Designing Charging Infrastructure for a Fleet of Electric Vehicles

Operating in Large Urban Areas

Michal Koh

ani

, Peter Czimmermann

, Michal V

, Matej Cebecauer

and

Lubo

s Buzna

1,3

Department of Mathematical Methods and Operations Research, University of

Zilina,

Univerzitn

a 8215/1, SK-01026

Zilina, Slovakia

Department of Transport Science, KTH Royal Institute of Technology, Teknikringen 10, SE-100 44 Stockholm, Sweden

ERA chair for Intelligent Transport Systems, University of

Zilina, Univerzitn

a 8215/1, SK-01026

Zilina, Slovakia

Keywords:

Electric Vehicles, Charging Infrastructure, Urban Areas, GPS Traces.

Abstract:

Here, we propose a method to design a charging infrastructure for a ﬂeet of electric vehicles such as a ﬂeet

of taxicabs, ﬂeet of vans used in the city logistics or a ﬂeet of shared vehicles, operating in large urban areas.

Design of a charging infrastructure includes decisions about charging stations location and number of charging

points at each station. It is assumed that the ﬂeet is originally composed of vehicles equipped with an internal

combustion engine, however, the operator is wishing to replace them with fully electric vehicles. To avoid an

interaction with other electric vehicles it is required to design a private network of charging stations that will be

speciﬁcally adapted to the operation of a ﬂeet. It is often possible to use GPS traces of vehicles characterizing

actual travel patterns of individual vehicles. First, to derive a suitable set of candidate locations from GPS

data, we propose a practical procedure where the outcomes can be simply controlled by setting few parameter

values. Second, we formulate a mathematical model that combines location and scheduling decisions to ensure

that requirements of vehicles can be satisﬁed. We validate the applicability of our approach by applying it to

the data characterizing a large taxicab ﬂeet operating in the city of Stockholm. Our results indicate that this

approach can be used to estimate the minimal requirements to set up the charging infrastructure.

1 INTRODUCTION

Road transport produces 20% of total carbon diox-

ide (CO

) emissions, which is the main greenhouse

gas. While these emissions decreased by 3.3% in

2012, they are still 20.5% higher than in 2011 and it

could have been even more if there is no economic

crises (Europen Commision, 2015). It is therefore

expected that in order to reduce CO

emission in

densely populated urban areas, it will be desired to

continue electriﬁcation of individual and public trans-

port. However, electriﬁcation of transport itself does

not ensure the reduction of CO

emission, also the the

higher penetration of renewable sources of electrical

energy is necessary. Advances in battery technologies

and continuously decreasing prices of electric vehi-

cles may soon increase the interest in converting large

ﬂeets of vehicles serving urban areas into electric, be-

cause the expected beneﬁts could be considerable due

to high utilization of such vehicles. Thus, high pur-

chase costs of a new electric vehicle can be more eas-

ily compensated by lower operational costs. To avoid

delays in charging, caused by interaction with other

electric vehicles, a choice of a ﬂeet operator can be to

build their own charging infrastructure.

The topic of planning charging infrastructure for

electric vehicles is rapidly growing in the scientiﬁc lit-

erature. The attention of researchers has been focus-

ing on creating models that would be able to predict

the future expansion of electric vehicles (Sears et al.,

2014) as well as models designed to estimate the size

of the future demand for charging vehicles (Yi and

Bauer, 2014). An approach, where GPS traces of ve-

hicles collected in two Italian cities were used to ex-

tract the travel behaviour and to estimate the expected

demand for charging vehicles, was used in (Paffumi

et al., 2015; Gennaro et al., 2015). Such analysis can

provide valuable hints when searching for suitable po-

sitions of charging stations. Data driven approach to

predict the penetration of EVs in the region of Lis-

bon and the future refuelling demand was proposed

in (Frade et al., 2011).

