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An Optimization Model for Structuring a Car-Sharing Fleet Considering Traffic Congestion Intensity

An Optimization Model for Structuring a Car-Sharing Fleet Considering Traffic Congestion Intensity Hindawi Journal of Advanced Transportation Volume 2023, Article ID 9283130, 13 pages https://doi.org/10.1155/2023/9283130 Research Article An Optimization Model for Structuring a Car-Sharing Fleet Considering Traffic Congestion Intensity 1 2 3 Parisa Ahani , Amilcar Arantes , and Sandra Melo CERIS, MIT Portugal Program, Sustainable Energy Systems, Instituto Superior Tecnico, Universidade de Lisboa, Lisbon, Portugal CERIS, Instituto Superior Tecnico, Universidade de Lisboa, Lisbon, Portugal CEiiA, Center of Engineering and Development, Matosinhos, Portugal Correspondence should be addressed to Parisa Ahani; prsahani1@gmail.com Received 18 April 2022; Revised 18 September 2022; Accepted 24 November 2022; Published 6 February 2023 Academic Editor: Mohammad Miralinaghi Copyright © 2023 Parisa Ahani et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ever-growing mobility and trafc congestion within urban areas make the need for a sustainable form of transport inevitable. Trafc congestion has a signifcant efect on the amount of energy consumption of a vehicle and, as a result, on its associated environmental impacts. Any decision-making regarding structuring a feet without taking into account the trafc congestion level (TCL) will lead to a less sustainable feet with higher environmental and economic costs. To address this issue, this study examines the efects of the trafc congestion intensity level on the feet structure of an urban car-sharing company over a certain planning period. We present a new optimization framework for fnding an optimal vehicle composition of the feet of an urban car-sharing company considering the energy consumption of vehicles at diferent trafc congestion levels. Te results show that electric vehicles (EVs) are more competitive than diesel vehicles (DVs) in high-peak trafc congestion from the outset of the planning period. In addition, we perform a sensitivity analysis to take into account the efects of specifc uncertain parameters such as the energy and purchasing costs of EVs on the total cost of ownership. As expected, the purchasing price of EVs, energy prices of DVs, and increase in diesel prices have the highest impact on the total cost. Chen and Kockelman [14] estimated a reduction of 51% in 1. Introduction energy consumption and greenhouse gas (GHG) emissions Te idea of several people sharing the same car can be traced for what they have defned as a “good candidate for shared back several decades ago [1]. Car-sharing is a type of shared mobility.” mobility that ofers renting cars on a needed basis for as little In two studies [10, 11], the authors conducted a survey of as 10minutes [2] and often by the hour when other modes of members of a car-sharing club in the US, looking specifcally transport are not available or are not suitable [3]. Te users at the impacts of car-sharing on household vehicle own- can be passengers, companies, and public agencies [4]. Te ership. Te results showed that the rate of vehicle ownership station of car-sharing is usually close to the location of among club members decreased from 0.47 to 0.24 vehicles transportation modes, and the payment is based on travel per household. In the last decade, the car-sharing market in distance or time spent [4]. Europe has expanded, and in Germany, as the largest car- Car-sharing has the potential to reduce vehicle use, sharing market in Europe, an increase in user usage from ownership, and delays in car purchases [5–7]. It is seen as a 0.26 million in 2012 to 1.29 million in 2020 was reported by solution to address the issues of congestion, pollutants, and Roblek et al. [15]. the occupancy rate of vehicles within urban areas [8, 9]. Tis Various research studies have shown that the demand leads to increasing urban sustainability from environmental, for car-sharing as a means of mobility in any form is in- economic, and societal points of view worldwide. [10–13]. creasing worldwide [16–19]. In many countries around the 2 Journal of Advanced Transportation paper ends in Section 6 with the enunciation of some world, car-sharing or short-term auto access [20] is known as a system to minimize ownership transportation costs and conclusions. the negative efects of car use. Te car-sharing industry has recently signifcantly increased its market [21, 22]. In the 2. Literature Review past decade, advancements in communication technologies and smartphone applications have led to the emergence of Various research studies have focused on feet optimization car-sharing companies such as DriveNow and Car2Go. for shared mobility systems [26–31]. In a study by Wallar Autolib in Paris is one of the known operators in car-sharing et al. [28], the authors provided a model for optimizing feet systems that ofers electric car-sharing services with at least composition to distributions of vehicles for shared mobility 1750 electric vehicles (EVs) and 65,000 members. Such service. Tey proposed an algorithm for determining the companies own a number of vehicles and deal with any cost required number of vehicles, where they should be located at related to the operation of their feet in the car-sharing the start point, and how they should be routed to satisfy all service. travel demands in a particular period of time while enabling Tere is a trend toward the use of electric vehicles such as many passengers to be served by the same vehicle. Based on gasoline-electric hybrids and electric vehicles in car-sharing an analysis of historical taxi data from Manhattan in New systems [20, 23]. EVs, in comparison to their conventional York City, they presented a model estimating the number of counterparts, have lower operational and maintenance costs, required passenger cars to meet all daily taxi demands, with and their zero tailpipe emissions are another option for an average waiting time and an extra travel delay. Monteiro operation in car-sharing services since they usually operate et al. [26] provided a model to optimize the feet size by in urban environments. Furthermore, with regard to energy maximizing the number of served clients to satisfy the consumption, their performance at lower speeds is better demand while minimizing the high number of parked ve- than that of internal combustion engine vehicles (ICEVs) hicles in the station using a mixed-integer linear program. [24], which is an additional advantage during peak-hour Nair and Miller-Hooks [29] presented an optimization trafc. Te purchase price of EVs has thus far been the main model for feet management of shared-vehicle services by barrier to their wider use. However, with increasing tech- using a stochastic mixed-integer program with joint chance nological advancement, the cost of EV batteries, which constraints and random demand across stations to minimize makes up a large portion of the price of an EV, has been on a cost car redistribution in a feet. downward trend in recent years. Following Nykvist et al. Some research studies developed optimization models [25]; the battery price decreased by 77% from 2007 to 2018, for electric mobility in car-sharing systems [32–36]. In reaching an average cost of $230per kWh. Tus, this another study by [32], the authors performed an extensive downward trend in battery prices will lead to a reduction in review of recent literature on car-sharing. Tey developed an EV purchase prices over time. In contrast, ICEVs have lower optimization framework for the feet composition of station- purchase prices. However, the fuel cost of an ICEV, which is based car-sharing systems with heterogeneous feets by the major cost during the lifetime of such a vehicle, is very considering three diferent types of vehicles: ICEVs, plug-in unpredictable. Te steep increase in oil prices and their wild hybrid electric vehicles (PHEVs), and EVs. Tey demon- fuctuations in recent years have afected the fuel cost of strated that existing infrastructure and well-established ICEVs. Accordingly, any decision for vehicle replacement technology help ICEV growth and make PHEVs the best based merely on the actual total cost of ownership of a alternative compared to the other two types of vehicles. Tey vehicle without taking into account the concerned uncer- concluded that EVs remain the best alternative considering tainties might increase the cost in the long term. environmental and global emissions and local pollutants, To the best of our knowledge, no research study has been especially over long-term periods. In a research study by conducted on an optimal feet replacement for a car-sharing Bubeck et al. [34]; the authors analyzed the total ownership service considering trafc congestion levels. Tis study in- cost of electric mobility by considering the CO subsidies troduces a new optimization framework to assist a car- ofered to EVs and buyer premiums as an incentive on the sharing company in selecting the best investment strategy German road up to 2050. Te results showed that full and for structuring its feet from diferent types of vehicle mild hybrid electric vehicles are currently more economical technology (EVs vs. ICEVs in particular) over a certain even without government subsidies. Moreover, they showed planning time period. Te novelty of the developed that buyer premiums are necessary to make EVs competitive framework lies in considering diferent trafc congestion in terms of cost, and from 2030 onward, EVs can survive as intensity levels and various demand levels for a car-sharing an economical option. service throughout a typical day of operation. Te optimi- Although there have been various research studies fo- zation framework will provide the operator with the best cusing on feet optimization in shared mobility and car- feet composition for its car-sharing company over a certain sharing systems, to the best of our knowledge, no research planning period. study has addressed optimizing car-sharing feet structure Te remainder of the paper is organized as follows: considering the efect of trafc congestion. In this study, Section 2 contains a literature review, and Section 3 de- motivated by research studies on the feet replacement scribes the model and the optimization framework. In problem in Urban Freight Transport (UFT) (see [37, 38],and Section 4, the data and assumptions are presented, and [39], we introduce a novel optimization framework to assist Section 5 is dedicated to the results and discussion. Te a car-sharing company in choosing the best investment Journal of Advanced Transportation 3 Tus, based on the average speed given there and the strategy for having diferent types of vehicles (in particular EVs vs. ICEVs) in its feet over some planning time period. amount of consumption for the corresponding velocity given by He et al. [40] and Gree ´ et al. [41]; we illustrate in Despite some similarities between vehicle replacement in urban freight and car-sharing, there are diferences between Figure 1 how a typical day of operation is divided into three these two types of problems, which each deserve their own blocks of low, medium, and high congestion levels. analysis. Tis work focuses on vehicle composition for car- Te developed optimization framework will determine a sharing companies, whereas the focus of previous research more sustainable car-sharing feet structure for the company studies has been on vehicle composition for UFT. Te nature over a certain planning period while satisfying the interests of the demand for urban freight transport throughout the of the concerned stakeholders. In addition, uncertainties day is diferent from that of car-sharing services. Tere are related to various parameters such as energy, purchase, limitations regarding the operation of freight vehicles within emission, and maintenance costs need to be addressed. Tese uncertainties have an impact on the total cost of a city during the day (in particular, during peak hours). However, there are no such restrictions in regard to pas- running a car-sharing service, and any decisions regarding the composition of the feet taken without considering these senger vehicle operations within urban areas. More im- portantly, the developed optimization framework takes into can result in extra costs for the company. Accordingly, we account the magnitude of trafc congestion, which is a novel perform a sensitivity analysis to analyze the efects of a approach even within the context of UFT. number of uncertain input parameters on the total cost. 3. Research Methodology 3.1. Mathematical Optimization Framework. Te mathe- matical optimization framework for structuring the feet of a Te aim ofthis researchis to determinethe best combination of diferent types of passenger vehicles for the feet of a car- car-sharing company considering trafc congestion levels over a certain planning period is presented and discussed