Optimal bus fleet management strategy for emissions reduction

Transportation Research Part D 41 (2015) 330–347

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Optimal bus fleet management strategy for emissions reduction Lu Li, Hong K. Lo ⇑, Xuekai Cen Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, China

a r t i c l e

i n f o

Article history: Available online 6 November 2015 Keywords: Bus fleet management Emissions reduction Remaining life additional benefit–cost analysis Government subsidy Vehicle replacement Diesel retrofits

a b s t r a c t Transportation is a major cause for environmental degradation via exhaust emissions. For many transit-oriented metropolitan areas, bus trips often constitute a sizeable mode share. Managing the bus fleet, in particular updating buses to comply with the newer emissions standards, therefore, can have a substantial impact on transportation-induced air quality. This paper presents the approach of remaining life additional benefit–cost (RLABC) analysis for maximising the total net benefit by either early-retiring or retrofitting the current bus fleet within their lifespans. By referring to the net benefits for different bus types estimated by RLABC analysis, the most beneficial management scheme for the current bus fleet can be identified. Optimal bus fleet management (BFM) models based on the RLABC analysis for the operator and the government are developed. Then a government subsidy plan is produced to achieve win–win solutions, which will offer efficient and flexible management schemes. To illustrate the approach, the largest bus company in Hong Kong, which carries more than 23% of the total trips in Hong Kong, is taken as a case study example. Instead of adopting a fixed retirement plan, such as replacing buses at the age of 17 as is currently practised, the proposed method develops an optimal BFM scheme that progressively phases out buses or retrofits them. This study produces promising results to demonstrate the large benefit of this approach for optimal bus fleet management. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction Road transportation is a major source for environmental degradation via exhaust emissions, causing considerable damage to human health and the ecosystem. According to Zegras (2007), four major areas can be considered to tackle vehicular greenhouse gas (GHG) emissions: activities, mode share, fuel intensity, and fuel type. In the context of Asian and European countries, where public transport is prevalent, how to manage the bus fleet to make it environmentally efficient is an important endeavour. Numerous studies have been conducted on vehicle fleet management. In the early days, the notion of ‘‘repair limit” was proposed, describing that the asset should be replaced when its repair cost exceeds a certain amount (Drinkwater and Hastings, 1967). Since then, the approach was extended to consider imperfect repair or cumulative repair-cost (e.g. Nguyen and Murthy, 1981; Beichelt, 1982; Dohi et al., 2000). These models tend to focus on the cost of one single repair, without considering the prospect for the whole system. And overall budgetary constraints were generally not taken into account. Subsequently, the parallel machine replacement problem (PMRP) was introduced by Jones et al. (1991), with the idea of minimizing the total replacement cost for a finite population of economically interdependent machines over the

⇑ Corresponding author. Tel.: +852 2358 8742; fax: +852 2358 1534. E-mail address: [email protected] (H.K. Lo). http://dx.doi.org/10.1016/j.trd.2015.10.007 1361-9209/Ó 2015 Elsevier Ltd. All rights reserved.

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

331

planning horizon. It offered two rules to replace the fleet, including the No-Splitting Rule – in any stage machines of the same age are either all kept or all replaced, and the Older Cluster Replacement Rule – a machine is replaced only if all older machines are replaced. Karabakal et al. (1994) described another PMRP for replacing multiple assets under capital rationing. McClurg and Chand (2002) developed a forward-time dynamic programming algorithm to better solve the PMRP. All of these studies are for deterministic PMPP with non-increasing marginal costs. To extend the consideration for the stochastic case, Childress and Durango-Cohen (2005) formulated a linear program to find optimal replacement policies for the infinitehorizon stochastic PMRP. These studies have taken into account many factors which affect machine replacement, such as purchase cost, operating and maintenance cost, salvage value, and budget constraint. For the vehicle replacement problem, however, the important factor of vehicular emissions has not been fully considered, which may make a big difference in the replacement decision. In recent years, as the environmental problems become increasingly acute, green fleet management strategies for emissions reduction have attracted much attention. Cook and Straten (2001) conducted a benefit–cost analysis for replacing the existing bus fleet in North California by alternative-fueled buses. The study found that although natural gas buses offered substantial benefits of emissions reduction, a considerable amount of capital cost was needed to upgrade the facilities for buses using alternative fuels. The point is that it is essential to consider the benefit of emissions reduction alongside the life-cycle costs of bus-fleet replacement. Dill (2004) provided a more accurate estimate of emissions reduction by changing the assumptions from a voluntary accelerated vehicle retirement program. It pointed out that incentives from the government will have a strong impact on the quality of vehicles to be retired. Gao and Stasko (2009) developed an integer program to minimize the net present value of the retrofit/replacement costs under budget and emission constraints. Later Stasko and Gao (2010) updated their approach to minimize the operational costs and penalties for emissions produced under capital budget constraints. Retrofit is incorporated as an alternate method for reducing emissions. Nevertheless, the purchase and resale costs of the new bus were not taken into consideration, which may result in an aggressive replacement plan. On the other hand, as the purchase cost is much larger than the other costs, if the purchase cost is directly added to the objective function, then the opposite may occur, i.e. early replacement will likely not happen. How the purchase costs of replacement buses should be incorporated appropriately, therefore, remains an important question. In terms of complying with emission regulations, Stasko and Gao (2012) developed a model to predict the expected cost of compliance, giving guidance to regulators and fleet managers. It presented an approximate dynamic programming approach for making vehicle purchase, resale, and retrofit decisions in a fleet setting with stochastic maintenance and repair costs and vehicle failures. The model formulation is oriented toward the objective of emissions reduction by making all the buses reach the standard in an efficient way. This paper proposes a novel approach called remaining life additional benefit–cost (RLABC) analysis to maximise the net benefit of managing the bus fleet within their lifespans for the common good of society. A bus fleet management (BFM) model based on the RLABC analysis is developed, which is arguably more realistic as it considers the additional net benefits generated by changing the BFM plans from their fixed retirement age, while considering the purchase, resale, retrofit, and operation costs, emission factors, as well as the budget constraints. The conventional BFM scheme typically takes into account the actual expenses, and leaves out certain indirect benefits and costs, which would lead to decisions that do not address the complete picture. The proposed approach here can tactfully alleviate the misgiving of the purchase cost issue by taking into account the indirect additional benefits and costs, as will be explained in Section ‘Methodology’. Besides, the private bus company will develop its management scheme for profit maximisation, not emissions reduction. To include this perspective of the private operator, a management model based on remaining life additional cost analysis is developed, which purely minimizes the actual additional cost while ignoring the additional benefits from emissions reduction. Based on the optimal management schemes generated by these two models, we develop a government subsidy plan to investigate what kind of subsidy to the private operator would provide sufficient incentive for it to implement the optimal BFM scheme that includes the objective of emissions reduction. Such an approach is arguably more realistic, as it considers both the government’s objective to reduce emissions and the private bus company’s objective to maximise profit. In this study, we consider six main types of emissions as a function of speed and emission standards, and convert them into monetary form by their corresponding external costs. To illustrate the methodology, we apply it to the biggest bus company in Hong Kong in the context of Euro IV franchised buses replacement a few years ago. Nevertheless, the methodology developed is applicable for a general context. The outline of this paper is as follows: Section ‘Methodology’ presents the methodology; Section ‘Case study – Hong Kong’ depicts the implementation of the methodology to the Hong Kong case study; and finally, Section ‘Concluding remarks’ provides some concluding remarks.

