction of mass. Then, the shortest energy paths betweenall vertices pairs (customers, depot, CSs) without chargingconstraint are determined by applying the Bellman-Fordalgorithm [112]. A nominal mass value between the mass offull and empty vehicle is used in the computation. The exper-iments showed an average energy estimation error of 2.28%and improved energy feasibility compared to some of theprevious consumptionmodels.The authors also reported thatthe use of average speed consumed at least 24% less energy.
Asamer et al. [107] analyzed the data collected from theBEV trips in order to determine the dependency betweenBEV energy share and average trip speed. Results showed thaton lower speeds V ≤ 30 km/h, most of the energy is spenton the acceleration and auxiliary devices, while on the higherspeeds V ≥ 80 km/h, approx. 70% of total energy is spent onovercoming the air drag force.The slope of the terrain in totalenergy consumption has the lowest share, and its value is evendecreasing with the increase of average trip speed.The rollingresistance energy consumption share does not depend on theaverage trip speed.
Preis et al. [35] analyzed the energy optimal routing ofBEV, where the routes were designed in different terrainslopes and battery capacity scenarios. The authors concludedthat energy savings grow linearly with the maximum altitudedifference and that decreasing the battery capacity of BEVsdoes not affect the recharging schedule but increases thetotal energy consumption. Fiori et al. [113] compared thepower-based consumption model of BEV and ICEV [114].The authors concluded that BEVs and ICEVs have differentfuel/energy-optimized assignment. The faster routes increase
14 Journal of Advanced Transportation
the BEV’s energy consumption while the congested and low-speed arterial routes consume less energy. Masmoudi etal. [84] compared the realistic energy consumption modelof Genikomsakis and Mitrentsis [85] to the constant con-sumption model (237.5 W/km) on instances for the dial-a-ride problem with EVs. The authors concluded that usingthe realistic model is more efficient with 0.14% differencebetween realistic and constant energy consumption from thebest-known solutions (BKS). To emphasize the importanceof the energy consumption model and energy minimiza-tion, Zhang et al. [36] compared the distance and energyminimization and concluded that the distance-minimizingobjective consumes 16.44% more energy than the energy-minimizing objective.
In real-life conditions, speeds on the roads are time-dependent and can be described as the speed profile over theobserved timeperiod. Speed profile depends on the road type,driver behavior, traffic (accidents, recurrent congestions),weather conditions, etc. [115, 116]. A large number of param-eters make it hard to predict a BEV’s energy consumption indifferent traffic scenarios. Therefore, some researchers applydata-driven approaches to predict the energy consumptionof a BEV. De Cauwer et al. [117] developed a model for BEVenergy consumption by applying multiple linear regression toreal-world measured BEV data. The proposed multiple linearregression model (MLR) has seven features: distance, speed,energy consumed by auxiliary devices, positive elevation,negative elevation, temperature, and kinetic energy changeper unit distance. Results showed that the prediction errorof trip energy consumption is within 25%. De Cauwer etal. [115] applied a similar MLR model for predicting energyconsumption on road segments, suited for BEV routing. Theauthors used a neural network based on the road-trafficand weather-related features to predict the speed profile ofa road segment. The error prediction of the trip’s energyconsumption is 12-14%. Lebeau et al. [52] used real-lifedata to model the energy consumed and recuperated onthe trip through least square analysis. The used functiondepends on the trip duration, measured energy consumption,temperature, and correction parameter.The𝑅2 for the energyconsumption model is 0.93 and 0.77 for the recuperatedenergymodel.Wu et al. [118] presented an empirical and ana-lytical method that can estimate a BEV’s instantaneous powerin real time and overall trip energy consumption, with theaverage prediction error up to 15.6%. Fiori andMarzano [119]proposed a backward microscopic power-based LDM energyconsumption model based on the known driving cycle. Theacceleration, speed, and regenerative braking efficiency weremodeled as functions of time. Based on the real driving BEVdata, for each vehicle, six parameters were optimized: threeparameters regarding the drivetrain and battery efficiency,the parameter for determining when the regenerative brakingis occurring, and two traction power thresholds. The authorsconcluded that the proposed model is flexible enough to beapplied to any kind of driving cycle and BEV type with givenkinematic profile and characteristics.