Optimization algorithms have been often used to

address this problem as well. In (Dickerman and Har-

360

KohÃ ˛ani M., Czimmermann P., VÃ ˛aÅ

La M., Cebecauer M. and Buzna Ä¡.

Designing Charging Infrastructure for a Fleet of Electric Vehicles Operating in Large Urban Areas.

DOI: 10.5220/0006194403600368

In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems (ICORES 2017), pages 360-368

ISBN: 978-989-758-218-9

rison, 2010) was used a city transportation model to

verify various locations of charging stations, which

were generated by the genetic algorithm. A bi-level

approach was proposed by (Jung et al., 2014). On

the upper level is solved the location problem (con-

sidering the capacity of charging stations), where the

total costs and waiting time are minimized. On the

lower level is used simulation approach to evaluate

each design. Simulation as a validation tool has

been used relatively often (Sweda and Klabjan, 2011).

In (Xi et al., 2013) authors developed the simulation-

optimization approach, where the area is divided into

regions. The OD-matrix for the regions is known and

it is used to estimate the EV ﬂows between them. Lin-

ear IP model is used to determine the location and size

of charging stations subject to limited budget. Simu-

lation model is used to estimate the expected number

of vehicles successfully charged at each candidate lo-

cation. (Dong et al., 2014) proposed an approach that

allows for analyzing the impact of public charging in-

frastructure deployment on increasing electric miles

travelled. A genetic algorithm is used to ﬁnd loca-

tions of charging stations and it is evaluated by the

activity-based assessment method. Combination of

a simulation approach with a genetic algorithm that

utilizes GPS traces of vehicles was presented in (Tu

et al., 2015).

Several authors considered a location problem

leading to a mixed integer programming problem. For

example, in (Chen et al., 2013) the demand for charg-

ing electric vehicles on public parking lots was esti-

mated, based on a trafﬁc survey conducted in the city

of Seattle. The suitable location of charging stations

was found by minimising the costs and the optimi-

sation problem was solved by a general purpose opti-

misation solver. A similar methodology was also used

for the city of Lyon (Baouche et al., 2014) and the city

of Coimbra (Cavadas et al., 2014). When designing

a network of charging stations, capacity constraints

are typically included in the model (Lam et al., 2014;

Ghamami et al., 2016) and apart from minimising

costs, the area covered within the driving distance

is maximised (Yi and Bauer, 2014). Methodologi-

cally different approach has been presented in (Mom-

tazpour et al., 2012). Here authors considered con-

straints implied by the daily activity of car users and

the capacity of electrical network and the location of

charging stations were found by the clustering algo-

rithm. The advantage of this approach is that several

types of constraints can be taken into account simul-

taneously, without signiﬁcantly affecting the compu-

tational complexity of the algorithm.

The special class of models was developed to

cover trajectories of vehicles (MirHassani and Ebrazi,

2013; Capar et al., 2013). This approach is applica-

ble in the design of the charging infrastructure along

a highway to cover for long distance trips. An elegant

way how to locate charging stations along the paths

was proposed by (MirHassani and Ebrazi, 2013). The

approach is based on adding artiﬁcial links to the net-

work graph conecting places that fulﬁl some reach-

ability rules. The model locates the minimum num-

ber of refuelling stations along paths to make the path

traversal feasible. The approach (Chung and Kwon,

2015) further extends (MirHassani and Ebrazi, 2013)

by considering multi-period case.

As our contribution, we propose an approach that

is purely based on an optimization approach where we

combine location and scheduling problems and thus

we avoid the need to validate the locations and ca-

pacity of charging stations by computer simulations.

Because the approach is based on historic data it can

be used to estimate the minimum design of the sys-

tem that is sufﬁcient to cope with various scenarios

occurring in the past.

The paper is organized as follow: in section 2 we

describe the data requirements and the methodology.

In section 3, we describe the data used in the case

study and we introduce the results of numerical exper-

iments. To conclude, we summarise our main ﬁndings

in section 4.