in sharing company over a certain planning period. Tere are this subsection. Te formulation is adapted and expanded various vehicles of diferent types that can be used by a from the optimization framework in Feng and Figliozzi [37]; company to run its car-sharing service. Each vehicle has its which was developed for the feet composition of an urban own characteristics, which afect the associated costs. Tese freight transport company. Since the trafc congestion level costs include the purchase price, energy costs, operation and is an important and efective factor in minimizing the total maintenance costs, and emission costs, to name the most important ones. In addition, depreciation rates for vehicles cost withinthe contextofcar-sharingservices,thepreviously developed framework needs to be adapted to take such a vary greatly, and accordingly, the corresponding salvage revenues are of various magnitudes. factor into consideration. Tese indices are used throughout the paper as follows: Energy consumption is one of the main costs associated with a vehicle during its lifetime. Speed is a principal factor (i) K ∈ k � {1, · · · , K} represents each type of vehicle afectingthe energyconsumption ofa vehicleand,as aresult, technology the amount of emissions that the vehicle produces. Fol- (ii) i ∈ A � 0, · · · , A represents the age of a vehicle of 􏼈 􏼉 lowing He et al. [40], the optimal fuel consumption occurs in type k the speed range of 45–80km/h, whereas EVs have lower energy consumption in the range of speeds between 20km/h (iii) t ∈ T � 0, · · · , T represents the year of the plan- { } and 40km/h [41]. On the other hand, during peak hours, ning time period trafc congestion afects the speed of a vehicle. In congested (iv) s ∈ S � {1, · · · , S} refers to the level of trafc con- areas, vehicles are faced with frequent stopping and going gestion in a day and operating in lower-level gears, which makes them Te decision variables are as follows: consume more energy. Terefore, the developed optimiza- tion framework considers these important factors by di- (i) X : number of age i type k vehicles used in year t i,t,k viding a typical day of operation into several blocks of time (ii) Y : number of age i, type k salvaged vehicles at the i,t,k depending on the trafc congestion level of that day. Te end of year t ideaofdividingatypicaldayoftheplanningtime periodinto (iii) Z : number of new type k purchased vehicles at the several blocks of time was motivated by previous research t,k beginning of year t studies on electricity supply planning Huang and Wu [42] and Wu and Huang [43]. To demonstrate the idea of di- (iv) x : total number of kilometers traveled by ve- i,t,k,s vidinga typicaldayofoperationintodiferent blocksof time, hicles of type k age i during the level of s trafc we use the data regarding the average speed given during congestion in year t 22hours of a day in Ji et al. [44], where the authors presented Te parameters are denoted as follows: the average speed of 20,000 taxi datasets recorded by GPS in part of the city of Shenzhen in China for 22hours from 1 AM (i) K: number of vehicle types to 11 PM on a weekday. An average speed of less than 30km/ (ii) T: span of the planning period h can be demonstrated more than 70% of the time, with the (iii) S: level of trafc congestion of a typical day of sharpest decline in average speed occurring during the peak operation hours of 6–8AM and 4–6PM. 4 Journal of Advanced Transportation 80 (ix) u : the maximum distance that can be traveled by i,t,k a vehicle of type k and age i in year t Low (x) v : purchase cost (€) per unit of type k vehicle 60 k,t during period t (xi) s : salvage revenue (€) of an age i, type k vehicle i,k (xii) e : per-km energy cost (€/km) of vehicle type k i,t,k,s 30 Medium of age i during level s of trafc congestion of year t (xiii) m : per-km operation and maintenance cost i,t,k,s (€/km) of vehicle k of age i during level s of trafc High congestion of year t 0 2 4 6 8 10 12 14 16 18 20 22 24 (xiv) em : CO emission cost (€/km) of vehicles of age i,k,s Time (h) i and type k during level s of trafc congestion Figure 1: Levels of trafc congestion considering speed and dif- ferent blocks of time. 3.1.1. Objective Function. Te objective function minimizes the total cost. Te total cost is composed of various cost (iv) A : maximum age of vehicle type k elements, namely, energy, operation and maintenance, (v) dr: discount rate for taking into account the de- purchase, and emission costs. We actualized the costs at the valuation of money with time beginning of the planning period. Since the objective (vi) b : budget of year t t function is linear and the decision variables take a non- negative integer and real values, problem (1) is thus a mixed- (vii) w d: working days in the year integer linear programming problem. Terefore, to mini- (viii) d : demand related to the level of s trafc con- t,s mize the total cost, the following optimization problem is gestion in year t solved as follows: T−1 k T K − t − t MinTC � 􏽘 􏽘 v z (1 + dr) − 􏽘 􏽘 􏽘 s Y (1 + dr) k,t t,k i,k i,t,k t�0 k�1 i�1 t�0 k�1 A −1 T−1 K S − t + 􏽘 􏽘 􏽘 􏽘 e + m + em x (1 + dr) , 􏼐 􏼑 i,t,k,s i,t,k,s i,k,s i,t,k,s i�0 t�0 k�1 s�1 s.t 􏽘 x ≤ w d u X ∀i ∈ A − 􏼈A 􏼉, ∀k ∈ K, ∀t ∈ T −{T}, i,t,k,s i,t,k i,t,k k s�1 A −1 􏽘 􏽘 x ≥ d ∀s ∈ S, ∀t ∈ T −{T}, i,t,k,s t,s i�0 k�1 (1) · 􏽘 v z ∀t ∈ {0,1,2, . . . , T − 1}, k,t t,k k�1 X � X + Y ∀t ∈ T, ∀k ∈ K, ∀i ∈ A −{0}, (i−1)(t−1),k i,t,k i,t,k Z � X ∀t ∈ T, ∀k ∈ K, t,k 0,t,k X � 0 ∀k ∈ K, ∀i ∈ A − 􏼈0, A 􏼉, i,T,k k X � 0 ∀t ∈ T, ∀k ∈ K, A ,t,k Y � 0 ∀t ∈ T, ∀k ∈ K, 0,t,k · Z , X , Y ∈ Z � {0,1,2, . . .}, t,k i,t,k i,t,k + + x ∈ R , where R represents the set of nonnegative real Purchase cost: i,tk,s numbers. T−1 K − t Te total cost (€) associated with the car-sharing service PC � 􏽘 v Z (1 + dr) . (2) k,t t,k business over the planning period consisted of the following t�0 k�1 components: Speed (km/h) Journal of Advanced Transportation 5 Salvage revenue: types are denoted as k=1 and k=2 for DVs and EVs, re- spectively. Tax incentives for diesel (https://taxfoundation. T K − t org/gas-taxes-europe-2019/) cars, better fuel economy in SR � 􏽘 􏽘 􏽘 s Y (1 + dr) . (3) i,k i,t,k most European countries, and lower tailpipe emissions of i�1 t�0 k�1 CO for diesel (https://autotraveler.ru/en/spravka/fuel- Energy cost: price-in-europe.html) [45] compared to gasoline are the main reasons for choosing this type of ICEV in our nu- A −1 k T−1 K S − t merical experiments. Te data regarding the two types of (4) EC � 􏽘 􏽘 􏽘 􏽘 e x (1 + dr) . i,t,k,s i,t,k,s vehicles and other input parameters are given in Table 1. i�0 t�0 s�1 k�1 With regard to the lifetime of vehicles, considering the Operation and maintenance cost: European Automobile Manufacturers Association (https:// A −1 T−1 K S www.aut.f/en/frontpage_vanha/statistics/international_ − t OP& MC � 􏽘 􏽘 􏽘 􏽘 m x (1 + dr) . (5) statistics/average_age_of_passenger_cars_in_some_ i,t,k,s i,t,k,s t�0 s�1 i�0 k�1 european_countries), which has reported an age of 8years for passenger cars in some European countries, and fol- Emission cost: lowing Mahut et al. [46]; we consider a lifetime of 8years for A −1 T−1 K S both passengers DVs and EVs. In addition, a discount rate of − t (6) EmC � 􏽘 􏽘 􏽘 􏽘 em x (1 + dr) . 5% [47] is used. By considering the foreseen daily utilization i,k,s i,t,k,s i�0 t�0 k�1 s�1 and EV battery lifetime of 160,000km [48, 49], each EV will need two batteries over its eight-year operational lifetime. Constraint (2) concerns the total distance (in kilometers) We include the discounted cost of the extra battery in the EV traveled in any year, which cannot be greater than the purchase price. maximum distance traveled by all types of vehicles used. In For the range limitation of EVs, the Nissan Leaf, the addition, in constraint (3), the distance traveled by all ve- electric car model that registered the highest number of sales hicles of any type and age for each demand level in any year in Europe in 2018 and the third leading passenger electric must be greater than the demand for the corresponding level vehicle in 2020 (https://www.statista.com/statistics/965507/ of s trafc congestion in that year. Constraint (4) shows that eu-leading-passenger-electric-vehicle-models/), was the EV the company has a yearly limited budget for purchasing new analyzed in this study. Te Leaf has a range of 264kilometers vehicles. Constraint (5) enforces that in any year of the with one full charge of battery. (https://www.nissanusa.com/ planningperiod,the numberofvehicles used andsalvaged of vehicles/electric-cars/leaf/features/range-charging-battery. any type must be equal to the number of vehicles used of the html). same type in the preceding year. Constraint (6) ensures that To calculate the salvage or resale value, we use the fol- in any planning period year, the new vehicles of any type lowing formula proposed by Feng and Figliozzi [37]: introduced into the feet must be the same as the number of purchased vehicles of that type. Constraint (7) forces all s � 1 − θ 􏼁 s � v 1 − θ 􏼁 , ∀k ∈ K, ∀i ∈ A −{1}, i,k k (i−1)k k k remaining vehicles to be sold at the end of the planning time (7) period. Constraint (8) ensures that when a vehicle reaches its maximum age, it must be salvaged. Constraint (9) ensures where θ is the rate at which vehicle type k is depreciated. that new vehicles cannot be salvaged immediately. Lastly, in Based on the values reported by Messagie et al. [50], we set constraint (10), decision variables Z , X and Y can t,k i,t,k i,t,k depreciationrates peryearof17%and 28%forDVs andEVs, take only non-negative integer values, and x can also i,t,k,s respectively. take nonnegative real values. For the medium TCL, we use an energy consumption of 0.062lit/km [51] and 0.145kWh/km [52] for DVs and EVs, 4. Data and Assumptions respectively. Based on the data given in Table 2, the energy costs per For the numerical experiments,we assume that a car-sharing kilometer are calculated using the formulas presented in the company has the goal of deriving an optimal combination of following equations: its feet from two available types of diesel and electric ve- hicles both with the same passenger capacity. Tese two lit f ·t e � R 􏼠 􏼡 × G × e ∀i ∈ A ∀t ∈ T ∀s ∈ S � {1,2,3}, (8) i,t,s,1 s,1 dv km kWh f ·t e � Q 􏼠 􏼡 × H × e ∀i ∈ A −{1} ∀t ∈ T ∀s ∈ S � {1,2,3}, (9) i,t,s,2 s,2 ev km 6 Journal of Advanced Transportation Table 1: Input-parameter data. Vehicle type DVs EVs Lifetime (years) A �8 A �8 1 2 Discount rate (%) 0.05 0.05 Annual use (km) 40000 40000 Daily use (km) 160 160 Planning time horizon (years) 16 16 Depreciation rate (%) 0.17 0.28 Energy cost growth rate (Pordata 2018) (%) 0.0582 0.0289 Purchase cost (Nissan, 2020) (€) 14000 28000 Energy consumption in low TCL (s ) 0.0465lit/km 0.1087kWh/km Energy consumption in medium TCL (s ) 0.062lit/km 0.145kWh/km Energy consumption in peak TCL (s ) 0.0775lit/km 0.1812kWh/km Energy cost (Pordata 2018) 1.16 €/lit 0.16 €/kWh CO emissions (well-to-wheel) 2.63kg/lit 0.47kg/kWh Table 2: Summary of characteristics of previous studies. Fleet Vehicle replacement/ References Method Model Context TCL size composition problem Mixed-integer linear [26] Opt Car-sharing system ✓ — — programming (MILP) [27] Opt (MILP) Car-sharing system ✓ — — Integer linear programming [28] Opt Car-sharing system ✓ ✓ — (ILP) Stochastic mixed-integer Fleet management shared-vehicle [29] Opt ✓ — — program (SMIP) system [32] Opt (ILP) Car-sharing system electric mobility ✓ ✓ — [34] Survey Total cost of ownership model Electric mobility — — — [31] Opt Mixed integer program (MIP) Shared mobility ✓ — — [35] Opt (MILP) Car-sharing system electric mobility ✓ — — [36] Opt Simulation model EV- sharing system ✓ — — Urban freight feet replacement [37] Opt (MIP) ✓ ✓ — problem Urban freight feet replacement and [38] Opt (MIP) ✓ ✓ — composition problem Mixed integer quadratic Urban freight feet replacement [39] Opt ✓ ✓ — programming (MIQP) problem Tis Opt (MILP) Car-sharing system ✓ ✓ ✓ research where R and Q represent the energy consumption per due to a lack of data regarding the energy consumption of s,1 s,2 km. G and H are the corresponding parameters for the vehicles with age, similar to Feng and Figliozzi [37] and dv ev energy cost of DVs and EVs as presented in Table 1, and f Ahani et al. [39]; we assumed that R and Q are fxed 1 s,1 s,2 and f are the annual growth rates of 5.82% and 2.89% [39] values for each i. for diesel and electricity prices, respectively. Te price On average, well-to-wheel CO emissions by DV and EV growth rates were defned on the basis of the annual diesel are approximately 2.63kg/lit and 0.47kg/kWh, respectively price history from 1980 to 2014 and the electricity price [53]. Te CO emission value for EVs is calculated by taking history from 1991 to 2014 in Portugal (https://www.pordata. into account the emissions produced by diferent types of pt/Portugal). power generation technologies. Terefore, the following We should mention that we made the right-hand side of