Methodology Remaining life additional benefit–cost (RLABC) analysis Description of RLABC analysis Early retiring or retrofitting the bus fleet before their nominal retirement age will generate additional benefit and cost. The question is how to strike a balance between the benefits of reduction in external costs arising from emissions and

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L. Li et al. / Transportation Research Part D 41 (2015) 330–347

the additional cost of upgrading the bus fleet to follow the latest emissions standards. In this study, we propose the approach of RLABC analysis. By calculating the RLABC of these management decisions for each type of buses, we produce net benefit relations or graphs to determine when and what kind of actions should be taken for different types of buses over time. Therefore, if there were no budget constraints, the optimal BFM strategy would be simply decided by referring to the RLABC graphs produced, as explained below. In this paper, the additional benefit associated with an early retirement or a retrofit is defined as the savings in external costs associated with emissions reduction in the remaining lifespan of the bus. For early retirement, replacing buses of older emission standards with buses that meet the latest emission standard ahead of their normal retirement age will save the external costs of pollution. Likewise, for bus retrofit, a certain amount of external costs will be saved due to the reduction in vehicle emissions arising from the retrofit. On the other hand, there is an additional cost accompanying these actions. When a bus is early retired by n years, there is a loss of disposing the residual value of the corresponding bus. Besides, considering the discounted value and price inflation, a price difference will arise for purchasing the new bus n years earlier. This is a very important component as it indicates the indirect cost caused by the early purchase of a bus ahead of its schedule which has not been noted before. In this way, we resolve the issue of taking the purchase cost of a replacement bus into consideration, neither ignoring this cost term as in some studies, which is big, nor lumping the whole replacement cost into one year, which exaggerates its short-term impact. Last but not least, the cost difference associated with operating different types of buses with different ages in the remaining life is also captured in the model. Hence, bus retrofit will generate additional benefit and cost before the normal retirement age. Assumptions For simplicity, the following assumptions are made in this study: 1. Given the latest technology for bus emissions, it is assumed that the price of the technology remains relatively stable to the end of the planning horizon with its price modified only by the inflation factor. If the price of the technology can be projected in the future, the result obtained would better reflect reality. 2. Fleet size remains unchanged overtime, i.e. the travel demand will not change drastically in the future. 3. The aging effect in vehicle emissions was ignored; we assume the emission rates remain the same as buses age, which would produce a less aggressive replacement scheme. 4. Two cost adjustment factors are taken into account. One is cost discounting – we convert all the monetary terms into present value terms at the beginning of the planning horizon using the interest rate. Obviously, the higher is the interest rate; the lower is the present value of the future cash flows. The other is price inflation, with a sustained increase in the general price level of goods and services, which results in a reduction of the number of buses that can be purchased per unit of money. 5. New buses are paid in full at the beginning, and old buses are sold at half the price of its depreciated value with an annual depreciation rate. In general, the benefits generated by the early retirement scheme will be underestimated due to the assumptions above. Thus, the findings of this study would be conservative. Notation

(1) Sets A I I0 J K O

set set set set set set

of of of of of of

running area old emission standard for bus new emission standard for bus vehicle emissions retrofit statuses non-retrofitted statuses

(2) Parameters Biy index for buses with i emission standard purchased in the year Y i , a bus with Euro II standard purchased in II the year 2000 is referred to as BEuro 2000 BaBi ;o;Y additional benefit (US$) of a bus of type Biy with retrofit o running in area a retired in the current year Y c y

c

BaBi ;Y

SchemeA

BaBi ;Y

SchemeB

y

y

BaBi ;ok;Y c y

additional benefit (US$) of a bus of type Biy running in area a retired in the optimal replacement year according to Scheme A additional benefit (US$) of a bus of type Biy running in area a retired in the optimal replacement year according to Scheme B additional benefit (US$) of a bus of type Biy running in area a switching from retrofit o to k in the current year Y c

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

BaBi ;ok;Y

SchemeA

BaBi ;ok;Y

SchemeB

y

y

caBi ;Y y

c

333

additional benefit (US$) of a bus of type Biy running in area a switching from retrofit o to k in the optimal retrofit year according to Scheme A additional benefit (US$) of a bus of type Biy running in area a switching from retrofit o to k in the optimal retrofit year according to Scheme B operation and maintenance cost (US$) of a bus of type Biy running in area a in the current year Y c

C aBi ;Y c

additional cost (US$) of a bus of type Biy running in area a retired in the current year Y c

C aBi ;Y

SchemeA

C aBi ;Y

SchemeB

additional cost (US$) of a bus of type Biy running in area a retired in the optimal replacement year according to Scheme A additional cost (US$) of a bus of type Biy running in area a retired in the optimal replacement year according to Scheme B additional cost (US$) of a bus of type Biy running in area a switching from retrofit o to k in the current year Y c

y

y

y

C aBi ;ok;Y c y C aBi ;ok;Y SchemeA y C aBi ;ok;Y y

SchemeB

da Eaioj Eanoj

additional cost (US$) of a bus of type Biy running in area a switching from retrofit o to k in the optimal retrofit year according to Scheme A additional cost (US$) of a bus of type Biy running in area a switching from retrofit o to k in the optimal retrofit year according to Scheme B distance (km) travelled per year by a single bus running in area a emission factor (kg/km) for pollutant j of a bus with emission standard i and retrofit o running in area a

EC j

emission factor (kg/km) for pollutant j of a bus with the new emission standard n and retrofit o running in area a external cost (US$/kg) of vehicle emission j

F aBi

fleet size of buses of type running in area a: Biy

F Bi y L M MY c Pi Pn r ok Yc Yi Y Y

fleet size of buses of type Biy lifespan of a bus, identical to the nominal retirement year of a bus in the original scheme overall budget (US$) annual budget (US$) purchase cost (US$) of a bus with emission standard i purchase cost (US$) of a bus with the latest emission standard retrofit cost (US$) of a bus switching from retrofit o to k index for the current year purchasing year for buses with i emission standard start year of the planning horizon final year of the planning horizon depreciation rate inflation rate interest rate additional subsidy for type Biy buses with retrofit o running in area a to be retired in the current year Y c

y

a b

c

daBi ;o;Y y

c

daBi ;ok;Y y

c

daBi ;o;Y schemeA y daBi ;ok;Y y

schemeA

additional subsidy for type Biy buses running in area a switching from retrofit o to k in the current year Y c additional subsidy for type Biy buses with retrofit o running in area a to be retired in the optimal replacement year according to Scheme A additional subsidy for type Biy buses running in area a switching from retrofit o to k in the optimal retrofit year according to Scheme A

(3) Decision variables N aBi ;o;Y number of buses of type Biy with retrofit o running in area a to be retired in the current year Y c in the c y government scheme or Scheme A NcaBi ;o;Y number of buses of type Biy with retrofit o running in area a to be retired in the current year Y c in the private c y bus company scheme or Scheme B a RBi ;ok;Y number of buses of type Biy running in area a switching from retrofit o to k in the current year Y c in the c y government scheme or Scheme A RcaBi ;ok;Y number of buses of type Biy running in area a switching from retrofit o to k in the current year Y c in the c y private bus company scheme or Scheme B a SBi ;o;Y subsidy for type Biy buses with retrofit o running in area a to be retired in the optimal year according to SchemeA y Scheme A a SBi ;ok;Y subsidy for type Biy buses running in area a switching from retrofit o to k in the in the optimal year according SchemeA y to Scheme A

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L. Li et al. / Transportation Research Part D 41 (2015) 330–347

RLABC formulation We first define the additional benefit and cost associated with early retirement and retrofit, which are crucial in this study.

BaBi ;o;Y c

8P a a i < j2J ½ðEioj Enoj Þda EC j ðY þLY c Þ ; if Y < Y i þ L c ðY c YÞ c Þ ð1þ ¼ ; : 0; if Y c P Y i þ L

8a 2 A; o 2 O [ K; i 2 I; n 2 I0 ; Biy ; Y c

ð1Þ

BaBi ;ok;Y c

8P a a i < j2J ½ðEioj Eikj Þda EC j ðY þLY c Þ ; if Y < Y i þ L c ðY c YÞ c Þ ð1þ ¼ ; : 0; if Y c P Y i þ L

8a 2 A; o 2 O [ K; k 2 K; i 2 I; Biy ; Y c

ð2Þ

y

y

C aBi ;Y c y

¼

8 > > > < > > > :

i

P i ð1aÞðY c Y Þ 2ð1þcÞðY c YÞ

 þ

ð1þbÞðY c YÞ ð1þcÞðY c YÞ

ðY i þLYÞ





 ð1þbÞðY i þLYÞ Pn 

YX þL1

ð1þcÞ



ca i

i

B ;Y c y

ca n

ð1þcÞ

Yc

B ;Y c y

ðY c YÞ

da

; if Y c < Y i þ L ;