2 METHODOLOGY

2.1 Data Requirements

The proposed method to design the network of pri-

vate charging stations relies on two datasets. The

ﬁrst dataset is expected to contain historical low-

frequency GPS data describing the mobility patterns

of individual vehicles that belong to the ﬂeet. Data

should be collected for several, typical and sufﬁ-

ciently long time periods representing relevant sce-

narios that should be included in the design of the

charging network. To collect low frequency data is

much easier in practice as there is no need to use ex-

pensive GPS trackers, however, such data are not pre-

cise enough to determine the travel distances. There-

fore we need the graph model of the road network

including data about nodes, edges and their elevation.

Using this data we can perform the map matching and

estime the travel distances much more precisely by in-

ducing them from the road network.

Designing Charging Infrastructure for a Fleet of Electric Vehicles Operating in Large Urban Areas

361

2.2 Algorithm to Determine a

Candidate Set of Charging Station

Locations

In this paper, we will explore the case where to

recharge an electric vehicle, we use only the time

when it is parking for a long enough time. Thus, if

possible, we do not wish to affect the current trajecto-

ries that are taken by vehicle drivers. The proposed

methodology allows then to evaluate what percent-

age of vehicles could be transformed to electric ve-

hicles without affecting their operation with the mini-

mal requirements on building the charging infrastruc-

ture. Therefore, we use the historic GPS data to iden-

tify the set of suitable candidate locations for charging

stations. Here, we aim to identify locations where the

large number of vehicles frequently parks. To do so,

we proposed the following two-phase procedure:

• Phase 1: Identify the set of candidate locations

for charging stations as locations where many ve-

hicles tend to park for a long enough time.

• Phase 2: Identify the set of vehicles that can be

served by selected set of candidate locations.

To determine the set of candidate locations, fol-

lowing parameters are used. As an parking event we

identify the time period, when the average speed of a

vehicle is below the maximum speed limit V

max

for at

least a time period of T

min

. To ensure that we select a

relevant set of candidate location we require for each

candidate to be associated with at least M

min

parking

events taking place in its circular neighbourhood de-

ﬁned by the radius of R

max

In the ﬁrst phase, we process one-by-one the GPS

traces of all vehicles executing the following steps

(see Figure 1):

• Step 1: Identify in the GPS trace the traversals

that have the average speed below the speed limit

max

• Step 2: Identify in the GPS trace the maximum

connected sequences of traversals longer than the

time period T

min

• Step 3: Identify as a candidate location the last

node of each connected sequence if there is no

other candidate location within the distance R

max

After processing all GPS traces we remove all

candidate locations that are associated with less than

min

parking events.

The second phase of the procedure evaluates the

proposed set of candidate locations and identiﬁes the

set of vehicles that could be replaced by the elec-

tric vehicles. For each vehicle we evaluate its trajec-

tory and we evaluate whether it could be sufﬁciently

Figure 1: Diagram illustrating the identiﬁcation of candi-

date locations. Nodes represent GPS position of the vehicle

in time t

, links are traversals between two GPS positions.

Black coloured links represent traversals, where the average

speed v

is below the limit V

max

and black coloured node

represents the candidate location.

recharged during parking events, to cover the travel

distances. Here we consider the unlimited capacity of

charging points being locating in each candidate lo-

cation. We assume that the capacity of each vehicle

is K (measured in kilometres), i.e. it corresponds to

the reachable driving distance. As a vehicle is driven

its state of charge is decreasing by substricting from

it the travel distance. Each time unit when the vehicle

is charged we increase its state of charge by the value

of P. We record the number of vehicles that cannot

be served by a given set of candidate locations. In the

mathematical model we consider only vehicles that

can be recharged, otherwise the proposed mathemati-

cal model has no feasible solution.