Pelletier et al. [104] presented battery degradation modelsthat could be used in BEV routing applications, as batteriesare a crucial part of the economic BEV routing. Several
lithium-ion battery degradation mechanisms with storageand operating conditions that affect battery lifespan weredescribed. Barco et al. [42] applied a battery degradationmodel based on the temperature, SoC, and depth of dischargein their airport shuttle service with BEVs. It was observed thatthe consideration of the battery degradation model affects thecharging patterns.
4. Variants of the Electric VehicleRouting Problem
Many different VRP variants were researched over the years.With BEV appearance, researchers started to adapt them tothe E-VRP context. Due to the specific characteristics of BEVrouting, some new problem-specific variants emerged. Here,we present some of the most relevant E-VRP variants andrelated problems.
4.1. Energy Shortest Path Problem and the Electric TravelingSalesman Problem. The energy shortest path problem (E-SPP) and electric TSP (E-TSP) can be considered as two ofthe simplest forms of the E-VRP. Inmost of the VRP variants,graph arcs have positive weight values that can representdistance, travel time, cost, etc. To compute the shortest pathbetween customers, the most commonly applied algorithmsare Dijkstra, Bellman-Ford, A∗, contraction hierarchies, etc.[108, 120]. By taking into account the recuperated energy ofBEV, some arc weights could have a negative value, whichmakes most of the shortest path algorithms inapplicable.To overcome this problem, Artmeier et al. [108] formalizedenergy-efficient routing with rechargeable batteries as aspecial case of the constrained SPP (CSPP) in which thebattery charge is limited with its capacity, and there is norecharging at CS. The authors adapted the Bellman-Fordshortest path algorithm with time complexity O(𝑛3) in orderto solve the energy CSPP. To overcome negative graph edges,Eisner et al. [121] used Johnson’s shifting technique [122]to transform negative edge cost functions into nonnegativeones and applied Dijsktra’s algorithm with time complexityof O(𝑛 log (𝑛) + 𝑚) [123]. Storandt [124] introduced CSPPfor EVs with battery swapping, while Sweda and Klabjan[125] added recharging events at CSs with a differentiablecharging function. Zündorf [50] solved the CSPP for BEVrouting with battery constraints, different types of CSs, andnonlinear charging process.The author developed a chargingfunction propagating algorithm in order to minimize traveltime and applied CH andA∗ algorithms to solve the problem.Liao et al. [103] considered the BEV’s shortest travel pathproblem and presented a dynamic programming algorithmfor solving the problem that runs in O(𝑘𝑛2), where 𝑘 is theupper bound on the number of BSSs. More recently, Strehleret al. [126] observed recharging events in the graph verticesand arcs for the energy-efficient shortest routes of BEVs andHEVs, while Zhang et al. [127] dealt with the electric vehicleroute planning with recharging problem (EVRC), whichminimizes the overall travel and charging time and takes intoaccount CSs’ locations, partial recharging, nonlinear charg-ing functions, service time duration, and service frequency atCS.
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As VRP is the generalization of the TSP, the E-VRP isclosely related to the E-TSP, in which a set of customershas to be served by only one BEV. Roberti and Wen [64]formulated the E-TSP with time windows (E-TSPTW) as acompact MILP program with binary variables for rechargingpaths with intermediate stops. The authors observed full andpartial recharge policies and applied three-phase heuristic forsolving the problem. The authors solved multiple instances,among them the 13 E-VRPTW instances of Schneider et al.[25], which were solved optimally with only one vehicle.Doppstadt et al. [58] formulated the HEV-TSP with fourworking modes of HEV and provided new test instances.Liao et al. [103] introduced the EV touring problem, as thegeneralization of TSP, with the minimization of the totalrequired time. Two scenarios with battery swap scheme wereobserved: the on-site station model, in which each city hasa BSS; the off-site station model, in which BSS is located atan acceptable distance from the city. The authors proposedefficient polynomial time algorithms for the problem.