8a 2 A; i 2 I; n 2 I0 ; Biy ; Y c

if Y c P Y i þ L

0;

ð3Þ

C aBi ;ok;Y c y

8 < ð1þbÞðY c YÞ r ok ; if Y c < Y i þ L ðY c YÞ ¼ ð1þcÞ ; : 0; if Y c P Y i þ L

Y 6 Y c 6 Y;

8a 2 A; o 2 O [ K; k 2 K; Biy ; Y c

ð4Þ

8Y c

ð5Þ

cP0

ð6Þ

(1) and (2) calculate the additional benefit of a bus of type

Biy

with retrofit o running in area a to be retired in the current

year Y c , BaBi ;o;Y c , and the additional benefit of a bus of type Biy running in area a switching from retrofit o to k in the current y

year Y c , BaBi ;ok;Y c , by estimating the external costs savings from emissions reduction through early retirement or retrofit. In this y

estimation, we assume that the external cost savings accrue at the time when the bus is retired before its normal retirement age. And these additional benefits are discounted to the beginning of the planning horizon or the base year Y for comparison purposes, as are all the other cost terms. (3) and (4) calculate the additional cost C aBi ;Y c and C aBi ;ok;Y c . C aBi ;Y c includes three parts, the loss of disposing part of the residy

y

y

ual value of a bus to be early retired, the price difference of purchasing a replacement bus of the latest emission standard earlier than scheduled, and the cost difference of operating an old emission standard bus and a new emission standard bus for the remaining life of the bus to be replaced. For the first term on the RHS of (3), we assume that half of the cost will be saved by recycling the old bus, as spare parts for repair or reconditioning and scrap metal, implying that half of the depreðY c Y i Þ

ciated value of the old bus will be lost, i.e. Pi ð1a2Þ . Discounting this cost to the base year, we have the first term on the RHS of (3). A bus to be early retired implies the need of purchasing a replacement bus of the latest emission standard ahead of time, i.e. before its nominal lifespan. The second term on the RHS of (3) captures this additional cost. The term ð1 þ bÞðY c YÞ ðY c YÞ

represents the inflation factor. Therefore, ð1þbÞ P n represents the value of purchasing a bus of the latest emission standard ð1þcÞðY c YÞ ðY i þLYÞ

in year Y c while adjusting for the inflation and interest factors to the base year Y, while ð1þbÞðY i þLYÞ Pn is the value of purchasing ð1þcÞ

a bus of the latest emission standard in its nominal scheduled year Y i þ L while similarly adjusting for the inflation and interest factors to the base year Y. The difference between these two terms gives the additional cost of early retiring a bus of standard i purchased in Y i and replacing it with a bus of the latest emission standard. The third term on the RHS of (3) represents the difference in operation costs between the bus to be retired and the new replacement bus for the remaining life of the bus to be retired, similarly discounted to the base year. (4) captures the retrofit cost, adjusted for inflation and discounted to the base year. By performing the RLABC analysis, for a specific bus retirement case, a graph can be drawn to indicate when and which action, if any, i.e. early retirement or retrofit, should be taken for each type of buses. However, to provide a systematic way to derive the optimal management scheme subject to budget constraints, as well as quantifying the net benefit obtained from the optimal plan, we develop an integer linear-program (ILP) to solve the problem in Section ‘Optimal bus fleet management scheme: societal perspective’, where the net benefit refers to the difference between the additional benefit and additional cost.

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L. Li et al. / Transportation Research Part D 41 (2015) 330–347

Optimal bus fleet management scheme: societal perspective For social welfare, the government will derive the optimal BFM scheme to maximise the total net benefit by early retiring or retrofitting certain buses through the decision variables N aBi ;o;Y c , i.e. number of buses of type Biy with retrofit o running in y

area a to be retired in the current year Y c , and RaBi ;ok;Y c , i.e. number of buses of type Biy running in area a switching from retrofit y

o to k in the current year Y c . The formulation can be expressed as: [SCHEME A]

z¼

maxa

Nai

B ;o;Y c y

; R

Bi ;ok;Y c y

(

X Y c ; a2A;Biy

  i X Xh a X a BBi ;o;Y c  C aBi ;Y c NaBi ;o;Y c þ BBi ;ok;Y c  C aBi ;ok;Y c RaBi ;ok;Y c y

y

o2O[K

y

o2O[K k2K

y

y

) ð7Þ

y

subject to

NaBi ;o;Y ¼ 0;

8a 2 A; o 2 K; Biy

ð8Þ

RaBi ;ok;Y ¼ 0;

8a 2 A; o 2 K; k0 2 K; Biy

ð9Þ

y

y

X a XX a NBi ;o;Y c þ RBi ;ok;Y c ¼ F aBi ; y

Yc

y

Y c k2K

8a 2 A; o 2 O; Biy

y

XX a XX a X a NBi ;o;Y c þ RBi ;ok;Y c ¼ RBi ;lo;Y c ; y

Yc

X a F Bi ¼ F Bi ; Yc X

NaBi ;o;Y c þ y

Y

X X a2A;Biy

Y c l2O[K

8a 2 A; o 2 K; Biy

y

ð11Þ

8Biy

y

y

a2A

y

Y c k2K

ð10Þ

Yc X X Y

ð12Þ

RaBi ;ok;Y c 6

YX c 1

y

k2K

X

Y l2O[K

8a 2 A; o 2 K; Y c P Y þ 1; Biy

RaBi ;lo;Y c ; y

ð13Þ

(" ð1 þ bÞðY c YÞ

) i # X ð1 þ bÞðY c YÞ Pi ð1  aÞðY c Y Þ a MY c a N 6 P  þ r R ; i i n ok By ;o;Y c By ;ok;Y c ðY c YÞ ð1 þ cÞðY c YÞ 2ð1 þ cÞðY c YÞ ð1 þ cÞðYcYÞ k2K ð1 þ cÞ

o2O[K

8Y c ; i 2 I; n 2 I0 ð14Þ

X

X

(" ð1 þ bÞðY c YÞ ð1 þ cÞðY c YÞ

Y c ;a2A;Biy o2O[K

NaBi ;o;Y c ; y

i

Pn 

Pi ð1  aÞðY c Y Þ

#

2ð1 þ cÞðY c YÞ

RaBi ;ok;Y c 2 Z

NaBi ;o;Y c y

þ

X ð1 þ bÞðY c YÞ k2K

ð1 þ cÞ

r Ra ðY c YÞ ok Biy ;ok;Y c

) 6 M;

8i 2 I; n 2 I0

ð15Þ

ð16Þ

y

Constraints (8) and (9) state that there are no replacement or retrofit at the beginning of the planning horizon Y. These initial conditions can be modified to reflect the actual situation. Constraints 10–13 are conservation conditions for buses of the same types. (10) indicates that for buses without prior retrofit, status o, running in each area a, the sum of them to be replaced and those with their retrofit to be upgraded to k from the current year to the end of the planning horizon should be equal to the initial fleet size. Similarly, for buses with prior retrofit upgrade to o running in each area a. (11) states that the sum of them to be replaced and those with further retrofit upgrade to k from the current year to the end of the planning horizon should be equal to the fleet size with retrofit status o to begin with. Constraint (12) states that summing the fleets running in each area a produces the total fleet size. Constraint (13) states that summing the buses with prior retrofit to o running in area a to be replaced or upgraded their retrofit to k between the beginning of the planning horizon and the current year Y c should be limited by the amount of buses switched to retrofit o before Y c . Constraints (14) and (15) are, respectively, the annual budget MY c and overall budget M, while both of the LHS terms are the actual expenditures for the operator, including the purchase costs, the resale revenues and the retrofit costs. The solution of this ILP provides the optimal BFM scheme under budget constraints. The optimal scheme N aBi ;o;Y c specifies the replacement of bus type Biy with retrofit status o running in region a in the optiy

mal year Y c . Let this optimal year of replacement for this bus type in Scheme A be Y schemeA . Putting this optimal year of replacement into (1) and (3), we obtain the associated additional benefit and cost of replacing this specific bus type in that year, expressed, respectively, as: BaBi ;Y ; C aBi ;Y . Treating the optimal retrofit scheme in a similar manner, and putting y