equations give the emission cost of each type of vehicle based (8) and (9) independent of the age of vehicles (i.e., i). In fact, on its age: tan lit em � 0.00263 × R × ec, ∀i ∈ A − A , 􏼒 􏼓 􏼠 􏼡 􏼈 􏼉 i,s,1 s,1 k lit km (10) kg kWh ton em � 0.47􏼠 􏼡 × Q 􏼠 􏼡 × 0.001􏼠 􏼡ec, ∀i ∈ A − 􏼈A 􏼉. i,s,2 s,2 k kWh km kg Journal of Advanced Transportation 7 Table 3: Model statistics. An ec value of €25/ton is considered [54]. Following the maintenance cost data analysis from Name Number Carstens[55], each carhas a cost ofapproximately 0.04euro/ Constraints 745 km. Te mileage and age of a vehicle afect its maintenance Variables 1565 cost. Te total maintenance cost for EVs is at most 60% of Discrete variables 646 the maintenance cost for ICEVs [50]. Hence, we use the Execution time 0.06seconds following quadratic functions extrapolated from the data adopted from Carstens [55] to estimate the maintenance vehicles in each year of the planning period. An elasticity costs of ICEVs and then use them to approximate the analysis is also performed to show the magnitude of the maintenance costs of EVs. efects of certain input parameters on the total cost. m � −0.0015i 2 − 0.011i + 0.076, ∀i ∈ A − 0 , { } i,1 Figure 2 shows the number of vehicles used each year for the two types of vehicles. Regarding the number of vehicles m � 0.6 −0.0015i 2 − 0.011i + 0.076􏼁, ∀i ∈ A −{0}. i,2 used, the share of electric vehicles in the feet increases over (11) time up to year 12 of the planning period and then remains constant until year 14 and then begins to decrease. Keeping Regarding other input parameters, the following are in mind that the initial feet has been composed of only DVs, assumed: the reason for the increase in the share of EVs and replacing (i) Te company has 20 diesel vehicles of diferent DVs in the feet is their low operating costs, especially when ages in its initial feet. 12 vehicles of ages 0–3years considering the trafc congestion level, which is a major with three vehicles of each age and 8 vehicles of factor afecting the fuel consumption of a vehicle. We can see ages 4–7years with two vehicles of each age. that the share of EVs in the feet begins to decrease after year (ii) Tere are three trafc congestion levels (TCLs): 14 of the planning period, and the main reasons are their high purchasepriceandhigh depreciationrate.Indeed,these low (s1), medium (s2), and high (s3) with vehicle two factors mean that EVs, when compared with DVs, are demands of 20%, 30%, and 50% of the total de- not competitive for just the last two years of the planning mand, respectively (i.e., time period. Had the planning period been infnite, then the d � 0.2d , d � 0.3d , an d d � 0.5d ). t,1 t t,2 t t,3 t share of EVs would have increased constantly over the (iii) We assume that both DVs and EVs are used course of the said planning period. Additionally, Figure 3 160km per day, which is equivalent to 40,000km shows the number of purchased DVs and EVs over the per year based on a total of 250 working days in a 16years of the planning period. Te number of EVs de- year. creases toward the end of the planning period because the (iv) An annual budget of 56,000 euros is assumed for depreciation rate for EVs is higher than that of DVs. Figure 4 purchasing new vehicles. shows the number of vehicles salvaged at the end of each (v) We assume that the energy consumption of DVs in year and at the end of the planning time period when all the low and high TCLs is 25% less and 25% more vehicles are salvaged due to the end of the operation. than that of the medium TCL, respectively. For a more thorough analysis, we present in Figures 5 and 6 the total traveled distance for each type of vehicle and (vi) We also assumed a scenario without incorporating the trafc congestion level. As stated previously, we assume TCL into the model. For this scenario, we consider that the initial feet of the car-sharing service company is the energy consumption of 0.062lit/km and made up of DVs only. Te fgures show that for a high TCL 0.145kWh/km for DVs and EVs, respectively. (s �3), the total distance traveled by EVs begins to increase (vii) During each year, the total demand for car-sharing year by year, and from year eight until year fourteen of the vehicles is supposed to be equivalent to the total planning period, the total traveled distance in this TCL is distance traveled by all 20 vehicles in the corre- covered only by EVs. In the case of medium TCL (s �2), sponding year (d � 40,000km × 20). albeit in comparison to high TCL with a slower increase in (viii) We assumed that R and Q are independent of s,1 s,2 the share of EVs, and only from year 9 to year 13 of the age. planning period is the entire demand in this TCL met by EVs. DVs remain competitive chiefy for low TCL (s �1), as the operational cost for this TCL is lower than those of the 5. Results and Discussion other two levels. As previously mentioned, the increase in Tis section presents the results of resolving the mixed- the share of traveled distance by DVs for the high and integer linear optimization problem (1) (see Table 3) using medium TCLs toward the end of the planning period can be the CPLEX solver of GAMS version 27.3 [56] on a laptop attributed to the high purchase price and the high depre- computer with CPU Intel core i3−4030U 1.90GHz and cation rate of EVs, which render them less economically RAM memory of 4GB running Windows 10 64bits. We viable for just a few years of use in the feet. present the total number of purchased vehicles, total dis- We also assumed a scenario without incorporating the tance traveled in each trafc congestion level by each type of trafc congestion level into the model to show that the trafc vehicle, number of vehicles used, and number of salvaged congestion level has an important impact on the total cost. 8 Journal of Advanced Transportation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year DVs Evs Figure 2: Number of vehicles used during the planning period. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year DVs Evs Figure 3: Number of purchased vehicles during the planning period. 1 2 3 4 5 6 7 8 9 1011121314151617 Year DVs Evs Figure 4: Number of salvaged vehicles during the planning period. Number Number Number Journal of Advanced Transportation 9 1 2 3 4 5 6 7 8 9 10111213141516 Year Low trafc level Medium trafc level High trafc level Figure 5: Traveled distance of diesel vehicles for diferent levels of trafc congestion. 1 23456789 10 11 12 13 14 15 16 Year Low trafc level Medium trafc level High trafc level Figure 6: Traveled distance of electric vehicles for diferent levels of trafc congestion. As we mentioned previously for this scenario, we consider increase of 18% (from 1,955,629.032 to 2,310,844.077) in the the energy consumption of 0.062lit/km and 0.145kWh/km total cost. for DVs and EVs, respectively. Tis scenario led to an traveled distance (Km) traveled distance (Km) 10 Journal of Advanced Transportation Table 4: Per-km discounted elasticity analysis of total cost for diferent factors. Factor (range of values) (unit) Baseline value EA (TC, p) Depreciation rate EVs (17–27) (%) 22% 0.012 Depreciation rate EVs (23–33) (%) 28% 0.053 Depreciation rate EVs (29–39) (%) 34% 0.068 DVs growth rate energy price (2.91–8.73) (%) 5.82% 0.256 EVs growth rate energy price (1.44–4.33) (%) 2.89% 0.018 Discount rate (3–7) (%) 5% −0.180 EVs purchase price (25200–30800) (€) 28000 € 0.398 Energy price (1.044–1.275) (€/lit) 1.16 €/lit 0.351 Energy price (0.144–0.176) (€/kWh) 0.16 €/kWh 0.072 Emission cost (22.5–27.5) (€/ton) 25 €/ton 0.023 Lifetime (6–10) years 8years 0.025 EVs maintenance cost (0.024–0.028) (€/km) 0.0260 €/km 0.037 5.1. Elasticity Analysis. As mentioned previously, there is a number of key parameters to test their impacts on the total cost. To this end, we used the arc elasticity formula [57]as degree of uncertainty associated with some of the input parameters. Variations in these parameters can also impact follows: the total cost. We performed an elasticity analysis on a %chance in total cost 􏼈p1 + p2􏼉 {TC2 − TC1} EA(TC, p) � � × , (12) %change in parameter p {TC1 + TC2} 􏼈P2 − p1􏼉 where EA (TC, p) represents the discounted total cost (TC) car-sharing service. Te numerical results showed that EVs, per km in response to a change in parameter p. compared to DVs, become more competitive year after year Elasticity analysis was performed for diferent ranges of during the planning period. Te reason for the increase in values to assist the operator in determining which parameter the share of EVs is their low operating costs. More im- has the main impact on its optimal vehicle replacement portant, their competitiveness increases with the intensity of decision. Regarding the deprecation rate of EVs, an elasticity trafc congestion. Terefore, any decision made by a car- analysis was performed for three diferent intervals. As sharing operator that ignores trafc congestion intensity throughout the day as a factor would result in an onus, in the expected, the purchase priceof EVs, the energyprices related to the operation of DVs, and the growth rate in diesel prices form of extra costs, for the company in question. have the highest impact on the total cost. Te results of the In this paper, an elasticity analysis is done to consider the elasticity analysis are presented in Table 4. A 1% change in uncertainty of input parameters such as the energy cost, one of these parameters leads to increases of 0.40%, 0.35%, maintenance cost, EV purchase price, and emission cost of and 0.26% in the total cost, respectively. For the discount diferent types of vehicles. In future work, it will be rate range, the elasticity is negative, which means that when worthwhile to analyze the efect of these uncertainty pa- the discount rate increases by 1%, the total cost decreases by rameters by using a portfolio theory approach such as the 0.18%. one developed by Ahani et al. [39]. We also assumed that the range limitation of EVs was not a determining factor for the purchase decision. Depending on the demand level for car- 6. Conclusions sharing services, there are some situations in which such an assumption seems unrealistic. Hence, another line of re- Car-sharing can help resolve trafc congestion and emission search could involve developing a vehicle replacement and issues arising from increasing mobility within urban areas. assignment optimization framework by considering the In comparison to diesel vehicles, EVs perform better in range restriction of EVs and uncertainties associated with regard to energy consumption during peak-hour trafc the network of available charging stations and demand for congestion and low-speed fows. Taking this crucial factor car-sharing service across an urban area. In this work, we did into consideration, an optimization framework for intro- not take into account the charging station location, and no ducing new vehicles of diferent types into the feet of a car- limitation was assumed with regard to the demand for sharing company over a certain planning period was pre- charging EVs in a network of charging stations. However, in sented. Te developed framework considers the energy real scenarios, the network of charging stations might have a consumption and emissions of diferent types of vehicles at limited capacity for satisfying the uncertain demands for diferent levels of trafc congestion. To the best of our recharging the EVs. Tere are various research studies on knowledge, this is the frst time that such a framework has fnding optimal locations for refueling stations under been presented for the optimal composition of the feet of a Journal of Advanced Transportation 11 [11] E. W. Martin and S. A. Shaheen, “Greenhouse gas emission diferent scenarios and conditions [58–64]. Terefore, from impacts of carsharing in North America,” IEEE Transactions the standpoint of an urban decision-maker, the integration on Intelligent Transportation Systems, vol. 12, no. 4, of the frameworks developed in the aforementioned studies pp. 1074–1086, 2011. into the optimization framework of the current research [12] L. Hu and Y. Liu, “Joint design of parking capacities and feet study will be another interesting future line of research. size for one-way station-based carsharing systems with road congestion constraints,” Transportation Research Part B: Data Availability Methodological, vol. 93, pp. 268–299, 2016. [13] S. A. Shaheen, N. D. Chan, and E. Farrar, “Carsharing’s Te data used to support the fndings of this study are in- impact and future,” in Book: Te Sharing Economy and the cluded within the article. Relevance for Transport, pp. 87–120, Elsevier, Amsterdam, Netherlands, 2019. Conflicts of Interest [14] T. D. Chen and K. M. Kockelman, “Carsharing’s life-cycle impacts on energy use and greenhouse gas emissions,” Te authors declare that they have no conficts of interest. Transportation Research Part D: Transport and Environment, vol. 47, pp. 276–284, 2016. Acknowledgments [15] V. Roblek, M. Meˇsko, and I.Podbregar, “Impact of car