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Energy 55 (2013) 869e878

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Energy

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The optimal lifetime of passenger cars based on minimization of CO2emission

Radomir Mijailovi�c*

Faculty of Transport and Traffic Engineering, University of Belgrade, Vojvode Stepe 305, Belgrade, Serbia

a r t i c l e i n f o

Article history:Received 30 November 2012Received in revised form2 February 2013Accepted 9 April 2013Available online 6 May 2013

Keywords:CO2

LifetimeLife cyclePassenger car

* Tel.: þ381 113091381.E-mail addresses: radomirm@beotel.rs, radomirm@

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.04.008

a b s t r a c t

The paper’s objective is to suggest a model for determining optimal lifetime of passenger car based onminimization of CO2 emission. The life cycle was modeled by eight main life cycle sequences. Combiningthe mathematical interpretations of the itch life cycle sequence is developed an optimization model. Inthis paper is suggested a new mathematical interpretation of following sequences: use, repair, distri-bution of passenger car and distribution of passenger car’s parts. Comparison of the obtained numericalresults was performed on examples for the data of new passenger car fleet from the EU14 countries.Special attention is given to analysis of dependencies between the optimal lifetime of passenger cars andDirective 2000/53/EC, trends of changing car weight, model year, kilometer driven and regulatory limit ofthe specific CO2 emission. The optimal lifetime in case where petrol car is replaced by diesel car wasanalyzed too.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

One of the world environmental targets is to decrease envi-ronmental burden of the CO2 emission. To that aim many EUcountries have released national long-term scenarios toward 2050,and their ambitious targets for CO2 emission reduction are aimingat a decrease of more than 50% of today’s emission [4]. A largenumber of authors have tried to solve this problem. They usedmodels of various scale of complexity.

Van Wee et al. [18] have concluded that by reducing the age ofthe current car fleet may result in an increase of life cycle CO2emissions. This research was focused on the relationship betweenthe average lifetime of cars and their life cycle energy requirementsand emissions. The authors have modeled life cycle by thefollowing sequences: production, materials, uses and scrapping ofcars (including recycling). The authors also analyzed differences inperformance and sequence “use” between old and new cars.

Zamel and Li [19] analyzed full life cycle (vehicle and fuel cycle)of an internal combustion engine vehicle and a fuel cell vehicle. Theauthors havemodeled vehicle life cycle by the following sequences:material production, assembly, distribution, maintenance anddisposal (recycling).

sf.bg.ac.rs.

All rights reserved.

Kim et al. [5] analyzed optimal fleet conversion policy based onminimization of total life cycle emissions (CO, NMHC, NOx and CO2).Authors have described vehicles lifetime emission as function ofkilometers driven, vehicle production, use, and retirement.

Kim et al. [6] determined optimal lifetimes using life cycleassessment, a comprehensive environmental measurement tool,dynamic programming and engineering optimization tool. Themodel inputs consist of a collection of life cycle inventoriesdescribing materials production, manufacturing, use, maintenance,and end-of-life environmental burdens as functions of productmodel years and ages.

Nederveen et al. [12] have concluded that good maintenance ofthe engines of old vehicles might have an equal or even biggerpositive impact on emission reductions.

Mayyas et al. [9] have concluded that the material selection forvehicular applications is a sensitive process not only to the vehiclelifetime, but also to the environmental burdens from the extractionstage and recyclability efforts.

Leduc et al. [7] solved the problem of the environmental impactsof new average diesel and petrol cars from a life cycle perspectiveusing complex process flow diagram of cars. In this reference, fivemain life cycle sequences were identified: production phase(including material production and car assembly), spare partsproduction (tires, batteries, lubricants and refrigerants), fueltransformation process upstream to fuel consumption, fuel con-sumption for car driving and car disposal and waste treatment.

R. Mijailovi�c / Energy 55 (2013) 869e878870

The paper’s objective is to suggest model for determiningoptimal lifetime of passenger car based on minimization of CO2emission. The main sequences of life cycle of passenger car are:material production, part manufacturing, assembling, car’s distri-bution, use, part’s distribution, repair and disposal. Model includesseveral different materials that are used in car’s production. Usingthis model is also defined transformation processes that are usedfor the material transformation. Sequence “use” is a function offuel type, engine displacement, car’s age and kilometers driven. Inthis paper is calculated coefficient of repair. Functions dependencebetween ratios CO2 emissions from a new car/car’s weight andyear when the car was produced are determined in the paper.Functions dependence between car’s weight and year when thecar was produced are determined too. Combining the mathe-matical interpretations of the itch life cycle sequence, an optimi-zation model is developed. Finally, the model was applied on theEU14 passenger car fleet. In this research are analyzed de-pendences between the optimal lifetime of passenger cars andDirective 2000/53/EC, trends of changing car weight, model year,kilometer driven and regulatory limit of the specific CO2 emission.The optimal lifetime in case where petrol car is replaced by dieselcar was analyzed too.

2. The life cycle sequences of passenger car

The life cycle of passenger car includes all the main sequencesrequired to make up the life cycle of that system. The life cycle ofpassenger car was modeled by eight main life cycle sequences(Table 1).

The total CO2 emission during life cycle of passenger car isdetermined by the following expression:

E ¼ P8[¼1

Ei; [ ¼ 1:::8 ; (1)

where [ denotes ordinal number of the life cycle sequences(Table 1).