4.2. Heterogeneous or Mixed Vehicle Fleet. In today’s vehiclefleets, mostly ICEVs are present. Transition to an almostwholly electric fleet is a very challenging economic task.Therefore, most companies are gradually integrating BEVsinto their existing ICEV fleet. Routing algorithms have to beupgraded and adapted for electric fleet characteristics, as on-time priority is harder to achieve.
Fleet size and mix VRP (FSM-VRP) was first introducedby Golden et al. [128], where the authors considered routinga fleet of vehicles with different acquisition costs and therouting cost is dependent on the vehicle type. Goeke andSchneider [30] formulated E-VRPTW and mixed fleet (E-VRPTWMF) with equal vehicle load capacities of BEVsand ICEVs, and equal BEV battery capacities. The authorscompared the percentage share of BEVs to the total trav-eled distance obtained with three objective functions: totaltraveled distance, total costs with battery costs, and totalcosts without battery costs. The traveled distance on onebattery pack was assumed to be 241,350 km (150,000 miles)with the payment of an additional $600 per kWh in caseof replacement. The results showed that the BEV’s share intotal traveled distance increased significantly when batterycosts are not considered, while in the other two scenariosICEVs performed most of the deliveries. Hiermann et al.[31] analyzed a similar problem, the electric fleet size andmix VRPTW and recharging stations (E-FSMFTW), withdifferent vehicle load and battery capacities. The authorsshowed the overall positive influence of the heterogeneousvehicle fleet on the generalized total cost function. In mostof the instances, three to four vehicle types are used in thefinal solution. A similar analysis on small-sized instanceswith different BEVs, ICEVs, and HEVs was undertaken byLebeau et al. [52].The authors defined seven groups of vehicletypes that could be used for the delivery, from small vans andquadricycles through diesel-only or electric-only groups to agroup of all vehicle types. The results showed the followingaspects of routing: (i) the fleet with different vehicle typesreduced the total routing costs; (ii) in the large van group,ICEVs outperformed BEVs; and (iii) HEVs showed a great
application in deliveries solelymade by trucks. Sassi et al. [47–49] also observed a heterogeneous fleet of ICEVs and BEVswith different load and battery capacities, different operatingcosts, time-dependent charges, and the compatibility of BEVsand chargers at CSs. The authors focused on the proceduresfor solving the problem, so they did not offer any compar-ison between the ICEV and BEV solutions. Hiermann etal. [96] introduced the Hybrid heterogeneous electric fleetrouting problem with time windows and recharging stations(H2E-FTW), in which the fleet consists of ICEVs, BEVs,and PHEVs. The authors compared the overall costs of thesolutions obtained with a homogeneous fleet of ICEVs, BEVs,and PHEVs to the optimized solution with a mixed fleet. Thegap for the ICEV fleet is the largest, with an average value of60% in the extreme case when the fuel cost is the highest. Incontrast, when the electric cost is the highest, the BEVfleet onaverage produces a 40% gap, while the PHEV fleet shows thelowest gap value, up to 25%. The authors pointed out that, inmixed solutions, BEVs are preferred for clustered instances,ICEVs for randomly distributed instances, and PHEVs forrandomly clustered and distributed instances. Overall, theresults showed that operational costs can be 7% lower in amixed case compared to the homogeneous case.