SchemeA

y

SchemeA

the optimal year of retrofit for the specific bus type into (2) and (4), we obtain the additional benefit and cost of retrofitting

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L. Li et al. / Transportation Research Part D 41 (2015) 330–347

this specific bus type in that year as: BaBi ;ok;Y y

SchemeA

; C aBi ;ok;Y SchemeA . These two pairs of coefficients have important implications for y

deciding the government subsidy scheme, as we will discuss in Section ‘Government subsidy consideration’. Optimal bus fleet management scheme: company perspective The model described in Section ‘Optimal bus fleet management scheme: societal perspective’ is to maximise the net benefit considering society as a whole, which involves an optimal tradeoff between the benefit of emissions reduction and the additional cost incurred in bus replacement and retrofit. However, if the bus company is privately operated, as in the case of Hong Kong and many metropolitan areas, its objective is primarily profitability, not societal welfare. Nevertheless, even from the company’s perspective, early replacement of certain buses from their nominal lifespan of 17 years may make sense, as long as this is profitable. For example, as can be seen from (3), under circumstances of high inflation rates but relatively low interest rates, early replacement may result in negative additional costs, encouraging early replacement. Hence the bus company will have another BFM scheme for its own sake, the one that minimizes the additional costs. Taking advantage of the formulation developed in Section ‘Remaining life additional benefit-cost (RLABC) analysis’, we can determine the optimal BFM scheme for the bus company by removing the additional benefits associated with emissions reduction and focusing only on the remaining life additional cost. The resultant objective function can be stated as follows. [SCHEME B]

Nca i

z¼

mina

B ;o;Y c y

; Rc

Bi ;ok;Y c y

"

X

X

o2O[K

Y c ; a2A;Biy

C aBi ;Y c NcaBi ;o;Y c y y

X X a þ C Bi ;ok;Y c RcaBi ;ok;Y c y

o2O[K k2K

#

ð17Þ

y

The objective function in (17) is to minimize the additional costs relative to the default retirement age of 17 through the decision variables NcaBi ;o;Y c , i.e. number of buses of type Biy with retrofit o running in area a to be retired in the year Y c , y

and RcaBi ;ok;Y c , i.e. number of buses of type Biy running in area a switching from retrofit o to k in the year Y c . Solving 8–17 by y

changing all the decision variables in the constraints to NcaBi ;o;Y c and RcaBi ;ok;Y c , the most beneficial BFM scheme for the bus y

y

company can be determined, which excludes the benefits from emissions reduction. The optimal scheme NcaBi ;o;Y c specifies y

the replacement of bus type Biy with retrofit status o running in region a in the optimal year Y c . Let this optimal year of replacement for this bus type be Y SchemeB . Putting this optimal year of replacement into (1) and (3), we obtain the associated additional benefit and cost of replacing this specific bus type in that year, denoted, respectively, as: BaBi ;Y ; C aBi ;Y : Treating the optimal retrofit scheme in a similar manner, and putting the optimal year of retrofit y

SchemeB

y

SchemeB

for the specific bus type into (2) and (4), we obtain the additional benefit and cost of retrofitting this specific bus type in that year as: BaBi ;ok;Y ; C aBi ;ok;Y . These two pairs of coefficients have important implications for deciding the govy

SchemeB

SchemeB

y

ernment subsidy scheme, as we will see next. Government subsidy consideration To entice the private operator to implement the socially optimal BFM scheme (i.e. Scheme A) for emissions reduction, which is different from the BFM scheme for cost minimization (i.e. Scheme B), some sort of incentive or subsidy may be needed. After all, one can also argue that the externality of emissions should not be borne by the bus company alone. Intuitively, the subsidy needed is equal to the extra expenses incurred by implementing this socially optimal Scheme A, or savings in the external cost for emissions reduction due to this scheme. On the other hand, the bus company may adopt a certain early replacement or retrofit scheme for cost minimization on its own, which requires no subsidy but still produces the positive side effect of emissions reduction. Only those bus early replacements and retrofits that do not reduce cost to the company but produce substantial emissions reduction need to be subsidized. The main idea is to make use of subsidy to entice the private company to generate the Scheme A plan under its own cost minimization. That is, by defining the subsidies appropriately for different types of buses and including them in the cost calculation, minimizing the cost for the company will produce a plan that is also socially optimal. In defining the subsidies, we make the simplifying assumption that there are no budget constraints to the government and the company in implementing the BFM scheme. Without budget constraints, each bus type can be considered independently without interaction with other bus types. By determining the most beneficial time for replacement or retrofit for a particular type of bus, all buses of the same type and attributes will be replaced or retrofitted accordingly at the same time. Without loss of generality, in the following, we derive the government subsidy for each bus type. The subsidy given is specific to the bus type, age, emission standard, retrofit status, and operating area. For each bus type with the above specific attributes, the subsidy is determined based on the comparison between its net benefit to society according to Scheme B, i.e. BaBi ;o;Y  C aBi ;Y for replacement and BaBi ;ok;Y  C aBi ;ok;Y for retrofit, and the net benefit y

SchemeB

y

SchemeB

y

SchemeB

y

SchemeB

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to society according to Scheme A, i.e. BaBi ;o;Y y

SchemeA

 C aBi ;Y SchemeA and BaBi ;ok;Y y

y

SchemeA

 C aBi ;ok;Y SchemeA . If the net benefit to society for y

replacing or retrofitting that bus type according to Scheme A is larger than that of Scheme B, i.e.

8 a < BBi ;o;Y y

 C aBi ;Y

SchemeA

: BaBi ;ok;Y y

y

SchemeA

SchemeA

 C aBi ;ok;Y y

> BaBi ;o;Y y

SchemeB

> BaBi ;ok;Y

SchemeA

y

 C aBi ;Y y

SchemeB

SchemeB

 C aBi ;ok;Y y

;

ð18Þ

SchemeB

then the following subsidy should be given to entice implementation:

SaBi ;o;Y y

 ¼ C aBi ;Y

SchemeA

y

SchemeA

 C aBi ;Y y



SchemeB

þ daBi ;o;Y y

  SaBi ;ok;Y SchemeA ¼ C aBi ;ok;Y SchemeA  C aBi ;ok;Y SchemeB þ daBi ;ok;Y y

y

y

8Biy ; a; o

SchemeA

y

ð19Þ

8Biy ; a; ok

SchemeA

ð20Þ

(19) and (20) ensure that following the early replacement and retrofit plan according to Scheme A does not incur any financial loss to the company as compared with its original Scheme B. It can be seen that the subsidy is com C aBi ;Y and posed of two parts. One is the basic subsidy to cover the additional implementing cost, i.e. C aBi ;Y SchemeA

y

C aBi ;ok;Y y

SchemeA

 C aBi ;ok;Y y

SchemeB

y

SchemeB

. That is, the subsidy neutralise any additional cost to the company. The other is the addi-

tional subsidy to further encourage implementation, denoted by daBi ;o;Y y

SchemeA

, the additional subsidy for type Biy buses

with retrofit o running in area a to be retired in the year Y SchemeA , and daBi ;ok;Y y

SchemeA

, the additional subsidy for type

Biy

buses running in area a switching from retrofit o to k in Y SchemeA . The additional subsidy is put there to ensure implementation of the Scheme A plan, which is a parameter to be adjusted or negotiated for the specific context. To some company, even a breakeven subsidy is sufficient; others may desire more. In any case, this is a parameter in the model. In the following, we show why the company will generate the Scheme A plan in its cost minimization with the subsidies provided. Let’s put SaBi ;o;Y and SaBi ;ok;Y into (17) and minimize the total cost for the company, and call this plan SchemeA

y

Scheme C: [SCHEME C]

Nca i

B ;o;Y c y

; Rc

X

z¼

mina Bi ;ok;Y c y

Y c ; a2A;Biy

y

"

SchemeA

X  a C Bi ;Y c  SaBi ;o;Y

o2O[K

y

y

SchemeA

 X X a C Bi ;ok;Y c  SaBi ;ok;Y NcaBi ;o;Y c þ y

o2O[K k2K

y

y

SchemeA

 RcaBi ;ok;Y c y

# ð21Þ

Without budget constraint, Scheme C can be solved bus type by bus type. That is, for each bus type, we find the minimum cost to early replace or retrofit it all at once as a type, as determined by the variables NcaBi ;o;Y c and RcaBi ;ok;Y c . Before subsidizay

y

tion, the coefficients have been calculated in Section ‘Optimal bus fleet management scheme: company perspective’, i.e. C aBi ;Y and C aBi ;ok;Y in Scheme B. Since subsidies are only given to those bus types with extra net benefits, there are y

SchemeB

SchemeB

y

two types of coefficients. Bus types not delivering extra net benefits to society receive no subsidy. The cost of replacing or retrofitting them in any particular year Y c is not smaller than the cost of replacing or retrofitting it in its optimal year according to Scheme B.