2.1. Material production

The CO2 emission duringmaterial production sequence dependson the CO2 emission during production of all materials used toproduce passenger car:

E1 ¼Xnmi¼1

E1;i; (2)

where nm denotes the number of different materials used to pro-duce passenger car.

The CO2 emission during production of material “i” is given byexpression:

Table 1The life cycle sequences.

Denotation The life cycle sequence

E1 Material productionE2 Passenger car’s parts manufacturingE3 AssemblingE4 Distribution of passenger carE5 UseE6 RepairE7 Distribution of passenger car’s partsE8 Disposal

E1;i ¼4412

$CEmpi: (3)

The carbon emission during the production of material “i”calculated as follows:

CEmpi ¼ ECmpi$Xnej¼1

efj$pmpj;i; (4)

where

e ECmpi e energy consumption of the production of material “i”,e efj e emission factor for type of energy “j”,e ne e number of different types of energy used to produce of

material “i”,e pmpj,i e participation of type of energy “j” in the production of

material “i”

Xnepmpj;i ¼ 1: (5)

j¼1

The emission factors for several types of energy (efj) can befound in the Refs. [8,19].

The energy consumption of the production of material “i” can bewritten by the following equation:

ECmpi ¼ eci$Mi: (6)

Energy consumption per kilogram during material “i” produc-tion is determined by:

eci ¼ ecv:m:i $ð1� reusei � recovi � recymiÞ þ ecr:m:

i $recymi;

(7)

where

e ecv:m:i e energy consumption per kilogram during material “i”

production breakdown for 100% virgin material,e ecr:m:

i e energy consumption per kilogram during material “i”production breakdown for 100% recycled material,

e reusei e reuse rate during production of material “i”,e recovi e recovery rate during production of material “i”,e recymi e recycling rate during production of material “i”.

The energy consumptions per kilogram during materials pro-duction (ecv:m:

i ,ecr:m:i ) and participations of types of energy in the

production of materials (pmpj,i) are determined in theRefs. [14,16,19].

Weight of material “i” is given by expression:

Mi ¼ qmi$M; (8)

where

e M e passenger car weight,e qmi e participation of material “i” in the passenger car weight

Xnmqmi ¼ 1; (9)

i¼1

e nm e number of different materials used in production ofpassenger car.

R. Mijailovi�c / Energy 55 (2013) 869e878 871

By application of the expressions (3,4,6e8) the CO2 emissionduring material production sequence (2) obtains its final form:

E1 ¼4412

$M$Xnmi¼1

qmi$�ecv:m:

i $ð1�reusei�recovi�recymiÞ

þecr:m:i $recymi

�$Xnej¼1

efj$pmpj;i:

(10)

2.2. Passenger car’s parts manufacturing

The CO2 emission during passenger car’s parts manufacturingcan be defined as the sum of emissions that depend (E2.1) andemissions that do not depend (E2.2) on weight of materials [15]:

E2 ¼ E2:1 þ E2:2: (11)

The CO2 emission during passenger car’s parts manufacturingthat depend on weight of materials is given by expression:

E2:1 ¼ M$Xnmi¼1

qmi$ð1� reuseiÞ$Xntph¼1

ptpi;h$emi;h (12)

where

e ntp e number of different transformation processes used topassenger car’s parts manufacturing,

e emi,h e the CO2 emission during the manufacturing of material“i” by type of transformation process “h”,

e ptpi,h e participation of type of transformation process “h” inthe manufacturing of material “i”

Xntph¼1

ptpi;h ¼ 1: (13)

The CO2 emissions during the materials manufacturing (emi,h)and participation of types of transformation process in the materialmanufacturing (ptpi,h) can be seen in the Ref. [15].

The CO2 emission during passenger car’s parts manufacturingthat do not depend on weight of materials includes emissionsresulting from the following processes: painting, HVAC&lighting,heating, material handling, welding and compressed air [15]:

E2:2 ¼ 889 kgCO2: (14)

2.3. Assembling

The CO2 emission during passenger car’s assembling is modeledas a linear function from the passenger car weight [19]. The CO2emission during assembling is calculated the same way as for thematerial production sequence and is expressed below:

E3 ¼ 4412

$CE3: (15)

The carbon emission during the passenger car’s assembling isdetermined by next expression:

CE3 ¼ EC3$Xnej¼1

efj$pasj; (16)

where

e EC3 e energy consumption of the passenger car’s assembling,e pasj e participation of type of energy “j” in passenger car’s

assembling [19]

Xnepasj ¼ 1: (17)

j¼1

The energy consumption of the assembling is given byexpression:

EC3 ¼ ecas$M; (18)

where ecas denotes the energy consumption per kilogram duringpassenger car’s assembling. It can be found in the Ref. [19].

By using (15), (16) and (18) the CO2 emission during passengercar’s assembling (15) can be rewritten in the form:

E3 ¼ 4412

$M$ecas$Xne

j¼1

efj$pasj: (19)

2.4. Distribution of passenger car

The sequence “distribution of passenger car” includes distribu-tion of passenger car from the assembly line to the dealer. The CO2emission during distribution of passenger car also depends on thepassenger car weight:

E4 ¼ Sdis$edis$M (20)

where

e Sdis e the average transportation distance,e edis e the specific CO2 emission during distribution of passen-

ger car [11].