2.3 Mathematical Model

We aim to minimize the costs that are required to set

up the charging infrastructure. Due to the fact that

in our approach we expect to locate charging stations

of the same type, we minimize just the number of

charging points. Previous studies (Sweda and Klab-

jan, 2011; Xi et al., 2013; Dong et al., 2014) indicated

that an important requirement is to consider queueing

behaviour of vehicles while charging. Therefore we

formulate a location optimization problem consider-

ing the scheduling problem to ensure that there exist

a feasible schedule how to recharge vehicles.

We assume that the algorithm introduced in the

previous section was used to produce the set of candi-

date location where it is possible to locate the charg-

ing infrastructure I. To schedule the individual charg-

ing time slots we split the time into the set of non-

overlapping time intervals T . Then for each vehicle

we distinguish two possible states (see Figure 2). A

vehicle is either parking at the candidate locations and

it is available for charging or it is located somewhere

else where it cannot be charged.

The maximum number of charging stations is lim-

ited to p. We consider that the ﬂeet is composed of

the set of vehicles C and each vehicle is equipped by

the battery, which when fully charged allows for driv-

ing the vehicle for the distance K. From the data we

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

362

Figure 2: Diagram illustrating the movement of individual

vehicles between the candidate locations. Vehicle is either

parking at the candidate locations and thus it is available for

charging (coloured rectangles) or it is located somewhere

where it cannot be charged (coloured dashed lines).

extract for each vehicle c ∈ C an ordered sequence of

parking events R

and we determine the list N

of all

time intervals t ∈ T that have an overlap with parking

event r ∈ R

. The fraction of the time interval t ∈ T

the vehicle c ∈ C is parking we denote as a

∈



0, 1



To simplify the description of the mathematical model

we deﬁne B

itc

∈ {0, 1}, where B

itc

= 1 if the vehicle

c ∈ C parks at the location i ∈ I during the time inter-

val t ∈ T and B

itc

= 0 otherwise. We use the graph of

the road network to extract the information about the

real travel distances. Vehicle c ∈ C drives u

kilome-

tres while driving from the parking event r − 1 to the

parking event r. Each vehicle enters into the model

with an ﬁctive parking event r = 0 of zero duration

and exits with an ﬁctive parking event r = r

of zero

duration. Symbol M denotes the big − M constant.

Decisions are described by the set of variables:

• y

∈ {0, 1} for i ∈ I, where y

= 1 if the charging

station is located at the candidate location i and

= 0 otherwise,

• s

∈ Z

for i ∈ I, representing the number of

charging points allocated to the station i ∈ I,

• x

∈ {0, 1} for c ∈ C, t ∈ T , where x

= 1 when

vehicle c ∈ C is being charged during the time in-

terval t ∈ T and x

= 0 otherwise, and

• d

≥ 0 for c ∈ C, r ∈ R

∪ {0} ∪ {r

} corresponds

to the distance that the vehicle c ∈ C at the begin-

ning of the parking event r ∈ R

is able to drive.

Making use of these notation we formulate the

location-scheduling problem that is shown in Fig-

ure 3.

In the objective function of the problem (1) we

minimize the number of located charging points.

Constraint (2) ensures that we do not locate more than

p charging stations. This constraints approximates the

limitations that are associated with the establishment

of a new charging station. Constraints (3) make sure

that we can assign charging points only to located

charging stations. In each time interval we cannot

use more charging points than available as it is spec-

iﬁed by the set of constraints (4). We initialize the

system by limiting the driving distance to αK, where

α > 0 is parameter of the model (see constraints (5)).

Constraints (6) ensure that battery capacity is not ex-

ceeded and constraints (7) ensure contiguity in charg-

ing and discharging of batteries.

3 NUMERICAL EXPERIMENTS

3.1 Data

In the case study we consider a ﬂeet of more than

1,500 taxicabs operating in the area of Stockholm dis-

trict, in Sweden. Each vehicle reported on average

every 90 seconds its id, GPS position, time-stamp

and information whether it is hired or not. For the

case study we selected four weeks (see Figure 4), al-

together comprised of 8,989,143 probe data records.