4.3. Hybrid Vehicles. As compensation for the limited drivingrange of BEVs, HEVs, which have both an internal com-bustion engine and an electric engine, have been developed.Two main types of HEVs are present on the market: theseries hybrid, in which only the electric motor drives the trainand the internal combustion engine is used to recharge thebattery pack, and the parallel hybrid, which uses both internalcombustion engine and electric engine to drive the train,where the electric engine is more efficient in stop-and-goactivities and the internal combustion engine ismore efficientat high speeds.We focus on the PHEVas a version of a parallelhybrid in which batteries can be recharged by connecting aplug to the electric power source. The PHEVs have an optionto decide during the route to run on either electric energyor fossil oil. This enables the visiting of customers far fromthe depot with almost no refuel/recharge during the route.As PHEVshave two engines, their load is heavier compared tothe BEVs and ICEVs, and therefore they have a higher energyconsumption rate.The time spent on the deliveries is shorter,whichmakes it easier to achieve time-precise deliveries and toreduce the costs of recharging, at the expense of higher costsdue to fossil oil consumption.
One of the first papers that dealt with the PHEVs routingproblem was published by Abdallah [41], where the authordefined the problem as the plug-in hybrid electric VRPTW(PHEVRPTW). The objective of the proposed problem isto minimize the routing costs on the internal combustionengine while satisfying the demand and time window con-straints. At each customer, the driver can either rechargethe vehicle battery or go to the next open time windowusing an internal combustion enginewhen the electric energyhas been depleted. Doppstadt et al. [58] defined the HEV-TSP in which the authors observed HEVs that are not plug-in and can only be charged while driving. Four workingmodes were observed, combustion-only mode, electric-only
16 Journal of Advanced Transportation
mode, charging mode, and boost mode, when the combinedinternal combustion engine and electric engine are used.As the authors assumed that there was not a charge leftfrom the day before, the initial charging of the battery wasset to zero. The authors presented the positive effects ofusing HEVs: (i) compared to the ICEV routes, the overallcosts for the HEV routes in the tested instances reduced upto 13% and driving time increased up to 11%; (ii) savingsdepend highly on the depot location, and not on the limitedbattery capacity, which was an a priori assumption. Mancini[71] introduced hybrid VRP (HVRP), in which PHEVs canchange propulsion mode at any time and the electric engine,rather than the internal combustion engine, is promoted.Vincent et al. [76] introduced a similar HVRP problem withPHEVs and mild-HEVs, which do not have an electric-onlymode of propulsion. The results showed that PHEVs havea lower average cost per mile in all scenarios compared tothe mild-HEVs and ICEVs. Hiermann et al. [96], in theirH2E-FTW, used the electric motor of the PHEV as prioritymode choice. When a time window of a PHEV route isviolated, the mode could be changed at any time during theroute by exchanging recharging time for the correspondingamount of fuel at no additional costs.The authors showed thepositive impact of a PHEV fleet compared to ICEV and BEVfleets, especially for randomly clustered instances. PHEVs areusually represented with only 20% of the overall number ofvehicles used in the solution due to their higher consumptionand utility costs but, still, they constitute an important part ofthe fleet configuration due to their flexibility.
4.4. Partial Recharging. In the beginning, in most of the E-VRP problems, full recharge was considered when a BEVvisited a CS [25]. This can be time-consuming because,depending on the SoC level, available charging technology,and battery capacity, the vehicle can charge from five min-utes to eight hours [15]. Therefore, in real-life applications,partial recharging should be taken into account. The batteryshould be charged enough to complete the whole route orto surpass a fear that vehicle range will not be enough toperform designated tasks, the so-called range anxiety [75].This particularly has an effect on customers with narrowtime windows, where efficient charge scheduling can enablethe feasibility of the route. On the economic side, significantsavings can be achieved by applying partial recharging as aminimal amount of energy could be recharged during theday when electricity cost and energy network load are higher,and the rest of the energy could be replenished during thenight [46, 47]. In some cases, it is natural to maintain theenergy reserve. This can be done by SoC range limitation,i.e., [20, 95] [42, 47, 80]. Having an energy reserve seems evenmore important if energy consumption and range anxiety aretaken into account because up to 30%of the consumed energycan be spent on BEV’s auxiliary devices [109]. Limiting SoCvalue also helps to preserve the battery as battery capacitydecreases by overcharging and overdischarging [104].