2.5. Use

Kaplanovic and Mijailovic have defined approximation func-tions of the average CO2 emissions on the vehicle age [3]. Authorshave defined different approximation functions for different enginedisplacements and fuel types. The functions do not include main-tenance. In this paper maintenance is included.

Kaplanovic and Mijailovic have defined following passenger cartypes [3]:

e k ¼ 1 e petrol car, engine displacement < 1400 cm3,e k ¼ 2 e petrol car, engine displacement ¼ 1400 ... 2000 cm3,e k ¼ 3 e petrol car, engine displacement >2000 cm3,e k ¼ 4 e diesel car, engine displacement <2000 cm3,e k ¼ 5 e diesel car, engine displacement �2000 cm3.

Let’s take a look of the specific CO2 emission (qTN ;k) of model yearTN and k type passenger car. Over a period of time (DtTN ;k) thispassenger car has timely repair. The period of time (DtTN ;k) will bedefined as repair interval. The repair interval can be defined as thenumber of years after which passenger car must be repaired. Now,the assumption is introduced: passenger car emission after repair isequal to emission that this passenger car hadwhen it was new. Thatmeans that specific CO2 emission increase but not unlimited. Thespecific CO2 emission limit value is higher than the emission fornew passenger car by the regulatory limit of the specific CO2emission (RLTN ;k) (Fig. 1). Therefore, the specific CO2 emission ofmodel year TN and k type passenger car during Ti year was writtenin this analysis in the form:

qTN ;k ¼ qnewTN ;k$n1þuk$

hTi�

�TNþ jTN ;k$DtTN ;k

�ivkofor TNþ jTN ;k$DtTN ;k�Ti<TNþ

�jTN ;kþ1

�$DtTN ;k; jTN ;k ¼ 1;:::;nTN ;k:

(21)

Fig. 1. Dependence specific CO2 emission (qTN ;k) of model year TN and k type passengercar upon year (T) (I e with repair, II e without repair).

Table 2Weights of component parts and their repair frequency.

Passenger car system Component part Mcpd, kg Sd, km

Engine Short block 2 308,928Exhaust pipe 9 50,000

Cooling Water pump 1 96,540Radiator and hoses 4 193,080

Ignition Starter 1.5 193,080Alternator 1.5 193,080

Transmission Transmission 6.8 115,848Electrical Window motor 0.3 77,232

Wiper motor 0.3 154,464Accumulator 8 80,000

Air Conditioning Blower and heater core 1 193,080Compressor 2.5 96,540

Suspension Tie rod 2.4 96,540Ball joint 0.3 96,540Struts/shocks 14 193,800

Fluid Motor oil 3.5 10,000Antifreeze 6.3 30,000

Tire Tire 27 60,000

R. Mijailovi�c / Energy 55 (2013) 869e878872

where

e Ti e year,e TN e passenger car model year, i.e. first year of life cycle of

passenger car (the author presume that the year of passengercar production is equal to first year of life cycle of passengercar),

e uk, vk e coefficients that they depend upon engine type andengine displacement [3],

e qTN ;k e the specific CO2 emission of model year TN and type k forTi year (Ti � TN),

e qnewTN ;k; kgCO2=km e the specific CO2 emission of model year TN

and type k for new passenger car (the CO2 emission for newpassenger car can be found in the passenger car catalog),

e jTN ;k e the repair ordinal number of model year TN and k typepassenger car,

e nTN ;k e number of repair that model year TN and k type pas-senger car had during his life cycle.

The CO2 emission increases with vehicle age. Pollution controlmust be realized in practice. In this paper the author suggestintroduction of regulatory limit of CO2 emission. Passenger carsmust go to inspection center. Inspection centers can measure theCO2 emission on passenger cars. He also suggest introduction ofnew assignment that inspection centers must apply. They mustcompare real CO2 emission with the emission limit. If the real CO2emission is higher than CO2 emission limit, inspection center willsend passenger car to maintenance center. It is one of the possi-bilities for timely repair implementation.

The regulatory limit of CO2 emission of used passenger carsdoes not exist in practice. Thus, it is of exceptional importance toanalyze it.

By analyzing Fig. 1 the specific CO2 emission limit may beobserved:

qlimitTN ;k ¼ qnewTN ;k þ RLTN ;k: (22)

The specific CO2 emission limit must be greater or equal to thereal specific CO2 emission:

qlimitTN ;k � qTN ;k

�T�: (23)

By using (21e23) the repair interval can be written in the form:

DtTN ;k � 1uk

$RLTN ;kqnewTN ;k

! 1vk

: (24)

The CO2 emission during sequence “use” is presented in thisresearch as:

E5 ¼XTEi¼ TN

Si$qTN ;k; (25)

where

e Si e passenger car’s kilometers driven for Ti year,e TE e the last year of life cycle of passenger car.

Substitution of expressions (21) into Eq. (25) yields:

E5 ¼XTEi¼ TN

Si$qnewTN ;k

$n1þ uk$

hTi �

�TN þ jTN ;k$DtTN ;k

�ivko: (26)

2.6. Repair

The CO2 emission during sequence “repair” depends uponweight of component parts, their repair frequency and CO2 emis-sion during following sequences: material production, passengercar’s parts manufacturing and assembling. Spitzley et al. [13]determined generic passenger car unscheduled repair frequencyfor 8 car’s systems and 18 component parts. Authors presentedrepair frequency values for three repair cases: baseline, durable andunreliable. Our established model includes Spitzley’s data forbaseline case. The author of this paper had added several compo-nent parts because he had concluded that added parts have sig-nificant impact on the CO2 emission during this sequence. Spitzleyet al. [13] analyzed generic passenger car. Authors did not deter-mined weights of component parts. In this paper they areestimated.