C aBi ;Y c P C aBi ;Y y

y

C aBi ;ok;Y c P C aBi ;ok;Y y

ð22Þ

SchemeB

y

ð23Þ

SchemeB

Therefore, in cost minimization, there is no incentive to change the replacement or retrofit plan of these bus types from the optimal year Y SchemeB to any other year. For bus types that receive subsidies, substituting (19) and (20), their cost coefficients in the year Y SchemeA change to:

C aBi ;Y SchemeA  SaBi ;o;Y SchemeA ¼ C aBi ;Y SchemeA  y

y

y

¼ C aBi ;Y y

SchemeB

h  C aBi ;Y SchemeA  C aBi ;Y SchemeB þ daBi ;o;Y y

y

 daBi ;o;Y

6 C aBi ;Y

y

C aBi ;ok;Y SchemeA  SaBi ;ok;Y SchemeA ¼ C aBi ;ok;Y SchemeA  y

y

y

¼ C aBi ;ok;Y y

SchemeB

SchemeA

y

y

i

ð24Þ

SchemeA

SchemeB

h  C aBi ;ok;Y SchemeA  C aBi ;ok;Y SchemeB þ daBi ;ok;Y y

 daBi ;ok;Y y

y

SchemeA

6 C aBi ;ok;Y y

y

SchemeB

i SchemeA

ð25Þ

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To take advantage of the subsidy, the company can minimize its cost by choosing to replace or retrofit the bus type Biy with retrofit status o running in a in the year Y SchemeA , whose cost is guaranteed to be no greater than to replace or retrofit it in the year Y SchemeB according to (24) and (25). Moreover, the additional subsidies daBi ;o;Y and daBi ;ok;Y will ensure that y

SchemeA

y

SchemeA

implementing the Scheme A plan will have a lower cost than the Scheme B plan. Hence, the cost minimization in Scheme C will reproduce the Scheme A plan, as we will validate in Section ‘Case study – Hong Kong’. This is also the minimal subsidy required to exactly reproduce the Scheme A plan. There are possibly other subsidy schemes to bring about positive net benefits as long as condition (18) holds, but their performance cannot be better than the subsidy plan as depicted in (19) and (20), since it will bring about the Scheme A plan which is guaranteed to produce the maximum net benefit. Case study – Hong Kong Background According to the Transport Department of the Hong Kong Special Administration Region (HKSAR), franchised buses in total carry 3.8 million journeys daily, or 33.6% of the total public transport daily passenger journeys. Franchised buses are one main source of roadside emissions on busy corridors in Hong Kong. It is recognised that vehicular emissions reduction in franchised buses by the use of cleaner buses can improve air quality (Environmental Protection Department, 2011). Although private cars contribute to the largest component of on-road vehicle GHG emissions, light-duty, medium-duty and heavy-duty trucks have been the major sources of increases in on-road vehicular emissions (United States Environmental Protection Agency, 2011). According to the Regulation of Air Pollution Control (Vehicle Design Standards) (Emission) (Amendment) enacted in 2006, from October 2006 onwards, all newly registered heavy-duty vehicles (including franchised buses) have to comply with the Euro IV emission standards (Legislative Council of Hong Kong, 2006). As the lifespan of each franchised bus in Hong Kong is at most 17 years (Legislative Council of Hong Kong, 2010), over time, even without active intervention, emissions arising from buses will be reduced naturally. The question is whether it is beneficial to replace them before their 17-year lifespan, considering the extra expenses for early replacement and budget constraints. In 2010, the Kowloon Motor Bus Company Limited (KMB), the biggest bus company in Hong Kong, which carries about 23% of public transport passenger journeys (Transport Department, 2010), will replace all its franchised buses with Euro IV standard buses within a specified period of time. We use this case as an example to illustrate the approach proposed in section 2 and give a satisfactory management strategy for both the bus company and the government. Model specification KMB bus fleet KMB bus fleet comprises of a range of Euro standards, and operated for a total of 320.8 million km in 2009 (Transport Department, 2010); the buses run in different areas with different average journey speeds, which are, respectively, 23 km/h in Kowloon (KWL), including Hong Kong Island in this case, and 43 km/h in New Territories (NT) (Transport Department, 2010). The KMB bus fleet is listed in Table 1 (Hong Kong Bus Resources and Information Centre, 2015; Transport Department, 2010).

Table 1 KMB bus fleet. Class and instalment phase

Purchase year (Y ib )

Age at 2010

Year of retirement

No. of buses (I)

Running area

Euro III – 2nd Euro III – 3rd Euro III – 4th Euro III – 5th Pre-Euro – 1st Euro I – 1st Euro I – 2nd Euro I – 3rd Euro I – 4th Euro II – 1st Euro II – 2nd Euro II – 3rd Euro III – 1st Euro III – 2nd

2003 2005 2006 2008 1994 1994 1995 1996 1997 1996 1998 1999 2002 2003

8 6 5 3 17 17 16 15 14 15 13 12 9 8

2020 2022 2023 2025 2011 2011 2012 2013 2014 2013 2015 2016 2019 2020

270 199 333 86 49 100 30 142 1010 22 698 234 357 119

KWL KWL KWL KWL NT NT NT NT NT NT NT NT NT NT

Remark: (a) Euro I – 1st installment was retired in 2009.

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According to company yearbooks, the cost of a new Euro IV bus is approximately HK$3,500,000 (about US$448,700) (Citybus and New World First Bus, 2007). As for the interest rate, we use the Hong Kong Bank’s current Hong Kong Dollar best lending rate started from 2008 for calculation, which is 5%; and the inflation rate is set at 2.02% for the transport section in Hong Kong, 2010 (Census and Statistics Department, 2011). The parameter values used include: (a) Running areas: a1 ¼ KWL; a2 ¼ NT. (b) Average travel distances: da1 ¼ da2 ¼ 87908:47 km. (c) Average travel speeds: v a1 ¼ 23 km=h; v a2 ¼ 43 km=h. (d) Planning horizon: Y ¼ 2010; Y ¼ 2025; L ¼ 17. qffiffiffi pffiffiffiffiffiffiffiffiffiffi (e) The depreciation rate: a ¼ 1  L PRi ¼ 1  17 0:05 ¼ 16:2%. (f) Interest and inflation rates: c ¼ 5%; b ¼ 2:02%. (g) Bus purchase cost: PEuro IV = US$ 448,700, PEuro PPre-Euro = US$ 358,960.