These four weeks represent different scenarios: week

1 is a typical spring week with 1542 taxicabs, week 2

represents typical summer week with 1526 taxicabs,

week 3 is the Christmas week with 1491 taxicabs and

week 4 is a special week, when the major disruption

of the public transport occurred due to many failed

railway connections, with 1550 taxicabs.

As the reporting frequency of probe data is rela-

tively low, to be able to measure the travel distances

more accurately we map-matched the probe data onto

the road network using the methodology proposed

in (Rahmani and Koutsopoulos, 2013). Thus, we use

the road network to estimate the travel distance. In

the digital model of the road network each link is at-

tributed a number of parameters, including the length,

presence of a trafﬁc signal, road class, speed limit and

etc. The graph of road network used in the case study

consists of 231,839 links. In Figure 5 we show ac-

cumulated number of traversals by taxicabs over all

four weeks for all links of the road network. We have

no traversals for 97,720 links, where 96% of these are

class 5 links. Conversely, the largest frequency of us-

age we observe on class 1 links connecting the city of

Stockholm with the airports and in the city centre.

3.2 Numerical Results

We set the following values of parameters: the driving

range of all vehicles K = 300 km, the initial fraction

of the driving range α = 0.5, the charging speed P =

5 km/min., we do not limit the number of charging

stations, i.e., p = |I|, V

max

= 0.1 m/s and T

min

= 15

min. When constructing the mathematical model we

Designing Charging Infrastructure for a Fleet of Electric Vehicles Operating in Large Urban Areas

363

Model formulation

Minimize

∑

i∈I

(1)

subject to

∑

i∈I

≤ p (2)

≥ s

for i ∈ I (3)

∑

c∈C

itc

≤ s

for i ∈ I,t ∈ T (4)

≤ αK (5)

∑

t∈N

c,r

P ≤ K for c ∈ C, r ∈ R

∪ {r

} (6)

≤ d

c,r−1

− u

∑

t∈N

c,r−1

P for c ∈ C, r ∈ R

∪ {r

} (7)

Figure 3: Mathematical formulation of the location-scheduling optimization problem.

Figure 4: The travel distance, the travel distance when the

taxicabs were hired, the number of unique taxicabs and

dates of individual weekdays in weeks 1-4 that we selected

for the case study.

discretize the time in steps of 15 minutes. Results of

experiments are shown in Tables 1 - 4.

Numerical experiments were performed on the

computer equipped with CPU Intel (R) Core i7-

5500U CPU with two 3 GHz cores and with 8 GB

RAM. Mathematical model was solved using IP-

solver FICO Xpress IVE 7.3.

Based on the initial experiments we selected

the folowing values of input parameters R

max

∈

{100, 500, 1000} meters and M

min

∈ {100, 150, 800}

parking events to cover the broad range of situations.

In tables we report the following output values ob-

tained from the algorithm that is used to determine

a set of candidate locations : |I| is the cardinality of

the set of candidate locations identiﬁed in the Phase

1, Cars is the number of taxicabs that are determined

in the Phase 2 as the vehicles that can be served by

the set of candidate locations. Optimization outputs

are the following: Stations is the number of located

charging stations, CP

total

represents the total number

of charging points in all charging stations and CP

max

is the maximal number of charging points located in

one charging station. Column Time contains compu-

tational time in seconds. We restricted the running

time of a single experiment to 30 minutes. If the op-

timal solution was not found within this time limit, in

the column Gap we report the relative gap between

the upper and lower bounds of the optimal solution.

In two cases the solver was not able to ﬁnd any fea-

sible integer solution within the given time limit what

is indicated by the symbols ’***’ in the particular row

of the table.

To verify the proposed approach, we visualised

the resulting locations of charging stations for the sce-

nario Week 1 and the parameter values R

max

= 100

meters and M

min

= 150 parking events. Results are

shown in the Figure 6.