Car’s component parts are grouped into two groups. Therefore,in this paper the CO2 emission during sequence “repair” wasexpressed as:

E6 ¼ E6:1 þ E6:2: (27)

The first group includes component parts whose replacementhas no direct influence on the CO2 emission. Their weights wereestimated (Table 2) for one of the best selling cars in this paper.Opel Astra is one of the best selling cars in Europe in 2009 [2] andtherefore it was chosen.

In this research are modeled influence parts weights and theirrepair frequency on the CO2 emission introducing coefficient ofrepair. Thus, following assumptions are introduced:

R. Mijailovi�c / Energy 55 (2013) 869e878 873

e ratio between weight of the component part of the passengercar and its whole weight are equal for all passenger car types(e.g. ratio between weight of compressor incorporated in theOpel Astra and weight of Opel Astra is equal to ratio betweenweight of compressor incorporated in the Peugeot and weightof Peugeot),

e repair frequencies for the same component part have the samevalues for all passenger car types,

e coefficients of repair for Opel Astra and other passenger carsare equal.

The coefficient of repair in this paper was modeled by:

rep ¼ 1Moa

$Xncpd¼1

McpdSd

; (28)

where

e Moa e weight of Opel Astra,e Mcpd e weight of component part “d”,e Sd e the transportation distance (kilometer driven) after which

will be necessity to component part “d” repair.

The coefficient of repair (28) using data (Table 2) has followingvalue:

rep ¼ 1:16$10�6 km�1: (29)

The passenger car’s kilometer driven for whole life cycle ofpassenger car is given by expression:

S ¼XTEi¼ TN

Si: (30)

The CO2 emission during sequence “repair” depends upon CO2emissions during material production sequence (E1), passengercar’s parts manufacturing (E2) and car’s assembling (E3). So, the E6:1in this paper was described as:

E6:1 ¼ S$rep$ðE1 þ E2 þ E3Þ: (31)

The second group of car’s parts includes component partswhose replacement has direct influence on the CO2 emission. Theirweight is much smaller than the first group weight. It is estimatedthat the second group weight is about 2.5 kg (mr ¼ 2.5 kg). Byapplication of the expressions (10), (12) and (19) the emission E6:2can be written in the form:

E6:2 ¼ mr$jTN ;k$

8<:Xnmi¼1

qmi$ð1� reuseiÞ$Xntph¼1

ptpi;h$emi;h

þ 4412

$ecas$Xne

j¼1

efj$pasj þ8<:4412

$Xnmi¼1

qmi$�ecv:m:

i $ð1

� reusei � recovi � recymiÞ

þ ecr:m:i $recymi

�$Xnej¼1

efj$pmpj;i

9=;9=; (32)

2.7. Distribution of passenger car’s parts

The CO2 emission during distribution of passenger car’s partsdepends on the CO2 emission during distribution of passenger car.It depends on the weight of repaired component parts and their

repair frequency. The CO2 emission during sequence “distributionof passenger car’s parts” in this research was modeled as:

E7 ¼ E7:1 þ E7:2: (33)

where

e E7.1 e the CO2 emission during distribution of parts whosereplacement has no direct influence on the CO2 emission,

E7:1 ¼ S$rep$E4; (34)

e E7.2 e the CO2 emission during distribution of parts whosereplacement has direct influence on the CO2 emission

E7:2 ¼ Sdis$edis$mr$jTN ;k: (35)

By using (20), (34) and (35) the CO2 emission during distributionof passenger car’s parts (33) can be rewritten in the form:

E7 ¼ Sdis$edis$�S$rep$M þmr$jTN ;k

�: (36)

2.8. Disposal

Disposal is the sequence that appears at the end of the life cycleof passenger car. The CO2 emission during the sequence “disposal”is defined as the sum of the CO2 emissions during its transportationfrom the dismantler to a shredder and the shredding CO2 emission.It is calculated the same way as for the material productionsequence and is expressed below:

E8 ¼ 4412

$CE8: (37)

The carbon emission during the disposal is determined by nextexpression:

CE8 ¼ EC8$Xne

j¼1

efj$pdij; (38)

where pdij is the participation of type of energy “j” in the sequence“disposal” [19].

The energy consumption of the disposal is given by expression:

EC8 ¼ ecdi$M; (39)

where ecdi is the energy consumption per kilogram during thesequence “disposal” [19].

By using (38) and (39) the CO2 emission during the sequence“disposal” (37) can be rewritten in the form:

E8 ¼ 4412

$M$ecdi$Xne

j¼1

efj$pdij: (40)

3. Defining of the optimization task

The difference between TE and TN can be defined as optimallifetime of passenger car:

topt ¼ TE � TN: (41)

R. Mijailovi�c / Energy 55 (2013) 869e878874

The performance of cars with regard to CO2 emission has showncontinuous improvement. Therefore, if we replace one passengercar per year, emission during following sequences use, repair anddistribution of passenger car’s parts will be smaller than if wereplace, for example, one passenger car per two or three years. Thefirst four sequences (material production, passenger car’s partsmanufacturing, assembling and distribution of passenger car) andsequence “disposal” do not depend on age (e.g. kilometer driven) ofpassenger car. Therefore, if we replace one passenger car per yearthe total CO2 emission (1) will be higher than if we replace, forexample, one passenger car per two or three years.