sharing on urban sustainability,” Sustainability, vol. 13, no. 2, p. 905, Te authors would like to acknowledge the Foundation for Science and Technology for the fnancial support with ref- [16] M. Balac, H. Becker, F. Ciari, and K. W. Axhausen, “Modeling erences (UIDB/04625/2020) and (SFRH/BD/89258/2012). competing free-foating carsharing operators–A case study for Te authors would also like to acknowledge funding from Zurich, Switzerland,” Transportation Research Part C: the project Horizon 2020 “ASSURED–UAM, Acceptance, Emerging Technologies, vol. 98, pp. 101–117, 2019. ˇ ˇ [17] D. Fiedler, M. Cap, ´ and M. Certicky,´ “Impact of mobility-on Safety, and Sustainability Recommendations for Efcient demand on trafc congestion: simulation-based study,” in Deployment of UAM” and the project “C-Tech–Climate Proceedings of the 2017 IEEE 20th International Conference on Driven Technologies for Low Carbon Cities” of the MIT- Intelligent Transportation Systems (ITSC), pp. 1–6, IEEE, Portugal Program. Yokohama, Japan, October 2017. [18] F. Ciari, B.Bock, and M. Balmer, “Modeling station-based and References free-foating carsharing demand: test case study for berlin,” Transportation Research Record Journal of the Transportation [1] R. Katzev, “Car sharing: a new approach to urban trans- Research Board, vol. 2416, no. 1, 2014. portation problems,” Analyses of Social Issues and Public [19] A. P. Cohen, S. A. Shaheen, and R. McKenzie, “Carsharing: a Policy, vol. 3, no. 1, pp. 65–86, 2003. guide for local planners,” Journal of Planning Advisory Service [2] S. Lee, “A review of carsharing research: with a focus on Memo, vol. 1040, 2008, http://escholarship.org/uc/item/ domestic thesis and research papers,” Inst. Korean Reg. 4kf3x31h,%20UCD-ITS-RP-08-16. Stud.vol. 62, pp. 3–17, 2015. [20] S. A. Shaheen and A. P. Cohen, “Carsharing and personal [3] S. A. Shaheen, N. D. Chan, A. Bansal, and A. P. Cohen, Shared vehicle services: worldwide market developments and Mobility: Defnitions, Industry Developments, and Early Un- emerging trends,” International Journal of Sustainable derstanding, Transportation Sustainability Research Center, Transportation, vol. 7, no. 1, pp. 5–34, 2012. Berkeley, CA, USA, 2015, http://innovativemobility.org/wp. [21] X. Li, J. Ma, J. Cui, A. Ghiasi, and F. Zhou, “Design framework [4] J. Jung and Y. Koo, “Analyzing the efects of car sharing of large-scale one-way electric vehicle sharing systems: a services on the reduction of greenhouse gas (GHG) emis- continuum approximation model,” Transportation Research sions,” Sustainability, vol. 10, no. 2, p. 539, 2018. Part B: Methodological, vol. 88, pp. 21–45, 2016. [5] Y. Hui, Y. Wang, Q. Sun, and L. Tang, “Te impact of car- [22] S. Frost, “Strategic insight of the global carsharing market,” sharing on the willingness to postpone a car purchase: a case Technical Reports Series 90-18, Frost & Sullivan, San Antonio, study in Hangzhou, China,” Journal of Advanced Trans- TX, USA, 2014. portation, vol. 2019, Article ID 9348496, 11 pages, 2019. [23] C. King, W. Griggs, F. Wirth, and R. Shorten, “Using a car [6] A. Millard-Ball, “Car-sharing: where and how it succeeds,” sharing model to alleviate electric vehicle range anxiety,” in vol. 60, Transportation Research Board, Washington, D.C, Proceedings of the 16th Yale Workshop on Adaptive and USA, 2005, TCRP Report 108. Learning Systems, pp. 130–135, New Haven, CT, USA, June [7] G. Cooper, D. A. Howe, and P. Mye, Te Missing Link: An Evaluation of Carsharing, Portland Inc, Portland, Oregon, [24] S. Mamarikas, S. Doulgeris, Z. Samaras, and L. Ntziachristos, “Trafc impacts on energy consumption of electric and [8] B. Yu, Y. Ma, M. Xue et al., “Environmental benefts from conventional vehicles,” Transportation Research Part D: ridesharing: a case of Beijing,” Applied Energy, vol. 191, pp. 141–152, 2017. Transport and Environment, vol.105, Article ID 103231, 2022. [25] B. Nykvist, F. Sprei, and M. Nilsson, “Assessing the progress [9] H. Nijland and J. van Meerkerk, “Mobility and environmental impacts of car sharing in Te Netherlands,” Environmental toward lower priced long range battery electric vehicles,” Energy Policy, vol. 124, pp. 144–155, 2019. Innovation and Societal Transitions, vol. 23, pp. 84–91, 2017. [10] E. Martin, S. A. Shaheen, and J. Lidicker, “Impact of car- [26] C. M. Monteiro, C. A. S. Machado, M. d. O. Lage, F. T. Berssaneti, C. A. Davis, and J. A. Quintanilha, “Opti- sharing on household vehicle holdings: results from North American shared-use vehicle survey. Transportation Research mization of carsharing feet size to maximize the number of clients served,” Computers, Environment and Urban Systems, Record,” Journal of the Transportation Research Board, vol. 2143, pp. 151–158, 2010. vol. 87, Article ID 101623, 2021. 12 Journal of Advanced Transportation [27] P. Strohle, ¨ C. M. Flath, and J. Garttner, ¨ “Leveraging customer [42] Y. H. Huang and J. H. Wu, “A portfolio risk analysis on fexibility for car-sharing feet optimization,” Transportation electricity supply planning,” Energy Policy, vol. 36, no. 2, pp. 627–641, 2008. Science, vol. 53, no. 1, pp. 42–61, 2019. [43] J.-H. Wu and Y.-H. Huang, “Electricity portfolio planning [28] A. Wallar, J. Alonso-Mora, and D. Rus, “Optimizing vehicle model incorporating renewable energy characteristics,” Ap- distributions and feet sizes for shared mobility-on-demand,” plied Energy, vol. 119, pp. 278–287, 2014. in Proceedings of the 2019 International Conference on Ro- [44] Y. Ji, J. Luo, and N. Geroliminis, “Empirical observations of botics and Automation (ICRA), pp. 3853–3859, IEEE, Mon- congestion propagation and dynamic partitioning with probe treal, Canada, May 2019. data for large-scale systems,” Transportation Research Record [29] R. Nair and E. Miller-Hooks, “Fleet management for vehicle Journal of the Transportation Research Board, vol. 2422, no.1, sharing operations,” Transportation Science, vol. 45, no. 4, pp. 1–11, 2014. pp. 524–540, 2011. [45] D. Magueta, M. Madaleno, M. Ferreira Dias, and M. Meireles, [30] J. Li, Y. S. Chen, H. Li, I. Andreasson, and H. V. Zuylen, “New cars and emissions: efects of policies, macroeconomic “Optimizing the feet size of a personal rapid transit system: a impacts and cities characteristics in Portugal,” Journal of case study in port of rotterdam,” in Proceedings of the 13th Cleaner Production, vol. 181, pp. 178–191, 2018. International IEEE Conference on Intelligent Transportation [46] F. Mahut, J. Daaboul, M. Bricogne, and B. Eynard, “Product- Systems (ITSC), pp. 301–305, IEEE, Funchal, Portugal, Sep- Service Systems for Servitization of the automotive industry: a tember 2010. literature review,” International Journal of Production Re- [31] H. Hosni, J. Naoum-Sawaya, and H. Artail, “Te shared-taxi search, vol. 55, no. 7, pp. 2102–2120, 2017. problem: formulation and solution methods,” Transportation [47] P. Baptista, S. Melo, and C. Rolim, “Energy, environmental Research Part B: Methodological, vol. 70, pp. 303–318, 2014. and mobility impacts of car sharing systems. Empirical results [32] R. F. Lemme, E. F. Arruda, and L. Bahiense, “Optimization from Lisbon, Portugal,” Procedia-Social and Behavioral Sci- model to assess electric vehicles as an alternative for feet ences, vol. 111, pp. 28–37, 2014. composition in station-based car sharing systems,” Trans- [48] G. Palmer and J. Floyd, “Chapter of Energy Primer for Storage portation Research Part D: Transport and Environment, Analysis in,” Book: Energy Storage and Civilization, Springer, vol. 67, pp. 173–196, 2019. Cham, Switzerland, pp. 41–56, 2020. [33] G. Brandstatter, M. Kahr, and M. Leitner, “Determining [49] A. Ajanovic and R. Haas, “Electric vehicles: solution or new optimal locations for charging stations of electric car sharing problem?” Environment, Development and Sustainability, systems under stochastic demand,” Transportation Research vol. 20, no. S1, pp. 7–22, 2018. Part B: Methodological, vol. 104, pp. 17–35, 2017. [50] M. Messagie, K. Lebeau, T. Coosemans, C. Macharis, and [34] S. Bubeck, J. Tomaschek, and U. Fahl, “Perspectives of electric J. van Mierlo, “Environmental and fnancial evaluation of mobility: total cost of ownership of electric vehicles in Ger- passenger vehicle technologies in Belgium,” Sustainability, many,” Transport Policy, vol. 50, pp. 63–77, 2016. vol. 5, no. 12, pp. 5020–5033, 2013. [51] D. Lois, Y. Wang, A. Boggio-Marzet, and A. Monzon, [35] S. Weikl and K. Bogenberger, “A practice-ready relocation “Multivariate analysis of fuel consumption related to eco- model for free-foating carsharing systems with electric ve- driving: interaction of driving patterns and external factors,” hicles – mesoscopic approach and feld trial results,” Trans- Transportation Research Part D: Transport and Environment, portation Research Part C: Emerging Technologies, vol. 57, vol. 72, pp. 232–242, 2019. pp. 206–223, 2015. [52] J. Zhang, Z. Wang, P. Liu, D. Cui, and X. Li, “Analysis on [36] S. Nakayama, T. Yamamoto, and R. Kitamura, “Simulation infuence factors of energy consumption of electric vehicles analysis for the management of an electric vehicle-sharing based on real-world driving data,” in Proceedings of the 11th system: case of the kyoto public-car system,” Transportation International Conference on Applied Energy 2019, (ICAE2019), Research Record Journal of the Transportation Research Board, ¨ ˚ pp. 12–15, vasteras, Sweden, January 2019. vol. 1791, no. 1, pp. 99–104, 2002. [53] I. Adeniran, Te Impacts of Sustainable Concepts in Urban [37] W. Feng and M. Figliozzi, “An economic and technological Freight Distribution-A Courier, Express and Parcel Case Study, analysis of the key factors afecting the competitiveness of Doctoral dissertation, Technische Universitat¨ Munchen, ¨ electric commercial vehicles: a case study from the USA Munich, Germany, 2020. market,” Transportation Research Part C: Emerging Technol- [54] R. Gerlagh, R. J. R. K. Heijmans, and K. E. Rosendahl, ogies, vol. 26, pp. 135–145, 2013. “COVID-19 tests the market stability reserve,” Environmental [38] O. Jabali and G. Erdogan, Continuous Approximation Models and Resource Economics, vol. 76, no. 4, pp. 855–865, 2020. for the Fleet Replacement and Composition Problem (No. [55] S. Carstens, “Increasing the competitiveness of maintenance CIRRELT-2015-64), CIRRELT, Montreal, Canada, 2015. contract rates by using an alternative methodology for the [39] P. Ahani, A. Arantes, and S. Melo, “A portfolio approach for calculation of average vehicle maintenance costs,” Journal of optimal feet replacement toward sustainable urban freight Transport and supply chain Management, vol. 2, no. 1, transportation,” Transportation Research Part D: Transport pp. 1–11, 2008. and Environment, vol. 48, pp. 357–368, 2016. [56] Gams, General Algebraic Modeling System (GAMS), GAMS [40] Y.M. He,J. Kang,Y. L.Pei,B. Ran,and Y.T.Song, “Studyon a Development Corporation, Washington, DC, USA, 2019. prediction model of superhighway fuel consumption based on [57] R. G. D. Allen, “Te concept of arc elasticity of demand: I,” the test of easy car platform,” Sustainability, vol. 12, no. 15, Te Review of Economic Studies, vol. 1, no. 3, pp. 226–229, p. 6260, 2020. [41] F. Gree, ´ V. Laznikova, B. Kim, G. Garcia, T. Kigezi, and [58] M. Miralinaghi, G. H. de Almeida Correia, S. E. Seilabi, and B. Gao, “Cloud-based big data platform for vehicle-to-grid S. Labi, “Designing a network of electric charging stations to (v2g),” World Electric Vehicle Journal, vol. 11, no. 2, p. 30, mitigate vehicle emissions,” in 2020 Forum on Integrated and 2020. Sustainable Transportation Systems (FISTS), pp. 95–100, Journal of Advanced Transportation 13 Institute of Electrical and Electronics Engineers (IEEE), Delft, Netherlands, 2020. [59] M. Miralinaghi, Y. Lou, B. B. Keskin, A. Zarrinmehr, and R. Shabanpour, “Refueling station location problem with trafc deviation considering route choice and demand un- certainty,” International Journal of Hydrogen Energy, vol. 42, no. 5, pp. 3335–3351, 2017. [60] M. Miralinaghi, B. B. Keskin, Y. Lou, and A. M. Roshandeh, “Capacitated refueling station location problem with trafc deviations over multiple time periods,” Networks and Spatial Economics, vol. 17, 2017. [61] M. Ghamami, A. Zockaie, and Y. Nie, “A General Corridor Model for Designing Plug-In Electric Vehicle Charging In- frastructure to Support Intercity Travel,” Transportation Re- search Part C: Emerging Technologies, vol. 68, 2016. [62] Z.-H. Zhu, Z.-Y. Gao, J.-F. Zheng, and H.-M. Du, “Charging station location problem of plug-in electric vehicles,” Journal of Transport Geography, vol. 52, pp. 11–22, 2016. [63] R. R. Desai, E. Hittinger, and E. Williams, “Interaction of consumer heterogeneity and technological progress in the US electric vehicle market,” Energies, vol.15, no.13, p. 4722, 2022. [64] H. Zheng, X. He, Y. Li, and S. Peeta, “Trafc equilibrium and charging facility locations for electric vehicles,” Networks and Spatial Economics, vol. 17, no. 2, pp. 435–457, 2016. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Advanced Transportation Hindawi Publishing Corporation