Several papers have analyzed strategies of partial recharg-ing and formulated the problem as E-VRPTW with partialrecharging (E-VRPTWPR). Bruglieri et al. [29, 51] andMoghaddam [53] modeled the concept of partial charging in
E-VRP. Felipe et al. [46], in GRVP with multiple technologiesand partial recharges (GVRP-MTPR), and Keskin and Çatay[28], in E-VRPTWPR, ensured that after every change inthe route configuration, at the previous CS, the BEV ischarged only with the amount of energy sufficient to finishthe segment of the route until the next CS or the depot.This results in the removal of certain CSs in the route,compared to full recharge strategy, and the arrival of a vehicleat the depot with an empty battery. The authors presentedthe positive impact of partial recharges on the total costsand energy savings. A similar procedure was applied bySassi et al. [47–49] but with multiple charging technologies,different charging periods, and BEV chargers compatibilitychecks. Schiffer and Walther [73] compared full and partialrecharge by solving small E-VRPTWPR test instances usingcommercial software. The authors concluded that, in somecases, a partial recharging strategy reduces the total traveleddistance and number of visits to CSs. Montoya [18] andMontoya et al. [72] formulated the FRVCP for BEVs in which,for a fixed sequence of customers in the route, CS positionand charging amount are optimized.The results on the newlyderived test instances showed that good solutions tend toexploit partial recharges. A similar procedure was applied byKeskin and Çatay [79], Hiermann et al. [96], Froger et al. [68],and Schiffer and Walther [88, 89] to enhance the incumbentbest solution by optimizing the charging decisions along theBEV route with a fixed customer sequence. Desaulniers et al.[57] presented the effects of partial recharging by optimallysolving E-VRPTW instances containing up to 100 customers.In a case with a single recharge per route, the partial rechargereduced the routing costs by 0.97% and the number ofvehicles by 2.25%, while in a case with multiple recharges perroute these values are 1.91% and 3.80%, respectively, with asignificant increase in the average number of recharges perroute.
4.5. Different Charging Technologies. Today, multiple charg-ing technologies are present: (i) slow, 3 kW (6-8 h); (ii)fast, 7-43 kW (1-2 h); and (iii) rapid, 50-250 kW (5-30min) [15, 129]. To better control charging time in the E-VRP context, the selection of possible charging technologycould also be optimized. This could make some customerswho have narrow time windows more accessible by fastcharging at previous CSs, or if the time windows are long,an economically better approach could be slow charging.Such a problem could be extended by taking into account CSworking hours, time-dependent charging costs, the numberof available chargers and their compatibility with BEVs, thepower grid load, the charger power, etc. [46–49, 68, 80, 81, 87].Felipe et al. [46] analyzed the effect of different chargingtechnologies on the recharge cost.The authors concluded thatnone of the technologies dominated the others. The rapidand fast charging options provided slightly better results thanthe slow charging, but the best results were obtained whenjoint technologies were used as the most appropriate onecould be chosen in each case. Çatay and Keskin [67] solvedsmall-sized instances to present the insights of the quickcharge option. The results showed that quick charging mightreduce the fleet size and decrease the cost of energy needed to
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operate BEVs. Keskin and Çatay [79] formulated E-VRPTWand fast charging (E-VRPTW-FC) with partial recharges andthree different charging technologies. The authors providedMILP formulation and minimized total recharging costswhile operating a minimum number of vehicles. The authorscompared two mixed integer programming (MIP) models:(i) model 1, in which binary variables are used as decisionvariables to choose which charging technology to use; (ii)model 2, based on the model of Schneider et al. [25] andKeskin and Çatay [28], in which the authors copied eachstation vertex three times depending on the charging tech-nology.The results showed that in all cases model 1 producedbetter results with shorter computation time. Testing onlarger instances showed that the fast charging option is morebeneficial when customers have narrow time windows andthat multiple charging technologies improved the overallresults (in 28 of 29 instances), while in the instances withlarger time windows the average improvement was 0.17%.