The optimal lifetime is described in this paper as the number ofyears for which the “loss” of CO2 emission equals the “gain” frombringing the new cleaner passenger cars:

Enew1 þ Enew2 þ Enew3 þ Enew4 þ Eold8

¼ Eold5 þ Eold6 þ Eold7 � Enew5 � Enew6 � Enew7 (42)

Old car was denoted by superscript “old”. The old passenger caris being replaced with new passenger car which was denoted bysuperscript “new”.

If we want to determine the optimal lifetime is necessary toknow following dependences: specific CO2 emission of new car emodel year, car’s weight e model year and annual kilometersdriven e car’s age.

3.1. Functional dependence CO2/M e model year

The ratio between specific CO2 emission of model TN year andtype k for new passenger car and passenger car weight wasapproximated in this paper based on EU14 data (data taken fromRef. [20]) by regression analysis:

qnewTN ;k

M¼ w1;k$ðTN � 1994Þw2;k : (43)

The coefficients w1,k, w2,k have following values:

e k ¼ 1, 2, 3 e w1,k ¼ 0.194, w2,k ¼ �0.12 (R2 ¼ 0.99),e k ¼ 4, 5 e w1,k ¼ 0.157, w2,k ¼ �0.153 (R2 ¼ 0.98),

where R2 denotes coefficient of determination.The specific CO2 emission of model TN year and type k for new

passenger car using the equation (43) can be rewritten as follows:

qnewTN ;k¼ M$w1;k$ðTN � 1994Þw2;k : (44)

Fig. 2. Dependence of optimal lifetime e passenger car weight for TN ¼ 1996.

3.2. Functional dependence passenger car weight e model year

Consumer markets show a rising tendency toward bigger andheavier vehicles [17]. The average passenger car weight in thisresearchwas approximated base on EU14 data (data taken from Ref.[20]) by regression analysis:

Maverage ¼ w3;k$ðTN � 1994Þw4;k : (45)

The coefficients w3,k, w4,k have following values:

e k ¼ 1, 2, 3 e w3,k ¼ 1067.7, w4,k ¼ 0.0236 (R2 ¼ 0.92),e k ¼ 4, 5 e w3,k ¼ 1209.2, w4,k ¼ 0.0492 (R2 ¼ 0.99).

The coefficient w3,k represent the average passenger car weightfor 1995 year.

The author has included assumption that every passenger carhas the same shape as function (45). Hence, the passenger carweight can be written in the form:

M ¼ m$ðTN � 1994Þw4;k ; (46)

where m denotes the passenger car weight for 1995 year.

3.3. Functional dependence annual kilometers driven e car’s age

The average annual kilometers driven tend to decrease withcar’s age [10]. The passenger car’s kilometers driven for Ti year wasapproximated based on data (data taken from Ref. [10]) byregression analysis:

Si ¼ 23613�w5$ðTi � TNÞ; (47)

where w5 ¼ 771.653 (R2 ¼ 0.98).

4. Results

The implementation of the model was performed on followingexamples. The numerical values of participation of materials in thepassenger car weight (qmi) were taken from Ref. [19]:qmferrous ¼ 0.669, qmcopper ¼ 0.007, qmzinc ¼ 0.005, qmlead ¼ 0.008,qmaluminum ¼ 0.061, qmmagnesium ¼ 0.008, qmglass ¼ 0.026,qmfluids ¼ 0.041, qmrubber ¼ 0.041, qmplastics ¼ 0.076, qmother ¼ 0.058.In this research is analyzed the optimal lifetime in case where theparticipation of material “i” in the passenger car weight has thesame value for all passenger cars. The results are obtained usingsoftware package Mathcad.

Member states of the European Union shall take the necessarymeasures to encourage the reuse of components which are suitablefor reuse, the recovery of components which cannot be reused andthe giving of preference to recycling when environmentally viable,without prejudice to requirements regarding the safety of vehiclesand environmental requirements such as air emissions and noisecontrol. Therefore, the European Parliament and of the Council wasformulated Directive 2000/53/EC [1] that deals with ELV (end-of-life vehicles) issues. The Directive has following ELV targets:

e Target 1: no later than 1 January 2006, for all end-of life vehi-cles, the reuse and recovery shall be increased to a minimum of85% by an average weight per vehicle and year. Within thesame time limit the reuse and recycling shall be increased to aminimum of 80% by an average weight per vehicle and year;

e Target 2: no later than 1 January 2015, for all end-of life vehi-cles, the reuse and recovery shall be increased to a minimum of95% by an average weight per vehicle and year. Within thesame time limit, the re-use and recycling shall be increased to aminimum of 85% by an average weight per vehicle and year.

Table 3Dependence of optimal lifetime and some CO2 emissions upon Directive’s targets fork ¼ 3, TN ¼ 1996 and RLTN ;k ¼ 10 g=km.