An Optimization Model for Structuring a Car-Sharing Fleet Considering Traffic Congestion Intensity

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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 9283130, 13 pages https://doi.org/10.1155/2023/9283130 Research Article An Optimization Model for Structuring a Car-Sharing Fleet Considering Traffic Congestion Intensity 1 2 3 Parisa Ahani , Amilcar Arantes , and Sandra Melo CERIS, MIT Portugal Program, Sustainable Energy Systems, Instituto Superior Tecnico, Universidade de Lisboa, Lisbon, Portugal CERIS, Instituto Superior Tecnico, Universidade de Lisboa, Lisbon, Portugal CEiiA, Center of Engineering and Development, Matosinhos, Portugal Correspondence should be addressed to Parisa Ahani; prsahani1@gmail.com Received 18 April 2022; Revised 18 September 2022; Accepted 24 November 2022; Published 6 February 2023 Academic Editor: Mohammad Miralinaghi Copyright © 2023 Parisa Ahani et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ever-growing mobility and trafc congestion within urban areas make the need for a sustainable form of transport inevitable. Trafc congestion has a signifcant efect on the amount of energy consumption of a vehicle and, as a result, on its associated environmental impacts. Any decision-making regarding structuring a feet without taking into account the trafc congestion level (TCL) will lead to a less sustainable feet with higher environmental and economic costs. To address this issue, this study examines the efects of the trafc congestion intensity level on the feet structure of an urban car-sharing company over a certain planning period. We present a new optimization framework for fnding an optimal vehicle composition of the feet of an urban car-sharing company considering the energy consumption of vehicles at diferent trafc congestion levels. Te results show that electric vehicles (EVs) are more competitive than diesel vehicles (DVs) in high-peak trafc congestion from the outset of the planning period. In addition, we perform a sensitivity analysis to take into account the efects of specifc uncertain parameters such as the energy and purchasing costs of EVs on the total cost of ownership. As expected, the purchasing price of EVs, energy prices of DVs, and increase in diesel prices have the highest impact on the total cost. Chen and Kockelman [14] estimated a reduction of 51% in 1. Introduction energy consumption and greenhouse gas (GHG) emissions Te idea of several people sharing the same car can be traced for what they have defned as a “good candidate for shared back several decades ago [1]. Car-sharing is a type of shared mobility.” mobility that ofers renting cars on a needed basis for as little In two studies [10, 11], the authors conducted a survey of as 10minutes [2] and often by the hour when other modes of members of a car-sharing club in the US, looking specifcally transport are not available or are not suitable [3]. Te users at the impacts of car-sharing on household vehicle own- can be passengers, companies, and public agencies [4]. Te ership. Te results showed that the rate of vehicle ownership station of car-sharing is usually close to the location of among club members decreased from 0.47 to 0.24 vehicles transportation modes, and the payment is based on travel per household. In the last decade, the car-sharing market in distance or time spent [4]. Europe has expanded, and in Germany, as the largest car- Car-sharing has the potential to reduce vehicle use, sharing market in Europe, an increase in user usage from ownership, and delays in car purchases [5–7]. It is seen as a 0.26 million in 2012 to 1.29 million in 2020 was reported by solution to address the issues of congestion, pollutants, and Roblek et al. [15]. the occupancy rate of vehicles within urban areas [8, 9]. Tis Various research studies have shown that the demand leads to increasing urban sustainability from environmental, for car-sharing as a means of mobility in any form is in- economic, and societal points of view worldwide. [10–13]. creasing worldwide [16–19]. In many countries around the 2 Journal of Advanced Transportation paper ends in Section 6 with the enunciation of some world, car-sharing or short-term auto access [20] is known as a system to minimize ownership transportation costs and conclusions. the negative efects of car use. Te car-sharing industry has recently signifcantly increased its market [21, 22]. In the 2. Literature Review past decade, advancements in communication technologies and smartphone applications have led to the emergence of Various research studies have focused on feet optimization car-sharing companies such as DriveNow and Car2Go. for shared mobility systems [26–31]. In a study by Wallar Autolib in Paris is one of the known operators in car-sharing et al. [28], the authors provided a model for optimizing feet systems that ofers electric car-sharing services with at least composition to distributions of vehicles for shared mobility 1750 electric vehicles (EVs) and 65,000 members. Such service. Tey proposed an algorithm for determining the companies own a number of vehicles and deal with any cost required number of vehicles, where they should be located at related to the operation of their feet in the car-sharing the start point, and how they should be routed to satisfy all service. travel demands in a particular period of time while enabling Tere is a trend toward the use of electric vehicles such as many passengers to be served by the same vehicle. Based on gasoline-electric hybrids and electric vehicles in car-sharing an analysis of historical taxi data from Manhattan in New systems [20, 23]. EVs, in comparison to their conventional York City, they presented a model estimating the number of counterparts, have lower operational and maintenance costs, required passenger cars to meet all daily taxi demands, with and their zero tailpipe emissions are another option for an average waiting time and an extra travel delay. Monteiro operation in car-sharing services since they usually operate et al. [26] provided a model to optimize the feet size by in urban environments. Furthermore, with regard to energy maximizing the number of served clients to satisfy the consumption, their performance at lower speeds is better demand while minimizing the high number of parked ve- than that of internal combustion engine vehicles (ICEVs) hicles in the station using a mixed-integer linear program. [24], which is an additional advantage during peak-hour Nair and Miller-Hooks [29] presented an optimization trafc. Te purchase price of EVs has thus far been the main model for feet management of shared-vehicle services by barrier to their wider use. However, with increasing tech- using a stochastic mixed-integer program with joint chance nological advancement, the cost of EV batteries, which constraints and random demand across stations to minimize makes up a large portion of the price of an EV, has been on a cost car redistribution in a feet. downward trend in recent years. Following Nykvist et al. Some research studies developed optimization models [25]; the battery price decreased by 77% from 2007 to 2018, for electric mobility in car-sharing systems [32–36]. In reaching an average cost of $230per kWh. Tus, this another study by [32], the authors performed an extensive downward trend in battery prices will lead to a reduction in review of recent literature on car-sharing. Tey developed an EV purchase prices over time. In contrast, ICEVs have lower optimization framework for the feet composition of station- purchase prices. However, the fuel cost of an ICEV, which is based car-sharing systems with heterogeneous feets by the major cost during the lifetime of such a vehicle, is very considering three diferent types of vehicles: ICEVs, plug-in unpredictable. Te steep increase in oil prices and their wild hybrid electric vehicles (PHEVs), and EVs. Tey demon- fuctuations in recent years have afected the fuel cost of strated that existing infrastructure and well-established ICEVs. Accordingly, any decision for vehicle replacement technology help ICEV growth and make PHEVs the best based merely on the actual total cost of ownership of a alternative compared to the other two types of vehicles. Tey vehicle without taking into account the concerned uncer- concluded that EVs remain the best alternative considering tainties might increase the cost in the long term. environmental and global emissions and local pollutants, To the best of our knowledge, no research study has been especially over long-term periods. In a research study by conducted on an optimal feet replacement for a car-sharing Bubeck et al. [34]; the authors analyzed the total ownership service considering trafc congestion levels. Tis study in- cost of electric mobility by considering the CO subsidies troduces a new optimization framework to assist a car- ofered to EVs and buyer premiums as an incentive on the sharing company in selecting the best investment strategy German road up to 2050. Te results showed that full and for structuring its feet from diferent types of vehicle mild hybrid electric vehicles are currently more economical technology (EVs vs. ICEVs in particular) over a certain even without government subsidies. Moreover, they showed planning time period. Te novelty of the developed that buyer premiums are necessary to make EVs competitive framework lies in considering diferent trafc congestion in terms of cost, and from 2030 onward, EVs can survive as intensity levels and various demand levels for a car-sharing an economical option. service throughout a typical day of operation. Te optimi- Although there have been various research studies fo- zation framework will provide the operator with the best cusing on feet optimization in shared mobility and car- feet composition for its car-sharing company over a certain sharing systems, to the best of our knowledge, no research planning period. study has addressed optimizing car-sharing feet structure Te remainder of the paper is organized as follows: considering the efect of trafc congestion. In this study, Section 2 contains a literature review, and Section 3 de- motivated by research studies on the feet replacement scribes the model and the optimization framework. In problem in Urban Freight Transport (UFT) (see [37, 38],and Section 4, the data and assumptions are presented, and [39], we introduce a novel optimization framework to assist Section 5 is dedicated to the results and discussion. Te a car-sharing company in choosing the best investment Journal of Advanced Transportation 3 Tus, based on the average speed given there and the strategy for having diferent types of vehicles (in particular EVs vs. ICEVs) in its feet over some planning time period. amount of consumption for the corresponding velocity given by He et al. [40] and Gree ´ et al. [41]; we illustrate in Despite some similarities between vehicle replacement in urban freight and car-sharing, there are diferences between Figure 1 how a typical day of operation is divided into three these two types of problems, which each deserve their own blocks of low, medium, and high congestion levels. analysis. Tis work focuses on vehicle composition for car- Te developed optimization framework will determine a sharing companies, whereas the focus of previous research more sustainable car-sharing feet structure for the company studies has been on vehicle composition for UFT. Te nature over a certain planning period while satisfying the interests of the demand for urban freight transport throughout the of the concerned stakeholders. In addition, uncertainties day is diferent from that of car-sharing services. Tere are related to various parameters such as energy, purchase, limitations regarding the operation of freight vehicles within emission, and maintenance costs need to be addressed. Tese uncertainties have an impact on the total cost of a city during the day (in particular, during peak hours). However, there are no such restrictions in regard to pas- running a car-sharing service, and any decisions regarding the composition of the feet taken without considering these senger vehicle operations within urban areas. More im- portantly, the developed optimization framework takes into can result in extra costs for the company. Accordingly, we account the magnitude of trafc congestion, which is a novel perform a sensitivity analysis to analyze the efects of a approach even within the context of UFT. number of uncertain input parameters on the total cost. 3. Research Methodology 3.1. Mathematical Optimization Framework. Te mathe- matical optimization framework for structuring the feet of a Te aim ofthis researchis to determinethe best combination of diferent types of passenger vehicles for the feet of a car- car-sharing company considering trafc congestion levels over a certain planning period is presented and discussed in sharing company over