III

= US$ 403,830, PEuro

II

= US$ 394,856, PEuro

I

= US$ 381,395,

Operating and retrofit costs Based on the notion of ‘‘repair limit”, we roughly estimate the operating costs, i.e. operation costs, maintenance costs, fuel costs, etc. for each type of buses at different ages. If the operating cost exceeds the expected value of a bus in a specific year, this bus should be replaced with a new one. We assume that the operating cost of a Euro IV bus aged 17 years (its nominal lifespan) is equal to its salvage value. In other words, the operating cost must be larger than its salvage value in the year after, and thus the bus should be retired. Moreover, we assume that the operating cost increases by 5% per year as the bus ages. Similarly, 5% extra cost is added into the operating cost from the newest emission standard type to the oldest, as shown in Fig. 1. Of course, if more exact operating cost of buses is available, we can use their exact figures for the analysis. There are three types of emission reduction devices in Hong Kong.  Diesel Oxidation Catalysts (DOCs)—Retrofitting pre-Euro and Euro I franchised buses can reduce their particulate emissions by about 30% and emissions of hydrocarbon and carbon monoxide by about 50%.  Diesel particulate filters (DPFs)—Retrofitting Euro II and Euro III buses can reduce the emissions of particulates, hydrocarbon and carbon monoxide by about 85%.  Selective catalytic reduction (SCR)—Retrofitting Euro II and Euro III buses can reduce the NOx emissions by about 60%. Retrofit costs are US$3226, US$7742, and US$32258 for DOCs, DPFs, and SCR respectively, including maintenance cost (Legislative Council of Hong Kong, 2011). Here, we allocate five retrofit and non-retrofitted statuses: 0 is for nonretrofitted; 1 is for DOCs; 2 is for DPFs; 3 is for SCR; and 4 is for DPFs + SCR. Therefore, we have the following:

r01 ¼ US$3226;

r02 ¼ US$7742;

r03 ¼ US$32; 258;

r04 ¼ US$40; 000;

r24 ¼ US$32; 258:

Vehicular emissions and external costs There are regulations from around the world to limit vehicle emissions from heavy-duty vehicles (HDVs). The European Union (EU) Emission Standards are among the most commonly used criteria, followed by the US federal emission standards and Japan’s emission standards. To estimate vehicular emissions from franchised buses in Hong Kong, which are exclusively

Fig. 1. Operating cost of different Euro emission types of buses in different ages.

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equipped with diesel engines according to Euro standards, we adopt the modeling tool COPERT IV, which is an enhanced version of COPERT III. COPERT III is among the most commonly used methodologies in Europe for calculating emissions (Ekstrom et al., 2004; Mensink et al., 2000). In the Road Transport Section of EMEP/EEA Air Pollutant Emission Inventory Guidebook 2009 (Ntziachristos et al. Springer, 2009), COPERT IV is adopted as the ‘‘Detailed methodology” for emissions calculation. According to the Guidebook adopted in this study, since over 90% of the franchised buses are double-decker buses (Transport Department, 2009), we approximate franchised buses in Hong Kong by the category of articulated urban bus, with weight larger than 18 tonnes, loading 100%, and running on level roads. The emission factors and corresponding parameters for this category of bus are shown in Appendix. Applying these parameters from Appendix, we obtain the emission factors of KMB franchised buses in Table 2. In conducting benefit–cost analyses, it is essential to convert the external costs associated with exhaust emissions into monetary terms. Romilly (1999) summarized that they can be estimated by tracing the links between emission sources and their effects on human health and climate change, then placing a value on these effects. Alternatively, they can be estimated through techniques such as hedonic pricing, where emission costs are inferred from observed market prices, such as in existing European Union carbon markets, or the revealed preferences of policy-makers, where the inference is based on the costs of meeting emission standards. A handbook released by the European Community (2008), jointly prepared by several transport research institutes, summarized the state of the art in the valuation of external costs. This handbook contains estimates of external costs for the transport sector, but with substantial variations for different countries and time scales. For consistency, this paper adopts the external costs adopted for the UK in 2010, because Hong Kong sort of follows the UK system as far as transport planning is concerned, with the vehicle types similarly classified. The external cost used is

Table 2 Bus emissions per km travel (Unit: g/km) at the speed of 23 km/h and 43 km/h. Class

PM2.5

CO2

SO2

CO

VOC

Running in KWL area at the speed of 23 km/h Pre-Euro 25.096 Euro I 15.498 Euro II 15.783 Euro III 13.825 Euro IV 8.399

NOx

1.337 0.697 0.366 0.278 0.060

1658.435 1471.878 1440.418 1478.947 1396.801

0.011 0.009 0.009 0.009 0.009

8.751 4.412 4.234 4.291 0.361

2.339 1.016 0.661 0.571 0.030

Running in NT area at the speed of 43 km/h Pre-Euro 18.273 Euro I 11.071 Euro II 11.273 Euro III 9.238 Euro IV 5.779

0.776 0.447 0.232 0.174 0.030

1164.428 1034.502 1033.736 1057.973 989.466

0.007 0.007 0.007 0.007 0.006

5.128 2.600 2.225 2.302 0.168

1.272 0.610 0.393 0.338 0.017

Table 3 External cost of vehicle-related emissions (United Kingdom). Emission

NOx

PM2.5

CO2

SO2

CO

VOC

US$/kg

3.61

360.49

0.02

6.11

0.52

1.02

Fig. 2. Net benefit curves for early replacement at different ages.

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composed of ‘‘air pollution cost” for NOx, PM2.5, SO2, CO, and VOC and ‘‘climate change cost” for CO2. Air pollution cost is generated to account for health costs, building and material damages, crop losses in agriculture and impacts on the biosphere, and impacts on biodiversity and ecosystems incurred by pollutant emission. Climate change cost adopted for CO2 is generated based on avoidance costs, which are the costs required for emission reduction to meet the Kyoto targets. These external costs are shown in Table 3, while those of NOx, PM2.5, SO2, and VOC are sourced from the handbook by European Community (2008) and CO from Matthews et al. (2001).

Net benefit ( thousand US$)

100 rere retrofit with DOCs

50

retrofit with DPFs 0

retrofit with SCR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 retrofit with DPFs+SCR

-50 Fig. 3. Net benefit curves for Euro I bus management.

(a) Euro III bus purchased in 2003 running inKWL

(b) Euro I bus purchased in 1997 running in NT Fig. 4. Net benefit curves of certain KMB buses based on RLABC.

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RLABC of KMB buses Different types of buses will have different net benefit curves based on RLABC due to their distinct emission standards and operating costs. Therefore, by referring to the net benefit curves for different bus types, it is possible to depict a most beneficial management plan under the situation without budget constraints. For the general case, considering that all bus types are new in the first year, and then their net benefit curves for early replacement are plotted in Fig. 2. Using the net benefit curves, we can figure out the best time to early replace a bus of a particular type. Take the Euro I bus running in NT (orange curve) for example; it reaches the peak net benefit at age 9. That means the most beneficial time to early replace a Euro I bus is when it is 9 years old. As for a pre-Euro bus running in NT (red curve), the best time is to replace them at age 2 or perhaps simply not to have them in the first place. Looking across the bus types, the trend seems to be that buses with newer emission standards tend to have longer beneficial lifespans. For bus types with negative net benefits, then they should not be early replaced. Besides, we can also construct the net benefit curves for retrofits using the same RLABC approach. To illustrate, we plot the net benefit curves of different retrofit options to the Euro-I bus, as shown in Fig. 3. The result shows that the best way is to retrofit it into DOCs at the very beginning. As time goes on, when it reaches age 5, the best plan is to early replace it by a bus with the latest emission standard. By producing the net benefit curves for all bus types, and considering them individually as discussed above, we can intuitively come up with the best BFM scheme for the current bus fleet. This simple procedure, of course, premises on the assumption that there are no budget constraints for replacing or retrofitting buses, and only the net benefits of buses are considered. Combining the various options of early replacement and retrofit and putting the exact year as the x-axis, to III I be specific, let’s look at two other examples to illustrate the approach, including BEuro in NT and BEuro 2003 1997 in KWL, with their results provided in Fig. 4. Each curve in Fig. 4(a) and (b) represents one management option. As zero net benefit is the ‘‘do-nothing” option, we only III need to consider the options with positive net benefits. For BEuro 2003 , the best plan is to retrofit it with DPFs in 2010, then retire I it in 2020, in its normal lifespan; while for BEuro 1997 , the best plan is to retire in 2010, 13 years after service. Similarly, considering all the other types of buses in KMB, we can find out the maximum net benefit for each bus type running in a different area among various management options. Therefore, by referring to the net benefit curves developed and combining the results for different bus types, a socially optimal BFM scheme can be derived. We can do so because there are no interactions among bus types in this analysis in the absence of budget constraints. Similarly, we can derive the company optimal BFM scheme, by referring to the additional cost curves without considering the benefits from emissions reduction. Under budget constraints, however, we need to consider which bus types and which management options have higher

Table 4 Socially optimal BFM scheme without budget constraints (company BFM scheme is bracketed if different). KWL