M, kg Target topt, year E (Eq. (1)) E1 þ E2 E5

kgCO2

1600 Target 1 11.7 88,527 6537 74,002Target 2 12.7 93,357 7443 77,492No limit 19.1 121,804 13,200 96,977

1800 Target 1 11.6 99,295 7243 83,089Target 2 12.6 104,795 8263 87,065No limit 19.3 137,113 14,739 109,276

2000 Target 1 11.5 109,416 7949 91,575Target 2 12.4 115,347 9082 95,825No limit 19.2 151,869 16,278 121,108

R. Mijailovi�c / Energy 55 (2013) 869e878 875

Based on the previous targets may be noticed necessity foranswering the following question: does the Directive 2000/53/EChas significant influence on the optimal lifetime of passenger cars?Fig. 2 shows the dependence of optimal lifetime e passenger carweight for 1996 year for different passenger car types (k) and fordifferent Directive’s targets (Target 1 and Target 2). The impact ofthe Directive 2000/53/EC on the optimal lifetime can be analyzedby comparing results with the results in the case where reuse, re-covery and recycling do not exist. Previous case is denoted by “Nolimit”. Fig. 2 also shows the results for “No limit” case. The resultspresented in Fig. 2 were calculated for RLTN ;k ¼ 10 g=km, TN¼ 1996,(Eq. (46)) and (Eq. (47)).

Analyzing the results (Fig. 2) it can be concluded that “No limit”case has maximum optimal lifetime. The passenger car optimallifetime decreases by increasing of reuse, recovery and recyclingrates. The minimum values have Target 1. The maximum discrep-ancy between optimal lifetimes occurs between cases “Target 1”and “No limit” is 12.7 years. It happens for following cases: k ¼ 4,M ¼ 1000 kg and k ¼ 5, M ¼ 1400 kg. The maximum discrepancybetween optimal lifetimes occurs between cases “Target 1” and “Nolimit” for petrol cars (k ¼ 1, 2, 3) is between 7.3 and 8.1 years. Thediscrepancy between two Directive targets is smaller e about 1year for petrol and 1.4 years for diesel cars.

The optimal lifetime for petrol cars is smaller than optimallifetime for diesel cars. For example, forM¼ 1800 kg and “Target 2”optimal lifetimes are: 12.2 years (k ¼ 2 e petrol cars), 12.6 years(k ¼ 3 e petrol cars), 15.8 years (k ¼ 4 and k ¼ 5 e diesel cars).

The maximum discrepancy between optimal lifetimes fordifferent car weights, in most cases, is smaller than 1 year. It de-pends upon passenger car type (k). The maximum discrepancy forcar types k ¼ 1, 2 (petrol car, engine displacement < 2000 cm3) isabout 1 year. Car types 3 and 5 have similarly discrepancy e about

Fig. 3. Dependences of optimal lifetime e passenger car m

0.4 year. Car type 5 (diesel car, engine displacement �2000 cm3) isthe only one that has bigger maximum discrepancy e 2 year.

If we apply stricter Directive’s limits the CO2 emissions duringmaterial production and car’s parts manufacturing sequences willbe smaller (Table 3). This conclusion leads to propose early intro-duction more energy-efficient and cleaner passenger cars. Let’sconsider case: k¼ 3 andM¼ 1600 kg. The optimal lifetimes are 11.7,12.7 and 19.1 years, respectively. Sums of emissions duringmaterialproduction and car’s parts manufacturing sequences for “Target 1”,“Target 2” and “No limit” are 6537 kgCO2, 7443 kgCO2 and13,200 kgCO2, respectively. Let’s consider new case: k ¼ 5 andM ¼ 2000 kg. The previous sums are higher: 7949 kgCO2,9082 kgCO2 and 16,278 kgCO2, respectively. The discrepancy be-tween sums of emissions during material production and car’sparts manufacturing sequences for “Target 1” and “Target 2” isabout 14%. The discrepancy for “Target 1” and “No limit” is higherthan 100%. The previous discrepancies have similar values for othercases (different car type and weight of car).

By analysis of EU passenger cars fleet it may be concluded thataverageweight of passenger car increases (Eq. (45)). The conclusionhas a negative consequence on CO2 emission because the specificCO2 emission increases with weight of car [21]. Automotive in-dustry tries to manufacture engines that emit less CO2. The effect ofprevious automotive industry attempts has been reduced becauseof the existences of a trend of increasing car weight. Thus may benoticed necessity for answering next question: does the trend ofweight change has significant influence on the optimal lifetime ofpassenger cars?

Fig. 3 shows the dependence of optimal lifetime (topt) uponpassenger car model year (TN) and passenger car weight for modelyear TN (MTN ). The results presented in Fig. 3 were calculated fordependence (Eq. (46)), k ¼ 2, RLTN ;k ¼ 10 g=km and Target 1 (ofDirective 2000/53/EC). Two graphs are presented in Fig. 3. The firstpresents results for w4,2 ¼ 0.0236 e trend of increasing car weight(Eq. (46)). The second graph presents results for the following casee the car weight does not change with model year (w4,2 ¼ 0).

The optimal lifetime of passenger cars has lower values forlower values of coefficient w4. Accordingly, if we get a decreasecurrent trend of increasing car weight we will have lower optimallifetime of passenger cars. Discrepancy between optimal lifetimesfor the same values of model year and weight is between 2.2 and5.7 years. Higher values arise for higher values of TN.

Analyzing the results it is noticed that passenger car model yearhas higher influence on optimal lifetime than its weight (MTN )(Fig. 3). For example, the maximum discrepancy between optimallifetimes for TN ¼ 2000 andw4,2 ¼ 0.0236 is about 2 years. Previousdiscrepancy forw4,2 ¼ 0 is smallere about 1.5 years. The maximum

odel year e passenger car weight for model year TN.