4.6. Nonlinear Charging Function. In most of the E-VRPrelated literature, either linear or constant charging timeis considered. Most of the BEVs have lithium-ion batter-ies installed, which are often charged in constant-currentconstant-voltage (CC-CV) phases: first by constant currentuntil approx. 80% of the SoC value and then by a constantvoltage. In the CC phase, SoC increases linearly, and in theCV phase, the current drops exponentially and SoC increasesnonlinearly in time, which prolongs charging time [102,104]. In only a few reviewed papers the author considerednonlinear charging process and solved the E-VRP either bylinearization per segments or by estimating charging timeby a data-driven approach [50, 68, 72, 87, 95]. Zündorf[50] developed a charging function propagation algorithmfor determining an EV battery-constrained route by takinginto account piecewise linear and concave functions of therecharging process. Montoya et al. [72] formulated the E-VRP with nonlinear charging functions (E-VRP-NL) andpresented theMILP formulation. The authors fitted piecewiselinear functions for 11, 22, and 44 kWCSs to the realmeasureddata. The results showed that neglecting the nonlinear chargecan lead to infeasible or overly expensive solutions: 12% ofthe routes in good solutions recharged the battery in thenonlinear part, after 80% of the SoC value. Froger et al. [95]proposed two new formulations for the E-VRP-NL: (i) theimproved MILP version of Montoya et al. [72] by arc-basedtracking of the SoC value; (ii) a path-based model withoutCS replication, where a sequence of vertices (a path) betweena pair of customers or depots is determined. The secondone yielded much better results with shorter computingtime. Froger et al. [68] explored similar formulations forthe E-VRP-NL with capacitated CSs (E-VRP-NL-C): (i) theCS replication-based formulation with flow and event-basedformulations forCS capacity constraints; (ii) recharging path-based formulation.
4.7. BEV Routing and CS Location. Due to the currently lowBEV market share, the number of CSs installed in the roadinfrastructure is also relatively low.Therefore, great potentiallies in the simultaneous decision-making of CS locations
and BEV routes. The classic location routing problem (LRP)consists of determining the locations of the depots andvehicle routes supplying customers from these depots [130].A modification of the LRP that deals with CS facilities isformulated as electric LRP (E-LRP) [11, 27, 73, 88].
Schiffer et al. [11, 27] presented a case study for solvingELRPTWPR. It was assumed that CSs can be located atcustomers’ locations and that service time can be usedfor recharging. Overall, results indicated the viability ofcombining CSs siting and BEV routing for specific caseswhen a delivery range is not far from the depot. Schifferand Walther [73] compared ELRPTWPR and E-VRPTWPRsolutions on down-scaled test instances and concluded thatthe ELRPTWPR gives a better solution in all instances. Thereason comes from the fact that BEV can be charged whileserving, which reduces the overall route time, as there isno travel time wasted on traveling to and from CS. Hofet al. [69] and Yang and Sun [56] addressed the problemof E-LRP but with BSSs. Results indicated that decreasingthe construction cost of BSS led to the expected increasein their number in the solution. Schiffer and Walther [88]formulated the LRP with intraroute facilities (LRPIF) as amore general problem, in which intraroute facilities can beused for refueling, loading, or unloading goods. Sun et al.[131] proposed a location model for CSs without routingbased on the travel demands of urban residents. For short-distance travelers, slow CSs are utilized, while for long-distance travelers, the rapid CSs are considered. The CSs’locations are determined to maximize coverage and flowaccording to the concept of vehicle refueling. In the casestudy, the authors pointed out two critical aspects: the BEVdriving range and the budget constraint.