a certain planning period. Tere are this subsection. Te formulation is adapted and expanded various vehicles of diferent types that can be used by a from the optimization framework in Feng and Figliozzi [37]; company to run its car-sharing service. Each vehicle has its which was developed for the feet composition of an urban own characteristics, which afect the associated costs. Tese freight transport company. Since the trafc congestion level costs include the purchase price, energy costs, operation and is an important and efective factor in minimizing the total maintenance costs, and emission costs, to name the most important ones. In addition, depreciation rates for vehicles cost withinthe contextofcar-sharingservices,thepreviously developed framework needs to be adapted to take such a vary greatly, and accordingly, the corresponding salvage revenues are of various magnitudes. factor into consideration. Tese indices are used throughout the paper as follows: Energy consumption is one of the main costs associated with a vehicle during its lifetime. Speed is a principal factor (i) K ∈ k � {1, · · · , K} represents each type of vehicle afectingthe energyconsumption ofa vehicleand,as aresult, technology the amount of emissions that the vehicle produces. Fol- (ii) i ∈ A � 0, · · · , A represents the age of a vehicle of 􏼈 􏼉 lowing He et al. [40], the optimal fuel consumption occurs in type k the speed range of 45–80km/h, whereas EVs have lower energy consumption in the range of speeds between 20km/h (iii) t ∈ T � 0, · · · , T represents the year of the plan- { } and 40km/h [41]. On the other hand, during peak hours, ning time period trafc congestion afects the speed of a vehicle. In congested (iv) s ∈ S � {1, · · · , S} refers to the level of trafc con- areas, vehicles are faced with frequent stopping and going gestion in a day and operating in lower-level gears, which makes them Te decision variables are as follows: consume more energy. Terefore, the developed optimiza- tion framework considers these important factors by di- (i) X : number of age i type k vehicles used in year t i,t,k viding a typical day of operation into several blocks of time (ii) Y : number of age i, type k salvaged vehicles at the i,t,k depending on the trafc congestion level of that day. Te end of year t ideaofdividingatypicaldayoftheplanningtime periodinto (iii) Z : number of new type k purchased vehicles at the several blocks of time was motivated by previous research t,k beginning of year t studies on electricity supply planning Huang and Wu [42] and Wu and Huang [43]. To demonstrate the idea of di- (iv) x : total number of kilometers traveled by ve- i,t,k,s vidinga typicaldayofoperationintodiferent blocksof time, hicles of type k age i during the level of s trafc we use the data regarding the average speed given during congestion in year t 22hours of a day in Ji et al. [44], where the authors presented Te parameters are denoted as follows: the average speed of 20,000 taxi datasets recorded by GPS in part of the city of Shenzhen in China for 22hours from 1 AM (i) K: number of vehicle types to 11 PM on a weekday. An average speed of less than 30km/ (ii) T: span of the planning period h can be demonstrated more than 70% of the time, with the (iii) S: level of trafc congestion of a typical day of sharpest decline in average speed occurring during the peak operation hours of 6–8AM and 4–6PM. 4 Journal of Advanced Transportation 80 (ix) u : the maximum distance that can be traveled by i,t,k a vehicle of type k and age i in year t Low (x) v : purchase cost (€) per unit of type k vehicle 60 k,t during period t (xi) s : salvage revenue (€) of an age i, type k vehicle i,k (xii) e : per-km energy cost (€/km) of vehicle type k i,t,k,s 30 Medium of age i during level s of trafc congestion of year t (xiii) m : per-km operation and maintenance cost i,t,k,s (€/km) of vehicle k of age i during level s of trafc High congestion of year t 0 2 4 6 8 10 12 14 16 18 20 22 24 (xiv) em : CO emission cost (€/km) of vehicles of age i,k,s Time (h) i and type k during level s of trafc congestion Figure 1: Levels of trafc congestion considering speed and dif- ferent blocks of time. 3.1.1. Objective Function. Te objective function minimizes the total cost. Te total cost is composed of various cost (iv) A : maximum age of vehicle type k elements, namely, energy, operation and maintenance, (v) dr: discount rate for taking into account the de- purchase, and emission costs. We actualized the costs at the valuation of money with time beginning of the planning period. Since the objective (vi) b : budget of year t t function is linear and the decision variables take a non- negative integer and real values, problem (1) is thus a mixed- (vii) w d: working days in the year integer linear programming problem. Terefore, to mini- (viii) d : demand related to the level of s trafc con- t,s mize the total cost, the following optimization problem is gestion in year t solved as follows: T−1 k T K − t − t MinTC � 􏽘 􏽘 v z (1 + dr) − 􏽘 􏽘 􏽘 s Y (1 + dr) k,t t,k i,k i,t,k t�0 k�1 i�1 t�0 k�1 A −1 T−1 K S − t + 􏽘 􏽘 􏽘 􏽘 e + m + em x (1 + dr) , 􏼐 􏼑 i,t,k,s i,t,k,s i,k,s i,t,k,s i�0 t�0 k�1 s�1 s.t 􏽘 x ≤ w d u X ∀i ∈ A − 􏼈A 􏼉, ∀k ∈ K, ∀t ∈ T −{T}, i,t,k,s i,t,k i,t,k k s�1 A −1 􏽘 􏽘 x ≥ d ∀s ∈ S, ∀t ∈ T −{T}, i,t,k,s t,s i�0 k�1 (1) · 􏽘 v z ∀t ∈ {0,1,2, . . . , T − 1}, k,t t,k k�1 X � X + Y ∀t ∈ T, ∀k ∈ K, ∀i ∈ A −{0}, (i−1)(t−1),k i,t,k i,t,k Z � X ∀t ∈ T, ∀k ∈ K, t,k 0,t,k X � 0 ∀k ∈ K, ∀i ∈ A − 􏼈0, A 􏼉, i,T,k k X � 0 ∀t ∈ T, ∀k ∈ K, A ,t,k Y � 0 ∀t ∈ T, ∀k ∈ K, 0,t,k · Z , X , Y ∈ Z � {0,1,2, . . .}, t,k i,t,k i,t,k + + x ∈ R , where R represents the set of nonnegative real Purchase cost: i,tk,s numbers. T−1 K − t Te total cost (€) associated with the car-sharing service PC � 􏽘 v Z (1 + dr) . (2) k,t t,k business over the planning period consisted of the following t�0 k�1 components: Speed (km/h) Journal of Advanced Transportation 5 Salvage revenue: types are denoted as k=1 and k=2 for DVs and EVs, re- spectively. Tax incentives for diesel (https://taxfoundation. T K − t org/gas-taxes-europe-2019/) cars, better fuel economy in SR � 􏽘 􏽘 􏽘 s Y (1 + dr) . (3) i,k i,t,k most European countries, and lower tailpipe emissions of i�1 t�0 k�1 CO for diesel (https://autotraveler.ru/en/spravka/fuel- Energy cost: price-in-europe.html) [45] compared to gasoline are the main reasons for choosing this type of ICEV in our nu- A −1 k T−1 K S − t merical experiments. Te data regarding the two types of (4) EC � 􏽘 􏽘 􏽘 􏽘 e x (1 + dr) . i,t,k,s i,t,k,s vehicles and other input parameters are given in Table 1. i�0 t�0 s�1 k�1 With regard to the lifetime of vehicles, considering the Operation and maintenance cost: European Automobile Manufacturers Association (https:// A −1 T−1 K S www.aut.f/en/frontpage_vanha/statistics/international_ − t OP& MC � 􏽘 􏽘 􏽘 􏽘 m x (1 + dr) . (5) statistics/average_age_of_passenger_cars_in_some_ i,t,k,s i,t,k,s t�0 s�1 i�0 k�1 european_countries), which has reported an age of 8years for passenger cars in some European countries, and fol- Emission cost: lowing Mahut et al. [46]; we consider a lifetime of 8years for A −1 T−1 K S both passengers DVs and EVs. In addition, a discount rate of − t (6) EmC � 􏽘 􏽘 􏽘 􏽘 em x (1 + dr) . 5% [47] is used. By considering the foreseen daily utilization i,k,s i,t,k,s i�0 t�0 k�1 s�1 and EV battery lifetime of 160,000km [48, 49], each EV will need two batteries over its eight-year operational lifetime. Constraint (2) concerns the total distance (in kilometers) We include the discounted cost of the extra battery in the EV traveled in any year, which cannot be greater than the purchase price. maximum distance traveled by all types of vehicles used. In For the range limitation of EVs, the Nissan Leaf, the addition, in constraint (3), the distance traveled by all ve- electric car model that registered the highest number of sales hicles of any type and age for each demand level in any year in Europe in 2018 and the third leading passenger electric must be greater than the demand for the corresponding level vehicle in 2020 (https://www.statista.com/statistics/965507/ of s trafc congestion in that year. Constraint (4) shows that eu-leading-passenger-electric-vehicle-models/), was the EV the company has a yearly limited budget for purchasing new analyzed in this study. Te Leaf has a range of 264kilometers vehicles. Constraint (5) enforces that in any year of the with one full charge of battery. (https://www.nissanusa.com/ planningperiod,the numberofvehicles used andsalvaged of vehicles/electric-cars/leaf/features/range-charging-battery. any type must be equal to the number of vehicles used of the html). same type in the preceding year. Constraint (6) ensures that To calculate the salvage or resale value, we use the fol- in any planning period year, the new vehicles of any type lowing formula proposed by Feng and Figliozzi [37]: introduced into the feet must be the same as the number of purchased vehicles of that type. Constraint (7) forces all s � 1 − θ 􏼁 s � v 1 − θ 􏼁 , ∀k ∈ K, ∀i ∈ A −{1}, i,k k (i−1)k k k remaining vehicles to be sold at the end of the planning time (7) period. Constraint (8) ensures that when a vehicle reaches its maximum age, it must be salvaged. Constraint (9) ensures where θ is the rate at which vehicle type k is depreciated. that new vehicles cannot be salvaged immediately. Lastly, in Based on the values reported by Messagie et al. [50], we set constraint (10), decision variables Z , X and Y can t,k i,t,k i,t,k depreciationrates peryearof17%and 28%forDVs andEVs, take only non-negative integer values, and x can also i,t,k,s respectively. take nonnegative real values. For the medium TCL, we use an energy consumption of 0.062lit/km [51] and 0.145kWh/km [52] for DVs and EVs, 4. Data and Assumptions respectively. Based on the data given in Table 2, the energy costs per For the numerical experiments,we assume that a car-sharing kilometer are calculated using the formulas presented in the company has the goal of deriving an optimal combination of following equations: its feet from two available types of diesel and electric ve- hicles both with the same passenger capacity. Tese two lit f ·t e � R 􏼠 􏼡 × G × e ∀i ∈ A ∀t ∈ T ∀s ∈ S � {1,2,3}, (8) i,t,s,1 s,1 dv km kWh f ·t e � Q 􏼠 􏼡 × H × e ∀i ∈ A −{1} ∀t ∈ T ∀s ∈ S � {1,2,3}, (9) i,t,s,2 s,2 ev km 6 Journal of Advanced Transportation Table 1: Input-parameter data. Vehicle type DVs EVs Lifetime (years) A �8 A �8 1 2 Discount rate (%) 0.05 0.05 Annual use (km) 40000 40000 Daily use (km) 160 160 Planning time horizon (years) 16 16 Depreciation rate (%) 0.17 0.28 Energy cost growth rate (Pordata 2018) (%) 0.0582 0.0289 Purchase cost (Nissan, 2020) (€) 14000 28000 Energy consumption in low TCL (s ) 0.0465lit/km 0.1087kWh/km Energy consumption in medium TCL (s ) 0.062lit/km 0.145kWh/km Energy consumption in peak TCL (s ) 0.0775lit/km 0.1812kWh/km Energy cost (Pordata 2018) 1.16 €/lit 0.16 €/kWh CO emissions (well-to-wheel) 2.63kg/lit 0.47kg/kWh Table 2: Summary of characteristics of previous studies. Fleet Vehicle replacement/ References Method Model Context TCL size composition problem Mixed-integer linear [26] Opt Car-sharing system ✓ — — programming (MILP) [27] Opt (MILP) Car-sharing system ✓ — — Integer linear programming [28] Opt Car-sharing system ✓ ✓ — (ILP) Stochastic mixed-integer Fleet management shared-vehicle [29] Opt ✓ — — program (SMIP) system [32] Opt (ILP) Car-sharing system electric mobility ✓ ✓ — [34] Survey Total cost of ownership model Electric mobility — — — [31] Opt Mixed integer program (MIP) Shared mobility ✓ — — [35] Opt (MILP) Car-sharing system electric mobility ✓ — — [36] Opt Simulation model EV- sharing system ✓ — — Urban freight feet replacement [37] Opt (MIP) ✓ ✓ — problem Urban freight feet replacement and [38] Opt (MIP) ✓ ✓ — composition problem Mixed integer quadratic Urban freight feet replacement [39] Opt ✓ ✓ — programming (MIQP) problem Tis Opt (MILP) Car-sharing system ✓ ✓ ✓ research where R and Q represent the energy consumption per due to a lack of data regarding the energy consumption of s,1 s,2 km. G and H are the corresponding parameters for the vehicles with age, similar to Feng and Figliozzi [37] and dv ev energy cost of DVs and EVs as presented in Table 1, and f Ahani et al. [39]; we assumed that R and Q are fxed 1 s,1 s,2 and f are the annual growth rates of 5.82% and 2.89% [39] values for each i. for diesel and electricity prices, respectively. Te price On average, well-to-wheel CO emissions by DV and EV growth rates were defned on the basis of the annual diesel are approximately 2.63kg/lit and 0.47kg/kWh, respectively price history from 1980 to 2014 and the electricity price [53]. Te CO emission value for EVs is calculated by taking history from 1991 to 2014 in Portugal (https://www.pordata. into account the emissions produced by diferent types of pt/Portugal). power generation technologies. Terefore, the following We should mention that we made the right-hand side of equations give the emission cost