Table 4Dependence of optimal lifetime upon trend of increasing car weight (w4,k) forRLTN ;k ¼ 10 g=km and Target 1

TN MTN , kg topt, year

w4,k ¼ 0.0236 w4,k ¼ 0

k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5

1996 1600 11.4 11.6 14.6 14.6 9.2 9.3 9.5 9.51800 11.3 11.6 14.5 14.5 9.1 9.4 9.4 9.42000 11.2 11.5 14.4 14.8 9.0 9.2 9.3 9.5

1997 1600 13.9 14.2 18.2 18.2 11.2 11.4 11.8 11.61800 13.8 14.5 18.0 18.0 11.0 11.4 11.5 11.52000 13.7 14.4 17.9 17.9 11.0 11.3 11.5 11.5

1998 1600 16.2 16.5 22.6 21.6 12.9 13.1 14.1 13.61800 16.1 16.7 21.5 21.4 12.8 13.3 13.5 13.52000 16.0 16.6 21.3 21.3 12.8 13.2 13.4 13.4

Fig. 4. Dependence of the ratio between specific CO2 emission of model TN year andtype k for new passenger car and passenger car weight e passenger car model year.

Fig. 5. Dependence of optimal lifetime e w5 (the kilometers driven) e car weight forTN ¼ 1996.

Table 5Dependence of optimal lifetime upon regulatory limit for TN ¼ 1996 and M ¼ 1600 kg.

RL, g/km topt, year

Target 1 Target 2

k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5 k ¼ 2 k ¼5 11.5 11.7 14.7 14.6 12.4 12.610 11.4 11.6 14.6 14.6 12.3 12.520 11.8 11.8 14.9 14.9 12.7 12.730 11.0 11.7 14.8 14.8 12.0 12.740 11.2 11.4 15.0 15.0 12.0 12.250 11.8 11.4 14.0 14.0 12.5 12.2

R. Mijailovi�c / Energy 55 (2013) 869e878876

discrepancy between optimal lifetimes for MTN ¼ 1600 kg andw4,2 ¼ 0.0236 is about 16 years. Previous discrepancy forw4,2 ¼ 0 isabout 13 years.

The difference between optimal lifetimes decreases with modelyear. For example for MTN ¼ 2000 kg and w4,2 ¼ 0.0236, the dif-ference between optimal lifetimes for TN ¼ 1996 and TN ¼ 1997 is2.5 years. The difference between optimal lifetimes for TN ¼ 2003and TN ¼ 2004 is 1.5 years. For w4,2 ¼ 0 the discrepancies aresmaller e 2 years (for TN ¼ 1996 and TN ¼ 1997) and 1.4 years (forTN ¼ 2003 and TN ¼ 2004).

The same conclusion is applicable for the other passenger cartypes (Table 4).

Fig. 4 shows the dependence of the ratio between specific CO2emission of model TN year and type k for new passenger car andpassenger car weight upon passenger car model year (Eq. (43)). Byanalysis of Fig. 4 it may be noticed that slopes of tangents to curvesdecreases with increasing model year. As a result, it can beconcluded that the currently engine manufacturers are reaching alimit with the exiting technology. This curve might potentiallychange with the insertion of new technologies.

If we have on mind obtained results (Figs. 3 and 4) it may benoticed that CO2 emission can be reduced in the future byencouraging purchasing cars with smaller weight.

Fig. 5 shows influence of the passenger car kilometer driven onthe optimal lifetime. Its influence was analyzed by varying co-efficients w5. The results presented in Fig. 5 were calculated fork ¼ 5, Target 1, RLTN ;k ¼ 10 g=km, TN ¼ 1996. Analyzing the Eq. (47)it may be noticed that kilometers driven are higher in cases wherevalues of w5 are smaller. The kilometer driven does not depend onthe car age for w5 ¼ 0. The real EU case was described forw5 ¼ 771.653 (Eq. (47)).

Analyzing the results (Fig. 5) it is noticed that kilometers drivenhas higher influence on optimal lifetime than car weight. Forexample, the maximum discrepancies between optimal lifetimesare smaller than 1 year for each value of w5. The discrepancy forw5 ¼ 771.653, 500 and 0 are 0.4, 0.9 and 0.4 year, respectively. Ifaverage annual kilometer driven is higher (i.e. if w5 is smaller) theoptimal lifetime will be smaller. The maximum discrepancies be-tween optimal lifetimes are smaller than 3.5 years for each value ofcar weight. The maximum discrepancies for M ¼ 1400, 1800 and2200 kg are 3.2, 2.7 and 2.7 years, respectively.

The regulatory limit of the specific CO2 emission has influenceon total CO2 emission during life cycle of passenger car. Analyzingthe results (Table 5) it can be concluded that the regulatory limithas smaller influence on the optimal lifetime in case where “old”and “new” cars have the same values of the regulatory limit. Themaximum discrepancies between optimal lifetimes for differentvalues of the regulatory limit are smaller than 1.5 years. Considerthe case where TN ¼ 1996, Target 1, M ¼ 1600 kg and k ¼ 4. Theoptimal lifetimes for RL¼ 5,10, 20, 30, 40 and 50 g/km are 14.7,14.6,14.9, 14.8, 15 and 14 years.