4.8. Battery Swap. Instead of charging at CS, at speciallydesigned BSS, empty or nearly empty batteries can bereplaced with fully charged ones [14]. The main advantagesof such procedure are the time in which it can be performedand the ability to recharge when energy network load andelectricity costs are lower, i.e., during the night. A wholereplacement procedure could last less than ten minutes,which is competitive to the refueling time of ICEVs andmuchfaster than one of the fastest charging BEV technologies.The drawbacks of such procedure are the nonstandardizedbatteries and their installation in BEVs, which makes ithard to swap empty batteries with fully charged ones. Adlerand Mirchandani [44] observed the E-VRP with swappablebatteries, already determined BSS’s locations, a fixed numberof batteries per BSS, full recharge of four hours, and afixed swapping time of two minutes. Full battery rechargeis considered so it is possible that when the vehicle arrivesat the station, there is no fully charged battery availableand the vehicle has to wait. First, the total routing cost isminimized and then the battery reservations aremade, so thatthe vehicle could avoid BSSs without available batteries. Yangand Sun [56] and Hof et al. [69] simultaneously determinedthe locations of BSSs and the vehicle routing plan andprovided different metaheuristics for solving the problem.Yang and Sun [56] formulated the problem as BSS-EV-LRPand compared the solutions of the BSS-EV-LRP instances
18 Journal of Advanced Transportation
to the corresponding best-known CVRP solutions. The totalrouting costs for 150 km and 300 km driving ranges increasedto 7% and 3.5%, respectively, and in some cases, there wasno gap between BSS-EV-LRP and CVRP solutions. Hof et al.[69] on the same problem reported that if construction costsof BSSs are equal to zero, the BSSs would be constructed in83% of total available candidate sites.
4.9. Two-Echelon Routing Problem. Breunig et al. [93] pro-posed the electric two-echelon VRP (E2EVRP), in whichgoods are transported in two echelons: (i) in the first echelon,goods are transported by conventional freight vehicles fromthe depot to the satellite facilities; (ii) in the second echelon,goods are transported from the satellite facilities to thecustomers by light BEVs. Two vehicle types are observed inthe problem: ICEVs with higher load capacity located at thedepot and BEVs with lower load capacity located at satellitefacilities. BEVs are used for the last-mile deliveries due totheir lower pollution, noise, and size.The authors formulatedthe problem on the multigraph and applied exact proce-dures on smaller instances to solve the problem optimallyand a metaheuristic procedure on larger newly developedinstances. The results showed that the increase in CS density𝜌 decreased the detour costs following the expression 1/𝜌1.24.Also, the vehicle range has a great impact on the solutionquality: a range below 70 km produced infeasible solutionswhile a range higher than 150 km decreased recharging visitsto almost zero. Jie et al. [97] analyzed a similar problem, thetwo-echelon capacitated E-VRP with BSS (2E-EVRP-BSS), inwhich, in both echelons, BEVs are used.The BEVs in the firstechelonhave higher load and battery capacities than theBEVsin the second echelon. The authors reported that the batterydriving range is themost important aspect of routing and thatit slightly depends on the number of BSSs used.
4.10. Charging Schedule. Many companies that use BEVsprefer charging the vehicles at their own facilities in order tocharge the vehicles between the delivery routes and duringspecific periods of the day. In such occasions, there are usuallya limited number of chargers at the depot, typically fewer thanthe fleet size; therefore, the efficient charging schedule at thedepot has to be determined.
Pelletier et al. [87] considered the electric freight vehiclescharge scheduling problem (EFV-CSP) at the depot for theBEVs that deliver goods to a set of customers over multipledays. The authors included multiple charging technologies atthe depot, realistic charging process (piecewise linearizationof nonlinear charging function), time-dependent chargingcosts, grid power restriction, battery degradation costs (cyclicand calendar aging), and facility-related demand (FRD)charges representing the maximal demand registered overthe billing period. The fixed vehicle routes are known inadvance and the number of charging events in the depot islimited to avoid impractical solutions of constantly moving avehicle from one charger to another. The authors presentedthe following aspects of charge scheduling tests conductedin summer (higher electricity costs) and winter (lowerelectricity costs) periods: (i) model tries to keep the SoClower when battery degradation costs are included; (ii) in
summer, vehicles are rarely charged in peak hours, whichresults in more vehicle charging simultaneously or the useof fast chargers that retrieve more power from the grid innonpeak hours but incur higher FRD charges; (iii) to avoidcycling the battery in high SoC, it is preferable to split the longroutes into smaller ones; (iv) fast chargers are heavily usedin a high BEV utilization context; (v) grid power restrictionincreases overall energy costs, especially in summer months,and leads to infeasible solutions, limiting the number ofvehicles simultaneously charging; and (vi) total costs arealways lower with larger batteries, as smaller batteries requirelarger discharge cycles.