4 EVALUATION OF RESULTS

AND CONCLUSIONS

In this contribution we present an initial design of

the method to deploy the charging infrastructure for

a ﬂeet of electric vehicles operating in large urban

areas. The operation of the ﬂeet is described by the

GPS traces characterizing the actual travel patterns of

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

364

Table 1: Results of numerical experiments for the scenario Week 1.

max

min

Cars | I | Stations CP

total

max

Time[s] Gap[%]

100 800 609 3 3 14 9 1.88 0.00

150 1186 27 27 38 6 1800.00 5.26

100 1287 44 44 54 6 22.10 0.00

500 800 1102 5 5 20 10 46.05 0.00

150 1442 46 40 44 5 1800.00 2.27

100 1475 77 51 54 4 1800.00 4.50

1000 800 1347 7 7 19 6 1800.00 21.05

150 1499 51 39 42 3 1800.00 4.57

100 1510 70 51 55 3 1800.00 46.90

Table 2: Results of numerical experiments for the scenario Week 2.

max

min

Cars | I | Stations CP

total

max

Time[s] Gap[%]

100 800 785 4 4 17 9 2.828 0.00

150 1292 30 30 35 4 16.642 0.00

100 1363 46 44 49 4 27.673 0.00

500 800 1188 5 5 18 7 1800.00 22.22

150 1477 46 36 38 2 218.37 0.00

100 1498 73 47 49 2 1800.00 272.97

1000 800 1409 8 8 19 5 1800.00 30.84

150 1506 50 38 63 3 1800.00 72.03

100 1513 69 *** *** *** *** ***

Table 3: Results of numerical experiments for the scenario Week 3.

max

min

Cars | I | Stations CP

total

max

Time[s] Gap[%]

100 800 449 2 2 4 2 0.34 0.00

150 1019 24 24 27 2 2.84 0.00

100 1094 36 36 37 2 6.83 0.00

500 800 843 4 4 5 2 6.17 0.00

150 1324 39 37 39 2 46.86 0.00

100 1359 57 52 53 2 291.05 0.00

1000 800 1172 6 6 11 2 27.80 0.00

150 1417 43 38 39 2 547.72 0.00

100 1445 65 47 48 2 898.37 0.00

Table 4: Results of numerical experiments for the scenario Week 4.

max

min

Cars | I | Stations CP

total

max

Time[s] Gap[%]

100 800 631 3 3 17 13 7.66 0.00

150 1221 33 33 39 7 1800.00 2.56

100 1325 50 49 53 5 38.21 0.00

500 800 1097 5 5 19 10 1800.00 5.26

150 1491 50 40 42 3 1800.00 2.38

100 1515 80 56 58 3 1800.00 16.5

1000 800 1408 9 9 21 6 1800.00 18.67

150 1525 29 27 39 7 128.50 0.00

100 1534 74 *** *** *** *** ***

individual vehicles. In the ﬁrst phase we used a prac-

tical procedure to derive from data a suitable set of

candidate locations for charging stations, where the

outcomes can be controlled by setting a few param-

eter values only. In the next step, vehicles that can

be served from the set of candidate locations are se-

lected. In the second phase, we formulated a mathe-

matical model that combines location decisions with

Designing Charging Infrastructure for a Fleet of Electric Vehicles Operating in Large Urban Areas

365

Figure 5: Visualisation of the road network considered in

the case study. Thickness of each link indicates the number

of traversals by the vehicles belonging to the taxicab ﬂeet.

scheduling decisions to ensure that for a given design

there exists a time schedule that allows satisfying re-

quirements of all vehicles selected in the ﬁrst phase.

The limits of the proposed approach were tested by

applying it to the real-world data characterizing the

driving behaviour of a large taxicab ﬂeet operating in

the city of Stockholm. From the numerical experi-

ments we derive the following main conclusions:

• Our results indicate that this approach can be used

to estimate the minimal requirements to set up the

charging infrastructure. The proposed method is

able to handle relatively large instances of prob-

lems independently on the scenario. Problems

Figure 6: Locations of charging points obtained for the sce-

nario Week 1 and the values of input parameters R

max

= 100

meters and M

min

= 150 parking events.

with R

max

∈ {100, 500} and M

min

∈ {150, 800}

are often solved to optimality or with small gap

only.