NT

Euro III

Pre-Euro

Euro I

2008

1994

1994

1995

1996

1997

1996

1998

1999

2002

2003

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 86(86)

49(0) 0(49) 0 0 0 0 0 0 0 0 0 0 0 0 0 0

100(0) 0(100) 0 0 0 0 0 0 0 0 0 0 0 0 0 0

30(0) 0 0(30) 0 0 0 0 0 0 0 0 0 0 0 0 0

142(0) 0 0 0(142) 0 0 0 0 0 0 0 0 0 0 0 0

1010(0) 0 0 0 0(1010) 0 0 0 0 0 0 0 0 0 0 0

0 0 0 22(22) 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 698(698) 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 234(234) 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 357(357) 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 119(119) 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 22 0 0 0

0 698 0 0 0

0 234 0 0 0

0 357 0 0 0

0 119 0 0 0

2003

2005

2006

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025

Bus replacement scheme 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 270(270) 0 0 0 0 0 0 199(199) 0 0 0 333(333) 0 0 0 0 0 0

R01 R02 R03 R04 R24

Bus retrofit scheme for 2010 (base year) 0 0 0 0 270 199 0 0 0 0 0 0 0 0 333 86 0 0 0 0

Euro II

Euro III

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

343

net benefits and therefore should be given higher priority for implementation. To achieve this, we need to use the model developed in Section ‘Optimal bus fleet management scheme: societal perspective’ and Section ‘Optimal bus fleet management scheme: company perspective’ to accomplish the most beneficial BFM strategies for different operators, as will be discussed in the next section.

Scenario analysis The Scenario without budget constraints In this scenario, the strategy for the government to maximise the net benefit without budget constraint is achieved by solving 1–16 while removing the budget constraints (14), (15). Note that the same result can be obtained by referring to the net benefit curves developed for the current bus fleet as discussed in Section ‘RLABC of KMB buses’. On the other hand, the strategy for the company to minimize the additional cost without budget constraints is achieved by solving 3–17 with the decision variables changed to NcaBi ;o;Y c and RcaBi ;ok;Y c . Both of the resultant schemes are shown y

y

in Table 4. It can be seen from Table 4 that, the optimal BFM scheme for KMB is to change nothing on the 17-year replacement plan. As for the scheme generated by the government, first of all, older buses tend to retire as early as possible, as it calls for immediate retirement of all Euro I and earlier buses. Secondly, newer buses tend to retrofit as early as possible, as all Euro II and later buses are retrofitted in the base year. Thirdly, all retrofitted buses will be retired in their normal retirement age. This optimum management scheme can obtain a total benefit of US$221 million with US$75 million extra expenses compared to the ‘‘do-nothing” scheme. Although the government BFM scheme produces considerable benefit from emissions reduction, it does not mean much to the bus operator who is after profitability. Therefore, for the sake of society, the government needs to offer incentives to the bus company for its implementation. Intuitively, an offer of US$75 million is needed to cover the extra expenses to the company. However, by solving (19) and (20) with the additional subsidy taken as 1 dollar extra, the bus company regenerates its own BFM scheme exactly the same as the socially optimal BFM scheme after US$53 million subsidization. Therefore, by offering a subsidy of US$53 million to KMB, a benefit of US$221 million of emissions reduction will be gained for society, which achieves a saving of US$23 million or about 30% for the government.

Net benefit (million US$)

Net benefit (million US$)

The Scenario with budget constraints In reality, it may not be realistic or feasible for a bus operator to replace a large portion of its fleet within a short period of time. Therefore, budget constraints, as (14) and (15), should be added to reflect the affordability issue. As each bus will be replaced naturally at the end of its normal lifespan of 17 years, so a budget is needed for this even without early replacement or retrofit. Early replacement and retrofit will add to this base budget, with the base budget constituting a lower bound of the normal expenses. We start with this base budget to study the effects of imposing different overall and annual budgets on the optimal BFM scheme. The resultant total net benefits and budget constraints are shown in Fig. 5. For the overall budget, we vary it from US$1.33 billion to US$1.41 billion and resolve 1–16 repetitively. It can be seen that the net benefit experiences a great change due to the overall budget. Generally, as is expected, a higher overall budget produces a higher net benefit, subject to an upper limit when the budget constraint is removed. Fig. 5 shows that when the overall budget reaches US$1.4 billion, there is no further substantial gain in net benefit. The annual budget constraint has more or less the same impact on the total net benefit. Generally, its curve is flatter as it does not affect the total net benefit as much as the overall budget. When the annual budget reaches US$605 million, there is no further substantial gain in the net benefit. The reason is that in the optimal replacement scheme, the largest single year spending occurs in 2010, amounting to US$605 million. So the annual budget constraint of US$605 million or above becomes non-binding, or has absolutely no effect on the optimal solution.

200 150 100 50 0

Overall budget (billion US$)

170 160 150 140 130

Annual budget (million US$)

Fig. 5. Net benefit distribution under different budget limitations.

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Table 5 BFM scheme for maximum net benefit with budget constraints (US$1.35 billion overall budget and US$500 million annual budget). KWL

NT

Euro III 2003

2005

2006

2010 2011 2012 2013 2014 2015 2016

Bus replacement scheme 0 0 0 0 0 0 270 0 0 0 199 0 0 0 333 0 0 0 0 0 0

R01 R02 R03 R04 R24

Bus retrofit scheme 0 0 270 199 0 0 0 0 0 0

Pre-Euro

Euro I

2008

1994

1994

1995

1996

1997

1996

1998

1999

2002

2003

0 0 0 0 0 0 86

49 0 0 0 0 0 0

100 0 0 0 0 0 0

30 0 0 0 0 0 0

142 0 0 0 0 0 0

1010 0 0 0 0 0 0

22 0 0 0 0 0 0

698 0 0 0 0 0 0

234 0 0 0 0 0 0

0 0 357 0 0 0 0

0 0 119 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 357 0 0 0

0 119 0 0 0

for 2010 (base year) 0 0 0 333 86 0 0 0 0 0 0 0 0 0 0

Euro II

Euro III

Table 6 BFM schemes without budget constraints at zero inflation rate (company scheme is bracketed). KWL

NT

Euro III

Pre-Euro Euro I

2003

2005

2006

Euro II

Euro III

2008

1994

1994

1995

1996

1997

1996

1998

1999

2002

2003

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 86(86)

49(0) 0(49) 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 100(100) 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 30(30) 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 142(142) 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1010(1010) 0 0 0 0 0 0 0 0 0 0 0

0 0 0 22(22) 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 698(698) 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 234(234) 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 357(357) 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 119(119) 0 0 0 0 0

0 0 0 0 0

100 0 0 0 0

30 0 0 0 0

142 0 0 0 0

1010 0 0 0 0

0 22 0 0 0

0 698 0 0 0

0 234 0 0 0

0 357 0 0 0

0 119 0 0 0

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025

Bus replacement scheme 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 270(270) 0 0 0 0 0 0 199(199) 0 0 0 333(333) 0 0 0 0 0 0

R01 R02 R03 R04 R24

Bus retrofit scheme for 2010 (base year) 0 0 0 0 270 199 0 0 0 0 0 0 0 0 333 86 0 0 0 0

Table 7 BFM schemes without budget constraints at 7% inflation rate (company scheme is bracketed). KWL

NT

Euro III

Pre-Euro

Euro I

2008

1994

1994

1995

1996

1997

1996

1998

1999

2002

2003

0 0 0 0 0 86(86)

49(49) 0 0 0 0 0

100(100) 0 0 0 0 0

30(30) 0 0 0 0 0

142(142) 0 0 0 0 0

1010(1010) 0 0 0 0 0

22(22) 0 0 0 0 0

698(698) 0 0 0 0 0

234(234) 0 0 0 0 0

357(357) 0 0 0 0 0

119(0) 0(119) 0 0 0 0

0

0

0

0

0

0

0

0

0

2003

2005

2006

2010 2011 2012 2013 2014 2015

Bus replacement 270(0) 0 0(270) 0 0 199(0) 0 0(199) 0 0 0 0

scheme 0 0 0 333(0) 0(333) 0

R02

Bus retrofit scheme for 2010 (base year) 0 199 333 86 0

Euro II

Euro III

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

345

We select the case with two budget constraints, overall budget of US$1.35 billion and annual budget of US$500 million, to illustrate the resultant optimal BFM scheme for the government. The results are shown in Table 5, with KMB keeping the same scheme due to the same inflation rate. As can be seen, the introduction of the budget constraints spreads out the replacement of buses over time and changes the retrofit devices, as compared with the case without budget constraints as shown in Table 4. What, however, perhaps worthwhile to note is that the total net benefit is also much reduced, from US$168 million (Table 4) to US$124 million (Table 5). Besides, the total net benefit is also smaller than the cases with one single budget constraint, as the total net benefit is US$133 million for overall budget (US$1.35 billion) and US$166 million for annual budget (US$500 million).