Barco et al. [34, 42] also analyzed charge scheduling forassigned routes in an airport shuttle scenario. The authorsdefined the set of charging actions (charge profile) over thedetermined programming horizon and minimized overalloperating costs. Sassi et al. [47, 49] also dealt with determin-ing the charging schedule of BEVs at the depot and includedtime-dependent charging costs and chargers compatibilitychecks with BEVs. Adler and Mirchandani [44] provided anonline routing model of BEVs by taking into account batteryreservations to minimize the average delay of all vehiclesby occasionally detouring them. Wen et al. [65] observedthe service time of CSs, meaning that a CS can be visitedonly in some specific time period, usually working hours.The authors proposed a battery reservation model in orderto charge the reserved battery at the defined time period.Sweda et al. [75] dealt with the possibility that a CS mightnot be available at some point in time and rerouting should beperformed.Theproblem is formulated as the adaptive routingand recharging policies for EVs. First, optimal a priori routingand recharging policies were determined and then heuristicprocedures were applied for the adaptive routing.
4.11. Dynamic Traffic Conditions. Most of the E-VRP researchconsiders static conditions on the road network. The trafficstates change recurrently, depending on the time of the day,day of the week, and season, or nonrecurrently when a trafficincident occurs, such as an accident [132–134]. TD-VRProutes a fleet of vehicles by taking into account variable traveltime on the road network [135, 136]. Shao et al. [74] observedBEVs in such time-dependent context in their E-VRP withcharging time and variable travel time (EVRP-CTVTT).The recharging time is fixed to 30 minutes and batteriesare always charged to full capacity. The authors discretizedone day into two-minute intervals and applied the dynamicDijkstra algorithm to find the shortest travel time path whenweights in the graph are not constant. The authors presenteda real-life problem and solved it by applying a geneticalgorithm with a running time of three hours. Omidvar andTavakkoli-Moghaddam [24] presented a model for routingAFVs that aims to avoid routing during congestion hours,when the pollution costs are high, by waiting at a customer’slocations. These costs were computed based on the roadspeed profile. Mirmohammadi et al. [62] presented MILPformulation for the periodic green heterogeneous VRP withtime-dependent urban traffic and time windows, which isgreen in terms of the emission minimization and not theutilization of AFVs. The planning horizon is divided into
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several periods, duringwhich static traffic conditions are con-sidered.
4.12. Related Problems
4.12.1. Route Scheduling and Other Electric Variants. Manyresearchers are dealing with the scheduling of bus/taxi routesthat are fixed or could be slightly altered. Li et al. [82]addressed themixed bus fleetmanagement problem (MBFM)composed of electric, diesel, compressed natural gas andhybrid-diesel buses. The authors maximized the total benefitof replacement of old vehicles with new ones under budgetconstraints while optimizing the route assignment for eachbus during the planning period. Two routing procedures weredeveloped to solve the recharging problem: single-periodrouting and routing across multiple periods of a day. Analysisof the results on the case study of Hong-Kong showed a cost-effective scheme of fleet configuration in the following order:mixed fleet, electric, natural gas, diesel, and then hybrid-diesel buses. Wen et al. [65] also dealt with the schedulingof electric buses (electric vehicle scheduling problem, E-VSP)in order to efficiently serve a set of timetabled bus trips. Thelinear partial and full recharge were considered, with theminimization of bus numbers and the total traveled distance.Lu et al. [83] addressed the problem of optimal scheduling ofa taxi fleet with mixed BEVs and ICEVs to service advancereservations. The authors presented a multilayer taxi-flowtime-space network in order to minimize the total operatingfleet cost.
Bruglieri et al. [77] for