of each type of vehicle based (8) and (9) independent of the age of vehicles (i.e., i). In fact, on its age: tan lit em � 0.00263 × R × ec, ∀i ∈ A − A , 􏼒 􏼓 􏼠 􏼡 􏼈 􏼉 i,s,1 s,1 k lit km (10) kg kWh ton em � 0.47􏼠 􏼡 × Q 􏼠 􏼡 × 0.001􏼠 􏼡ec, ∀i ∈ A − 􏼈A 􏼉. i,s,2 s,2 k kWh km kg Journal of Advanced Transportation 7 Table 3: Model statistics. An ec value of €25/ton is considered [54]. Following the maintenance cost data analysis from Name Number Carstens[55], each carhas a cost ofapproximately 0.04euro/ Constraints 745 km. Te mileage and age of a vehicle afect its maintenance Variables 1565 cost. Te total maintenance cost for EVs is at most 60% of Discrete variables 646 the maintenance cost for ICEVs [50]. Hence, we use the Execution time 0.06seconds following quadratic functions extrapolated from the data adopted from Carstens [55] to estimate the maintenance vehicles in each year of the planning period. An elasticity costs of ICEVs and then use them to approximate the analysis is also performed to show the magnitude of the maintenance costs of EVs. efects of certain input parameters on the total cost. m � −0.0015i 2 − 0.011i + 0.076, ∀i ∈ A − 0 , { } i,1 Figure 2 shows the number of vehicles used each year for the two types of vehicles. Regarding the number of vehicles m � 0.6 −0.0015i 2 − 0.011i + 0.076􏼁, ∀i ∈ A −{0}. i,2 used, the share of electric vehicles in the feet increases over (11) time up to year 12 of the planning period and then remains constant until year 14 and then begins to decrease. Keeping Regarding other input parameters, the following are in mind that the initial feet has been composed of only DVs, assumed: the reason for the increase in the share of EVs and replacing (i) Te company has 20 diesel vehicles of diferent DVs in the feet is their low operating costs, especially when ages in its initial feet. 12 vehicles of ages 0–3years considering the trafc congestion level, which is a major with three vehicles of each age and 8 vehicles of factor afecting the fuel consumption of a vehicle. We can see ages 4–7years with two vehicles of each age. that the share of EVs in the feet begins to decrease after year (ii) Tere are three trafc congestion levels (TCLs): 14 of the planning period, and the main reasons are their high purchasepriceandhigh depreciationrate.Indeed,these low (s1), medium (s2), and high (s3) with vehicle two factors mean that EVs, when compared with DVs, are demands of 20%, 30%, and 50% of the total de- not competitive for just the last two years of the planning mand, respectively (i.e., time period. Had the planning period been infnite, then the d � 0.2d , d � 0.3d , an d d � 0.5d ). t,1 t t,2 t t,3 t share of EVs would have increased constantly over the (iii) We assume that both DVs and EVs are used course of the said planning period. Additionally, Figure 3 160km per day, which is equivalent to 40,000km shows the number of purchased DVs and EVs over the per year based on a total of 250 working days in a 16years of the planning period. Te number of EVs de- year. creases toward the end of the planning period because the (iv) An annual budget of 56,000 euros is assumed for depreciation rate for EVs is higher than that of DVs. Figure 4 purchasing new vehicles. shows the number of vehicles salvaged at the end of each (v) We assume that the energy consumption of DVs in year and at the end of the planning time period when all the low and high TCLs is 25% less and 25% more vehicles are salvaged due to the end of the operation. than that of the medium TCL, respectively. For a more thorough analysis, we present in Figures 5 and 6 the total traveled distance for each type of vehicle and (vi) We also assumed a scenario without incorporating the trafc congestion level. As stated previously, we assume TCL into the model. For this scenario, we consider that the initial feet of the car-sharing service company is the energy consumption of 0.062lit/km and made up of DVs only. Te fgures show that for a high TCL 0.145kWh/km for DVs and EVs, respectively. (s �3), the total distance traveled by EVs begins to increase (vii) During each year, the total demand for car-sharing year by year, and from year eight until year fourteen of the vehicles is supposed to be equivalent to the total planning period, the total traveled distance in this TCL is distance traveled by all 20 vehicles in the corre- covered only by EVs. In the case of medium TCL (s �2), sponding year (d � 40,000km × 20). albeit in comparison to high TCL with a slower increase in (viii) We assumed that R and Q are independent of s,1 s,2 the share of EVs, and only from year 9 to year 13 of the age. planning period is the entire demand in this TCL met by EVs. DVs remain competitive chiefy for low TCL (s �1), as the operational cost for this TCL is lower than those of the 5. Results and Discussion other two levels. As previously mentioned, the increase in Tis section presents the results of resolving the mixed- the share of traveled distance by DVs for the high and integer linear optimization problem (1) (see Table 3) using medium TCLs toward the end of the planning period can be the CPLEX solver of GAMS version 27.3 [56] on a laptop attributed to the high purchase price and the high depre- computer with CPU Intel core i3−4030U 1.90GHz and cation rate of EVs, which render them less economically RAM memory of 4GB running Windows 10 64bits. We viable for just a few years of use in the feet. present the total number of purchased vehicles, total dis- We also assumed a scenario without incorporating the tance traveled in each trafc congestion level by each type of trafc congestion level into the model to show that the trafc vehicle, number of vehicles used, and number of salvaged congestion level has an important impact on the total cost. 8 Journal of Advanced Transportation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year DVs Evs Figure 2: Number of vehicles used during the planning period. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year DVs Evs Figure 3: Number of purchased vehicles during the planning period. 1 2 3 4 5 6 7 8 9 1011121314151617 Year DVs Evs Figure 4: Number of salvaged vehicles during the planning period. Number Number Number Journal of Advanced Transportation 9 1 2 3 4 5 6 7 8 9 10111213141516 Year Low trafc level Medium trafc level High trafc level Figure 5: Traveled distance of diesel vehicles for diferent levels of trafc congestion. 1 23456789 10 11 12 13 14 15 16 Year Low trafc level Medium trafc level High trafc level Figure 6: Traveled distance of electric vehicles for diferent levels of trafc congestion. As we mentioned previously for this scenario, we consider increase of 18% (from 1,955,629.032 to 2,310,844.077) in the the energy consumption of 0.062lit/km and 0.145kWh/km total cost. for DVs and EVs, respectively. Tis scenario led to an traveled distance (Km) traveled distance (Km) 10 Journal of Advanced Transportation Table 4: Per-km discounted elasticity analysis of total cost for diferent factors. Factor (range of values) (unit) Baseline value EA (TC, p) Depreciation rate EVs (17–27) (%) 22% 0.012 Depreciation rate EVs (23–33) (%) 28% 0.053 Depreciation rate EVs (29–39) (%) 34% 0.068 DVs growth rate energy price (2.91–8.73) (%) 5.82% 0.256 EVs growth rate energy price (1.44–4.33) (%) 2.89% 0.018 Discount rate (3–7) (%) 5% −0.180 EVs purchase price (25200–30800) (€) 28000 € 0.398 Energy price (1.044–1.275) (€/lit) 1.16 €/lit 0.351 Energy price (0.144–0.176) (€/kWh) 0.16 €/kWh 0.072 Emission cost (22.5–27.5) (€/ton) 25 €/ton 0.023 Lifetime (6–10) years 8years 0.025 EVs maintenance cost (0.024–0.028) (€/km) 0.0260 €/km 0.037 5.1. Elasticity Analysis. As mentioned previously, there is a number of key parameters to test their impacts on the total cost. To this end, we used the arc elasticity formula [57]as degree of uncertainty associated with some of the input parameters. Variations in these parameters can also impact follows: the total cost. We performed an elasticity analysis on a %chance in total cost 􏼈p1 + p2􏼉 {TC2 − TC1} EA(TC, p) � � × , (12) %change in parameter p {TC1 + TC2} 􏼈P2 − p1􏼉 where EA (TC, p) represents the discounted total cost (TC) car-sharing service. Te numerical results showed that EVs, per km in response to a change in parameter p. compared to DVs, become more competitive year after year Elasticity analysis was performed for diferent ranges of during the planning period. Te reason for the increase in values to assist the operator in determining which parameter the share of EVs is their low operating costs. More im- has the main impact on its optimal vehicle replacement portant, their competitiveness increases with the intensity of decision. Regarding the deprecation rate of EVs, an elasticity trafc congestion. Terefore, any decision made by a car- analysis was performed for three diferent intervals. As sharing operator that ignores trafc congestion intensity throughout the day as a factor would result in an onus, in the expected, the purchase priceof EVs, the energyprices related to the operation of DVs, and the growth rate in diesel prices form of extra costs, for the company in question. have the highest impact on the total cost. Te results of the In this paper, an elasticity analysis is done to consider the elasticity analysis are presented in Table 4. A 1% change in uncertainty of input parameters such as the energy cost, one of these parameters leads to increases of 0.40%, 0.35%, maintenance cost, EV purchase price, and emission cost of and 0.26% in the total cost, respectively. For the discount diferent types of vehicles. In future work, it will be rate range, the elasticity is negative, which means that when worthwhile to analyze the efect of these uncertainty pa- the discount rate increases by 1%, the total cost decreases by rameters by using a portfolio theory approach such as the 0.18%. one developed by Ahani et al. [39]. We also assumed that the range limitation of EVs was not a determining factor for the purchase decision. Depending on the demand level for car- 6. Conclusions sharing services, there are some situations in which such an assumption seems unrealistic. Hence, another line of re- Car-sharing can help resolve trafc congestion and emission search could involve developing a vehicle replacement and issues arising from increasing mobility within urban areas. assignment optimization framework by considering the In comparison to diesel vehicles, EVs perform better in range restriction of EVs and uncertainties associated with regard to energy consumption during peak-hour trafc the network of available charging stations and demand for congestion and low-speed fows. Taking this crucial factor car-sharing service across an urban area. In this work, we did into consideration, an optimization framework for intro- not take into account the charging station location, and no ducing new vehicles of diferent types into the feet of a car- limitation was assumed with regard to the demand for sharing company over a certain planning period was pre- charging EVs in a network of charging stations. However, in sented. Te developed framework considers the energy real scenarios, the network of charging stations might have a consumption and emissions of diferent types of vehicles at limited capacity for satisfying the uncertain demands for diferent levels of trafc congestion. To the best of our recharging the EVs. Tere are various research studies on knowledge, this is the frst time that such a framework has fnding optimal locations for refueling stations under been presented for the optimal composition of the feet of a Journal of Advanced Transportation 11 [11] E. W. Martin and S. A. Shaheen, “Greenhouse gas emission diferent scenarios and conditions [58–64]. Terefore, from impacts of carsharing in North America,” IEEE Transactions the standpoint of an urban decision-maker, the integration on Intelligent Transportation Systems, vol. 12, no. 4, of the frameworks developed in the aforementioned studies pp. 1074–1086, 2011. into the optimization framework of the current research [12] L. Hu and Y. Liu, “Joint design of parking capacities and feet study will be another interesting future line of research. size for one-way station-based carsharing systems with road congestion constraints,” Transportation Research Part B: Data Availability Methodological, vol. 93, pp. 268–299, 2016. [13] S. A. Shaheen, N. D. Chan, and E. Farrar, “Carsharing’s Te data used to support the fndings of this study are in- impact and future,” in Book: Te Sharing Economy and the cluded within the article. Relevance for Transport, pp. 87–120, Elsevier, Amsterdam, Netherlands, 2019. Conflicts of Interest [14] T. D. Chen and K. M. Kockelman, “Carsharing’s life-cycle impacts on energy use and greenhouse gas emissions,” Te authors declare that they have no conficts of interest. Transportation Research Part D: Transport and Environment, vol. 47, pp. 276–284, 2016. Acknowledgments [15] V. Roblek, M. Meˇsko, and I.Podbregar, “Impact of car sharing on urban