Sensitivity analysis  In this study, we found that the second term in (3), i.e.

ð1þbÞðY c YÞ ð1þcÞðY c YÞ

 ðY i þLYÞ  ð1þbÞðY i þLYÞ P n , has a great influence on the net benefit, ð1þcÞ

and hence on the early retirement scheme. As the interest rate c remains stable overtime, we conducted sensitivity analyses for a range of the inflation rate b. The results showed that when the inflation rate is small, as is often the case in technology development – while the technology improves, the price remains relatively the same over time, the beneficial management scheme will be inclined to replace the new buses later, following a longer retirement plan. With the increase of the inflation rate, the beneficial management scheme will be inclined to replace the buses to new ones in a shorter time frame, as the purchasing cost will be larger if the new bus is bought one year later. For KMB, the optimal solutions start to change from 4% of the inflation rate. When the inflation rate reaches 13%, the optimal BFM scheme generated by KMB will be replacing all the buses in the base year, while the same results will be achieved for government with the inflation rate slightly less than 13%. We select two cases to illustrate the impacts on the optimal schemes due to different inflation rates, i.e. zero and 7% respectively. The results are shown in Tables 6 and 7. It can be seen from Table 6 that, US$171 million of total benefits for emissions reduction can be earned by executing the BFM scheme under a zero inflation rate, with a government subsidy of US$36 million. When the inflation rate changes to 7%, by implementing the BFM scheme with a subsidy of US$6 million, US$235 million can be gained for the society. It is noticeable that the higher the inflation rate is, the larger the total benefit will be.

Concluding remarks This study proposed an approach called remaining life additional benefit–cost (RLABC) analysis to determine the bus fleet management (BFM) strategy. Under the situation without budget constraints, the optimal BFM scheme can be derived by simply working with the net benefit graphs developed for individual bus types. Under budget constraints, an integer linear program (ILP) based on RLABC is developed to optimise the BFM scheme. Two measures are taken into account to make the problem more realistic: savings in the external costs associated with emissions reduction are considered as an additional benefit; and the additional expenses on replacing and retrofitting the buses before their nominal retirement are considered as an additional cost, while taking the interest and inflation rates into consideration. This study provided two perspectives for optimal bus fleet management, including the profitability of the private bus company, as well as the overall social benefit in emissions reduction, and determined the level of subsidy needed to implement the socially optimal bus fleet management plan. To achieve this, this study developed three formulations to provide a broader consideration of the impact of optimal bus fleet management: namely, two BFM schemes, one to maximise the total net benefits and the other is to minimize the total additional costs; and one subsidy scheme for the government to entice the implementation of the socially beneficial BFM scheme by the private company. The mathematical programs developed can produce sophisticated management schemes that are efficient and beneficial. The results were surprising in the sense that the magnitude of the total benefit can be considerable. In the case of KMB, a return of a factor of three could be achieved. And even simple early retirement schemes would produce sizeable benefits, depending on inflation rates, which have a great impact on the retirement scheme – higher inflation rates lead to larger total benefits. Finally, the mathematical programs developed here are generic and applicable to not just Hong Kong, but also to other vehicle replacement strategies, such as for trucks or private cars elsewhere. Generally speaking, it is formulated to cater for future vehicle technology developments and vehicle fleet replacement.

Acknowledgements The study is supported by Research Grant SBI13EG04-B, General Research Funds #616113 and #16206114 of the Research Grants Council of the HKSAR Government, and Strategic Research Funding Initiative SRFI11EG15.

346

Appendix A Equations of vehicular emission by articulated bus, diesel fuel, weight > 18 tonnes, 100% loading (Source: EMEP/EEA air pollutant emission inventory guidebook 2009). Emission type

Vehicletechnology

CO

Pre-euro Euro I Euro II Euro III

NOx

vÞ

y¼aþb 

Pre-euro Euro I Euro II Euro III Euro IV

y ¼ e þ a  expðb  v Þ þ c  expðd  1 y ¼ c  v 2 þb  vbþa

y ¼ exp a þ v þ c  lnðv Þ y ¼ c þ a  expðb  v Þ y ¼ e þ a  expðb  v Þ þ c  expðd 

Pre-euro Euro I

y¼a  y¼a 

Euro III Euro IV FC

vþ

ðcbÞ  ð1expðd  d

Euro IV

Euro II

⁄

 vÞ y ¼ a þ b  v þ ðcbÞ  ð1expðd d

y ¼ exp a þ vb þ c  lnðv Þ

y ¼ exp a þ vb þ c  lnðv Þ

y ¼ exp a þ vb þ c  lnðv Þ

Pre-euro Euro I Euro II Euro III Euro IV

vÞ

vÞ

v þb  v þc  v þd v3 þ b  v2 þ c  v þ d  vÞ y ¼ a þ b  v þ ðcbÞ  ð1expðd d ðcbÞ  ð1expðd  v Þ y¼aþb  v þ d  vÞ y ¼ a þ b  v þ ðcbÞ  ð1expðd d y¼aþb y¼cþa y¼cþa y¼cþa y¼cþa

3

    

2

vþ expðb expðb expðb expðb

ðcbÞ  ð1expðd  d

   

vÞ

vÞ vÞ vÞ vÞ

Emission type

Vehicle technology i

CO2

i;Diesel ECO2 ;i;Diesel ¼ 44:011  12:011þ1:008rH:C;Diesel þ16:000r O:C;Diesel

SO2

ESO2 ;i ¼ 2  kS;Diesel  FC i;Diesel

a

b

c

d

e

33.14253

0.04304

2.47093

0.090938

#N/A

4.773259

4.41201

0.98776

#N/A

#N/A

5.565393

6.20136

1.22873

#N/A

#N/A

5.494445

6.32505

1.20008

#N/A

#N/A

1.315256

0.00082

0.08257

0.069846

#N/A

1.791191 0.39948

0.038256 0.047608

3.966837 0.00011

0.135693 #N/A

0.419165 #N/A

1.965461 0.558096 0.166138

4.8008 0.05522 0.059664

0.88111 0.121562 0.410746

#N/A #N/A 0.301384

#N/A #N/A 0.017575

0.00013 0.00011

0.021971 0.017984

1.3637 1.03687

46.38288 31.17394

#N/A #N/A

36.29923

0.03673

1.74478

0.069118

#N/A

56.22678

0.07843

4.98365

0.111534

#N/A

24.91316

0.03709

1.65289

0.090223

#N/A

1321.673 743.6589 646.0476 676.1323 675.7683

1.28005 0.05534 0.04979 0.05075 0.05343

70.3253 260.8661 253.531 260.9267 247.4274

0.073886 #N/A #N/A #N/A #N/A

#N/A #N/A #N/A #N/A #N/A

Parameter value FC

r H:C;Diesel ⁄ 2 kS;Diesel ⁄

Remarks: (i) Range of v is 6–75 km/h. (ii) FC = Fuel Combustion. (iii) r H:C;Diesel and r H:C;Diesel are ratio of hydrogen to carbon and that of oxygen to carbon of diesel fuel respectively. (iv) kS;Diesel is the sulphur content in diesel, which is equals to 0.00005 in HKSAR (Legislative Council of Hong Kong (2005)).

r O:C;Diesel ⁄ 0 0.00005

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

PM2.5

y = emission (Unit: g/km); x = speed (unit: km/h)

L. Li et al. / Transportation Research Part D 41 (2015) 330–347

347

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