• Charging points are typically located at parking

lots in the vicinity of airports, railways stations

and other public spaces, which seem to be natural

locations for them.

• When comparing the results across selected sce-

narios we ﬁnd similar numbers of located stations

in weeks 1, 2 and 4 and signiﬁcantly smaller num-

ber of charging points in week 3, which is the

most quiet week.

• We did not limit the number of charging stations

by setting the value of the parameter p. Hence,

the number of charging stations was limited only

by the set of candidate locations |I|. From the

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

366

solutions we can see that if |I| is large enough,

the optimization model has the tendency to se-

lect the large set of charging stations with only

few charging points more frequently than locat-

ing only few charging stations with many charg-

ing points. Such design can be also favourable

for the electricity network as it will not load the

network largely at few locations, but the load is

spatially more distributed.

• When we set the radius of charging points to

max

= 1000 meters, the number of charging op-

portunities gets high and the solved problem,

especially during the busy weeks, becomes in-

tractable when solved by a general purpose solver.

This result indicates the limits of this methodol-

ogy.

Although these initial results look promising, fur-

ther steps are needed to reﬁne the proposed approach.

Considering the scheduling problem in the optimiza-

tion model makes sure that there exists a time sched-

ule to recharge all vehicles. However, this informa-

tion is derived from the past data and it remains un-

clear how hard it is to ﬁnd a feasible schedule in the

system operation when the drivers do not have the

prior information about the departure from the park-

ing positions. Moreover, we assume that the parame-

ter R

max

determines the maximum distance the drivers

accept to drive from the parking position to the clos-

est charging station. It could be beneﬁcial to consider

more complex strategies to determine the charging

station the driver decides to use. Another challenge

is in combining scenarios in a way that the resulting

problem can still be solved for the long enough time

period and we obtain as an output the robust design of

the charging infrastructure that is suitable for all con-

sidered scenarios. To overcome the limits of proposed

methodology, it would be beneﬁcial to use heuristic

apporoaches to expand the size of solved problems.

ACKNOWLEDGEMENTS

This work was supported by the research grants

VEGA 1/0463/16, APVV-15-0179, and it was facil-

itated by the FP 7 project ERAdiate [621386].

REFERENCES

Baouche, F., Billot, R., Trigui, R., and Faouzi, N. E. E.

(2014). Efﬁcient Allocation of Electric Vehicles

Charging Stations: Optimization Model and Appli-

cation to a Dense Urban Network. IEEE Intelligent

Transportation Systems Magazine, 6(3):33–43.

Capar, I., Kuby, M., Leon, V. J., and Tsai, Y.-J. (2013). An

arc cover–path-cover formulation and strategic anal-

ysis of alternative-fuel station locations. European

Journal of Operational Research, 227(1):142–151.

Cavadas, J., Correia, G., and Gouveia, J. (2014). Electric

Vehicles Charging Network Planning, pages 85–100.

Springer International Publishing, Cham.

Chen, T., Kockelman, K., and Khan, M. (2013). Locat-

ing Electric Vehicle Charging Stations. Transporta-

tion Research Record: Journal of the Transportation

Research Board, 2385:28–36.

Chung, S. H. and Kwon, C. (2015). Multi-period planning

for electric car charging station locations: A case of

Korean Expressways. European Journal of Opera-

tional Research, 242(2):677–687.

Dickerman, L. and Harrison, J. (2010). A New Car, a New

Grid. IEEE Power and Energy Magazine, 8(2):55–61.