No limit

3 k ¼ 4 k ¼ 5 k ¼ 2 k ¼ 3 k ¼ 4 k ¼ 5

16.0 16.0 18.3 19.2 26.5 26.515.9 15.9 18.6 19.1 27.2 26.216.7 16.7 19.3 19.2 27.1 27.115.9 15.9 18.8 19.0 27.4 27.416.2 16.2 18.2 19.0 26.3 26.216.4 15.3 19.3 19.7 26.7 26.0

Table 6The optimal lifetime in case where petrol car is replaced by diesel car for M ¼ 1400 kg, Target 1, TN ¼ 1996.

kold knew topt, year kold knew topt, year kold knew topt, year

TN ¼ 1996 TN ¼ 2000 TN ¼ 1996 TN ¼ 2000 TN ¼ 1996 TN ¼ 2000

1 1 12.1 20.7 2 1 11.7 21.2 3 1 13.1 24.91 2 11.9 21.7 2 2 11 22.2 3 2 12.9 26.11 3 11 18.1 2 3 10.7 18.5 3 3 11.9 21.61 4 5.4 7.4 2 4 5.3 7.5 3 4 5.7 8.11 5 5.4 7.3 2 5 5.3 7.3 3 5 5.7 7.9

R. Mijailovi�c / Energy 55 (2013) 869e878 877

Figs. 2, 3 and 5 show the results for case than passenger carstypes of “old” and “new” cars are the same. Zervas et al. [22]analyzed replacement possibility of petrol by diesel cars inGreece. The author has also analyzed optimal lifetime in casewherepetrol car is replaced by diesel car. By analysis the caseM¼ 1400 kg,Target 1, TN ¼ 1996 (Table 6) can be concluded that optimal life-times in casewhere petrol cars are replaced by petrol cars are abouttwo times higher than the case where petrol cars are replaced bydiesel cars. For example, for kold ¼ 1 and knew ¼ 3 the optimallifetime is 11 years. The optimal lifetime in case where petrol car isreplaced by diesel car (kold ¼ 1 and knew ¼ 4) is smaller e 5.4 years.The optimal lifetimes for following cases kold ¼ 2 e knew ¼ 3 andkold ¼ 2 e knew ¼ 4 are 10.7 and 5.3, respectively. The differencesbetween the optimal lifetimes for previous cases increase withpassenger car model year. Consider the case where TN ¼ 2000. Theoptimal lifetimes in cases kold¼ 1e knew¼ 3 and kold¼ 1e knew¼ 4are 18.1 and 7.4, respectively (ratio is 2.4). The ratio betweenoptimal lifetimes for TN ¼ 2004 is higher. For example, the optimallifetimes for cases kold ¼ 1 e knew ¼ 3 and kold ¼ 1 e knew ¼ 4 are24.6 and 8.5, respectively (ratio is 2.9).

Numerical data and analysis are available upon request from theauthor.

5. Conclusion

In this paper was performed the determination of optimal life-time of passenger cars. The analysis was carried out based on CO2emission. The life cycle was modeled by eight main life cycle se-quences. In this paper is suggested a new mathematical interpre-tation of following sequences: use, repair, distribution of passengercar and distribution of passenger car’s parts. Comparison of theobtained numerical results was performed on examples for thedata of new passenger car fleet from the EU14 countries.

Analyzing the results it can be concluded that the optimal life-time for petrol cars is smaller than optimal lifetime for diesel cars. Itis also concluded that the passenger car optimal lifetime decreasesby increasing targets of the Directive 2000/53/EC. If we applystricter Directive’s limits the CO2 emissions during material pro-duction and car’s parts manufacturing sequences will be smaller.The discrepancy between sums of emissions during material pro-duction and car’s parts manufacturing sequences for targets of theDirective 2000/53/EC is about 14%.

By analysis of EU passenger cars fleet it may be concluded thataverage weight of passenger car increases. If we get a decreasecurrent trend of increasing car weight we will have lower optimallifetime of passenger cars.

If we have on mind obtained results it may be noticed that CO2

emission can be reduced in the future by encouraging purchasingcars with smaller weight. Looking at obtained results it also may benoticed that kilometers driven has higher influence on optimallifetime than car weight.

It also had been analyzed the optimal lifetime in case wherepetrol car is replaced by diesel car. By analysis the caseM¼ 1400 kg,Target 1, TN ¼ 1996 can be concluded that optimal lifetimes in case

where petrol cars are replaced by petrol cars are about two timeshigher than the case where petrol cars are replaced by diesel cars.The differences between the optimal lifetimes for previous casesincrease with passenger car model year.

Further investigations may be directed towards establishing amodel for multi-criteria analysis. Future model should includeeconomic constraint functions and other fuel engines. The model,besides CO2, also should include the pollutants whose emissionsare regulated by the Euro standards. It would be significant todetermine benefit from the replacement of “traditional” fuel car(petrol or diesel) by the other fuel ones, which emit less pollutant.

Acknowledgment

The research presented in this paper has been realized in theframework of the technological project named “Development ofthe model for managing the vehicle technical condition in order toincrease its energy efficiency and reduce exhaust emissions”financed by theMinistry of Science and Technological Developmentof the Republic of Serbia (Grant No. 36010). The author would liketo thank two anonymous reviewers for their helpful comments andvaluable suggestions.

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