sustainability,” Sustainability, vol. 13, no. 2, p. 905, Te authors would like to acknowledge the Foundation for Science and Technology for the fnancial support with ref- [16] M. Balac, H. Becker, F. Ciari, and K. W. Axhausen, “Modeling erences (UIDB/04625/2020) and (SFRH/BD/89258/2012). competing free-foating carsharing operators–A case study for Te authors would also like to acknowledge funding from Zurich, Switzerland,” Transportation Research Part C: the project Horizon 2020 “ASSURED–UAM, Acceptance, Emerging Technologies, vol. 98, pp. 101–117, 2019. ˇ ˇ [17] D. Fiedler, M. Cap, ´ and M. Certicky,´ “Impact of mobility-on Safety, and Sustainability Recommendations for Efcient demand on trafc congestion: simulation-based study,” in Deployment of UAM” and the project “C-Tech–Climate Proceedings of the 2017 IEEE 20th International Conference on Driven Technologies for Low Carbon Cities” of the MIT- Intelligent Transportation Systems (ITSC), pp. 1–6, IEEE, Portugal Program. Yokohama, Japan, October 2017. [18] F. Ciari, B.Bock, and M. Balmer, “Modeling station-based and References free-foating carsharing demand: test case study for berlin,” Transportation Research Record Journal of the Transportation [1] R. Katzev, “Car sharing: a new approach to urban trans- Research Board, vol. 2416, no. 1, 2014. portation problems,” Analyses of Social Issues and Public [19] A. P. Cohen, S. A. Shaheen, and R. McKenzie, “Carsharing: a Policy, vol. 3, no. 1, pp. 65–86, 2003. guide for local planners,” Journal of Planning Advisory Service [2] S. Lee, “A review of carsharing research: with a focus on Memo, vol. 1040, 2008, http://escholarship.org/uc/item/ domestic thesis and research papers,” Inst. Korean Reg. 4kf3x31h,%20UCD-ITS-RP-08-16. Stud.vol. 62, pp. 3–17, 2015. [20] S. A. Shaheen and A. P. Cohen, “Carsharing and personal [3] S. A. Shaheen, N. D. Chan, A. Bansal, and A. P. Cohen, Shared vehicle services: worldwide market developments and Mobility: Defnitions, Industry Developments, and Early Un- emerging trends,” International Journal of Sustainable derstanding, Transportation Sustainability Research Center, Transportation, vol. 7, no. 1, pp. 5–34, 2012. Berkeley, CA, USA, 2015, http://innovativemobility.org/wp. [21] X. Li, J. Ma, J. Cui, A. Ghiasi, and F. Zhou, “Design framework [4] J. Jung and Y. Koo, “Analyzing the efects of car sharing of large-scale one-way electric vehicle sharing systems: a services on the reduction of greenhouse gas (GHG) emis- continuum approximation model,” Transportation Research sions,” Sustainability, vol. 10, no. 2, p. 539, 2018. Part B: Methodological, vol. 88, pp. 21–45, 2016. [5] Y. Hui, Y. Wang, Q. Sun, and L. Tang, “Te impact of car- [22] S. Frost, “Strategic insight of the global carsharing market,” sharing on the willingness to postpone a car purchase: a case Technical Reports Series 90-18, Frost & Sullivan, San Antonio, study in Hangzhou, China,” Journal of Advanced Trans- TX, USA, 2014. portation, vol. 2019, Article ID 9348496, 11 pages, 2019. [23] C. King, W. Griggs, F. Wirth, and R. Shorten, “Using a car [6] A. Millard-Ball, “Car-sharing: where and how it succeeds,” sharing model to alleviate electric vehicle range anxiety,” in vol. 60, Transportation Research Board, Washington, D.C, Proceedings of the 16th Yale Workshop on Adaptive and USA, 2005, TCRP Report 108. Learning Systems, pp. 130–135, New Haven, CT, USA, June [7] G. Cooper, D. A. Howe, and P. Mye, Te Missing Link: An Evaluation of Carsharing, Portland Inc, Portland, Oregon, [24] S. Mamarikas, S. Doulgeris, Z. Samaras, and L. Ntziachristos, “Trafc impacts on energy consumption of electric and [8] B. Yu, Y. Ma, M. Xue et al., “Environmental benefts from conventional vehicles,” Transportation Research Part D: ridesharing: a case of Beijing,” Applied Energy, vol. 191, pp. 141–152, 2017. Transport and Environment, vol.105, Article ID 103231, 2022. [25] B. Nykvist, F. Sprei, and M. Nilsson, “Assessing the progress [9] H. Nijland and J. van Meerkerk, “Mobility and environmental impacts of car sharing in Te Netherlands,” Environmental toward lower priced long range battery electric vehicles,” Energy Policy, vol. 124, pp. 144–155, 2019. Innovation and Societal Transitions, vol. 23, pp. 84–91, 2017. [10] E. Martin, S. A. Shaheen, and J. Lidicker, “Impact of car- [26] C. M. Monteiro, C. A. S. Machado, M. d. O. Lage, F. T. Berssaneti, C. A. Davis, and J. A. Quintanilha, “Opti- sharing on household vehicle holdings: results from North American shared-use vehicle survey. Transportation Research mization of carsharing feet size to maximize the number of clients served,” Computers, Environment and Urban Systems, Record,” Journal of the Transportation Research Board, vol. 2143, pp. 151–158, 2010. vol. 87, Article ID 101623, 2021. 12 Journal of Advanced Transportation [27] P. Strohle, ¨ C. M. Flath, and J. Garttner, ¨ “Leveraging customer [42] Y. H. Huang and J. H. Wu, “A portfolio risk analysis on fexibility for car-sharing feet optimization,” Transportation electricity supply planning,” Energy Policy, vol. 36, no. 2, pp. 627–641, 2008. Science, vol. 53, no. 1, pp. 42–61, 2019. [43] J.-H. Wu and Y.-H. Huang, “Electricity portfolio planning [28] A. Wallar, J. Alonso-Mora, and D. Rus, “Optimizing vehicle model incorporating renewable energy characteristics,” Ap- distributions and feet sizes for shared mobility-on-demand,” plied Energy, vol. 119, pp. 278–287, 2014. in Proceedings of the 2019 International Conference on Ro- [44] Y. Ji, J. Luo, and N. Geroliminis, “Empirical observations of botics and Automation (ICRA), pp. 3853–3859, IEEE, Mon- congestion propagation and dynamic partitioning with probe treal, Canada, May 2019. data for large-scale systems,” Transportation Research Record [29] R. Nair and E. Miller-Hooks, “Fleet management for vehicle Journal of the Transportation Research Board, vol. 2422, no.1, sharing operations,” Transportation Science, vol. 45, no. 4, pp. 1–11, 2014. pp. 524–540, 2011. [45] D. Magueta, M. Madaleno, M. Ferreira Dias, and M. Meireles, [30] J. Li, Y. S. Chen, H. Li, I. Andreasson, and H. V. Zuylen, “New cars and emissions: efects of policies, macroeconomic “Optimizing the feet size of a personal rapid transit system: a impacts and cities characteristics in Portugal,” Journal of case study in port of rotterdam,” in Proceedings of the 13th Cleaner Production, vol. 181, pp. 178–191, 2018. International IEEE Conference on Intelligent Transportation [46] F. Mahut, J. Daaboul, M. Bricogne, and B. Eynard, “Product- Systems (ITSC), pp. 301–305, IEEE, Funchal, Portugal, Sep- Service Systems for Servitization of the automotive industry: a tember 2010. literature review,” International Journal of Production Re- [31] H. Hosni, J. Naoum-Sawaya, and H. Artail, “Te shared-taxi search, vol. 55, no. 7, pp. 2102–2120, 2017. problem: formulation and solution methods,” Transportation [47] P. Baptista, S. Melo, and C. Rolim, “Energy, environmental Research Part B: Methodological, vol. 70, pp. 303–318, 2014. and mobility impacts of car sharing systems. Empirical results [32] R. F. Lemme, E. F. Arruda, and L. Bahiense, “Optimization from Lisbon, Portugal,” Procedia-Social and Behavioral Sci- model to assess electric vehicles as an alternative for feet ences, vol. 111, pp. 28–37, 2014. composition in station-based car sharing systems,” Trans- [48] G. Palmer and J. Floyd, “Chapter of Energy Primer for Storage portation Research Part D: Transport and Environment, Analysis in,” Book: Energy Storage and Civilization, Springer, vol. 67, pp. 173–196, 2019. Cham, Switzerland, pp. 41–56, 2020. [33] G. Brandstatter, M. Kahr, and M. Leitner, “Determining [49] A. Ajanovic and R. Haas, “Electric vehicles: solution or new optimal locations for charging stations of electric car sharing problem?” Environment, Development and Sustainability, systems under stochastic demand,” Transportation Research vol. 20, no. S1, pp. 7–22, 2018. Part B: Methodological, vol. 104, pp. 17–35, 2017. [50] M. Messagie, K. Lebeau, T. Coosemans, C. Macharis, and [34] S. Bubeck, J. Tomaschek, and U. Fahl, “Perspectives of electric J. van Mierlo, “Environmental and fnancial evaluation of mobility: total cost of ownership of electric vehicles in Ger- passenger vehicle technologies in Belgium,” Sustainability, many,” Transport Policy, vol. 50, pp. 63–77, 2016. vol. 5, no. 12, pp. 5020–5033, 2013. [51] D. Lois, Y. Wang, A. Boggio-Marzet, and A. Monzon, [35] S. Weikl and K. Bogenberger, “A practice-ready relocation “Multivariate analysis of fuel consumption related to eco- model for free-foating carsharing systems with electric ve- driving: interaction of driving patterns and external factors,” hicles – mesoscopic approach and feld trial results,” Trans- Transportation Research Part D: Transport and Environment, portation Research Part C: Emerging Technologies, vol. 57, vol. 72, pp. 232–242, 2019. pp. 206–223, 2015. [52] J. Zhang, Z. Wang, P. Liu, D. Cui, and X. Li, “Analysis on [36] S. Nakayama, T. Yamamoto, and R. Kitamura, “Simulation infuence factors of energy consumption of electric vehicles analysis for the management of an electric vehicle-sharing based on real-world driving data,” in Proceedings of the 11th system: case of the kyoto public-car system,” Transportation International Conference on Applied Energy 2019, (ICAE2019), Research Record Journal of the Transportation Research Board, ¨ ˚ pp. 12–15, vasteras, Sweden, January 2019. vol. 1791, no. 1, pp. 99–104, 2002. [53] I. Adeniran, Te Impacts of Sustainable Concepts in Urban [37] W. Feng and M. Figliozzi, “An economic and technological Freight Distribution-A Courier, Express and Parcel Case Study, analysis of the key factors afecting the competitiveness of Doctoral dissertation, Technische Universitat¨ Munchen, ¨ electric commercial vehicles: a case study from the USA Munich, Germany, 2020. market,” Transportation Research Part C: Emerging Technol- [54] R. Gerlagh, R. J. R. K. Heijmans, and K. E. Rosendahl, ogies, vol. 26, pp. 135–145, 2013. “COVID-19 tests the market stability reserve,” Environmental [38] O. Jabali and G. Erdogan, Continuous Approximation Models and Resource Economics, vol. 76, no. 4, pp. 855–865, 2020. for the Fleet Replacement and Composition Problem (No. [55] S. Carstens, “Increasing the competitiveness of maintenance CIRRELT-2015-64), CIRRELT, Montreal, Canada, 2015. contract rates by using an alternative methodology for the [39] P. Ahani, A. Arantes, and S. Melo, “A portfolio approach for calculation of average vehicle maintenance costs,” Journal of optimal feet replacement toward sustainable urban freight Transport and supply chain Management, vol. 2, no. 1, transportation,” Transportation Research Part D: Transport pp. 1–11, 2008. and Environment, vol. 48, pp. 357–368, 2016. [56] Gams, General Algebraic Modeling System (GAMS), GAMS [40] Y.M. He,J. Kang,Y. L.Pei,B. Ran,and Y.T.Song, “Studyon a Development Corporation, Washington, DC, USA, 2019. prediction model of superhighway fuel consumption based on [57] R. G. D. Allen, “Te concept of arc elasticity of demand: I,” the test of easy car platform,” Sustainability, vol. 12, no. 15, Te Review of Economic Studies, vol. 1, no. 3, pp. 226–229, p. 6260, 2020. [41] F. Gree, ´ V. Laznikova, B. Kim, G. Garcia, T. Kigezi, and [58] M. Miralinaghi, G. H. de Almeida Correia, S. E. Seilabi, and B. Gao, “Cloud-based big data platform for vehicle-to-grid S. Labi, “Designing a network of electric charging stations to (v2g),” World Electric Vehicle Journal, vol. 11, no. 2, p. 30, mitigate vehicle emissions,” in 2020 Forum on Integrated and 2020. Sustainable Transportation Systems (FISTS), pp. 95–100, Journal of Advanced Transportation 13 Institute of Electrical and Electronics Engineers (IEEE), Delft, Netherlands, 2020. [59] M. Miralinaghi, Y. Lou, B. B. Keskin, A. Zarrinmehr, and R. Shabanpour, “Refueling station location problem with trafc deviation considering route choice and demand un- certainty,” International Journal of Hydrogen Energy, vol. 42, no. 5, pp. 3335–3351, 2017. [60] M. Miralinaghi, B. B. Keskin, Y. Lou, and A. M. Roshandeh, “Capacitated refueling station location problem with trafc deviations over multiple time periods,” Networks and Spatial Economics, vol. 17, 2017. [61] M. Ghamami, A. Zockaie, and Y. Nie, “A General Corridor Model for Designing Plug-In Electric Vehicle Charging In- frastructure to Support Intercity Travel,” Transportation Re- search Part C: Emerging Technologies, vol. 68, 2016. [62] Z.-H. Zhu, Z.-Y. Gao, J.-F. Zheng, and H.-M. Du, “Charging station location problem of plug-in electric vehicles,” Journal of Transport Geography, vol. 52, pp. 11–22, 2016. [63] R. R. Desai, E. Hittinger, and E. Williams, “Interaction of consumer heterogeneity and technological progress in the US electric vehicle market,” Energies, vol.15, no.13, p. 4722, 2022. [64] H. Zheng, X. He, Y. Li, and S. Peeta, “Trafc equilibrium and charging facility locations for electric vehicles,” Networks and Spatial Economics, vol. 17, no. 2, pp. 435–457, 2016.

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