Dong, J., Liu, C., and Lin, Z. (2014). Charging infras-

tructure planning for promoting battery electric ve-

hicles: An activity-based approach using multiday

travel data. Transportation Research Part C: Emerg-

ing Technologies, 38:44–55.

Europen Commision (2015). Road transport:

Reducing CO2 emissions from vehicles.

http://ec.europa.eu/clima/policies/transport/vehicles/.

Frade, I., Ribeiro, A., Gonc¸alves, G., and Antunes, A.

(2011). Optimal location of charging stations for elec-

tric vehicles in a neighborhood in Lisbon, Portugal.

Transportation research record: journal of the trans-

portation research board, (2252):91–98.

Gennaro, M. D., Paffumi, E., and Martini, G. (2015).

Customer-driven design of the recharge infrastructure

and Vehicle-to-Grid in urban areas: A large-scale ap-

plication for electric vehicles deployment. Energy,

82:294–311.

Ghamami, M., Nie, Y. M., and Zockaie, A. (2016). Plan-

ning charging infrastructure for plug-in electric vehi-

cles in city centers. International Journal of Sustain-

able Transportation, 10(4):343–353.

Jung, J., Chow, J. Y., Jayakrishnan, R., and Park, J. Y.

(2014). Stochastic dynamic itinerary interception re-

fueling location problem with queue delay for elec-

tric taxi charging stations. Transport.Research Part

C: Emerging Technologies, 40:123–142.

Lam, A. Y. S., Leung, Y. W., and Chu, X. (2014). Elec-

tric Vehicle Charging Station Placement: Formula-

tion, Complexity, and Solutions. IEEE Transactions

on Smart Grid, 5(6):2846–2856.

MirHassani, S. A. and Ebrazi, R. (2013). A Flexible Refor-

mulation of the Refueling Station Location Problem.

Transportation Science, 47(4):617–628.

Momtazpour, M., Butler, P., Hossain, M. S., Bozchalui,

M. C., Ramakrishnan, N., and Sharma, R. (2012). Co-

ordinated Clustering Algorithms to Support Charging

Infrastructure Design for Electric Vehicles. In Pro-

ceedings of the ACM SIGKDD International Work-

shop on Urban Computing, UrbComp ’12, pages 126–

133, New York, NY, USA. ACM.

Paffumi, E., Gennaro, M. D., Martini, G., and Scholz, H.

(2015). Assessment of the potential of electric vehi-

Designing Charging Infrastructure for a Fleet of Electric Vehicles Operating in Large Urban Areas

367

cles and charging strategies to meet urban mobility re-

quirements. Transportmetrica A: Transport Science,

11(1):22–60.

Rahmani, M. and Koutsopoulos, H. N. (2013). Path infer-

ence from sparse ﬂoating car data for urban networks.

Transportation Research Part C: Emerging Technolo-

gies, 30:41–54.

Sears, J., Glitman, K., and Roberts, D. (2014). Forecasting

demand of public electric vehicle charging infrastruc-

ture. In Technologies for Sustainability, 2014 IEEE

Conference, pages 250–254.

Sweda, T. and Klabjan, D. (2011). An agent-based deci-

sion support system for electric vehicle charging in-

frastructure deployment. In 2011 IEEE Vehicle Power

and Propulsion Conference, pages 1–5.

Tu, W., Li, Q., Fang, Z., Shaw, S.-l., Zhou, B., and Chang,

X. (2015). Optimizing the locations of electric taxi

charging stations: A spatial–temporal demand cov-

erage approach. Transportation Research Part C:

Emerging Technologies, pages –.

Xi, X., Sioshansi, R., and Marano, V. (2013). Simulation–

optimization model for location of a public electric

vehicle charging infrastructure. Transportation Re-

search Part D: Transport and Environment, 22:60–69.

Yi, Z. and Bauer, P. H. (2014). Spatio-Temporal Energy

Demand Models for Electric Vehicles. In 2014 IEEE

Vehicle Power and Propulsion Conference (VPPC),

pages 1–6.

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