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Minimizing the Health and Climate Impacts of Emissions from HeavyDuty Public Transportation Bus Fleets through Operational Optimization Brian Gouge,*,† Hadi Dowlatabadi,†,‡,§ and Francis J. Ries∥ †

Institute for Resources, Environment and Sustainability, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada ‡ Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States § Resources for the Future, Washington, DC 20036, United States ∥ Metro Vancouver, Burnaby, British Columbia, V5H 4G8, Canada S Supporting Information *

ABSTRACT: In contrast to capital control strategies (i.e., investments in new technology), the potential of operational control strategies (e.g., vehicle scheduling optimization) to reduce the health and climate impacts of the emissions from public transportation bus fleets has not been widely considered. This case study demonstrates that heterogeneity in the emission levels of different bus technologies and the exposure potential of bus routes can be exploited though optimization (e.g., how vehicles are assigned to routes) to minimize these impacts as well as operating costs. The magnitude of the benefits of the optimization depend on the specific transit system and region. Health impacts were found to be particularly sensitive to different vehicle assignments and ranged from worst to best case assignment by more than a factor of 2, suggesting there is significant potential to reduce health impacts. Trade-offs between climate, health, and cost objectives were also found. Transit agencies that do not consider these objectives in an integrated framework and, for example, optimize for costs and/or climate impacts alone, risk inadvertently increasing health impacts by as much as 49%. Cost−benefit analysis was used to evaluate trade-offs between objectives, but large uncertainties make identifying an optimal solution challenging.

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INTRODUCTION The environmental benefits of public transportation have been widely touted;1,2 however, the buses that make up transit fleets, typically powered by heavy-duty diesel or compressed natural gas (CNG) engines, emit pollutants that adversely impact both public health and the climate.1,3−7 While a large number of studies have evaluated the potential of technological and capital control strategies (e.g., aftertreatment devices) to reduce these impacts, surprisingly few have investigated how to minimize these impacts by incorporating them into the operational planning of public transportation systems, and more specifically, as objectives in the vehicle scheduling problem.8−11 In addition to this research gap, many previous studies suffer from one or more of the following limitations. First, they have typically analyzed public health and climate impacts independently and not explicitly considered how control strategies targeting one impact may affect another. Such approaches have been shown to lead to detrimental and unintended outcomes.12 To avoid these outcomes and identify win−win control strategies with cobenefits across multiple impact dimensions, integrated assessment (i.e., multiobjective) frameworks need to be adopted.13−15 Second, past studies have typically employed © 2013 American Chemical Society

regional scale analyses that focus on total emissions rather than exposure (i.e., the contact of pollutants and people in space and time). A number of studies have shown that regional scale analyses (i.e., analyses that focus on the relationship between total emissions, ambient pollutant concentrations, and health impacts) may underestimate exposure and health effects because they do not account for variability in the intraregional spatial and temporal distribution of pollutants and people and the relationships between them.5,16−19 Intraregional scale analyses make it possible to both address the problem of bias in regional scale analyses and evaluate how exposure and health impacts are affected by changes in the spatial distribution of emissions within a region, due, for example, to different vehicle scheduling strategies. Finally, of the studies that have specifically explored incorporating climate and health impacts as objectives in the vehicle scheduling problem,8,9 none have previously considered the impacts of emerging pollutants of Received: Revised: Accepted: Published: 3734

October 7, 2012 January 28, 2013 March 11, 2013 March 11, 2013 dx.doi.org/10.1021/es304079p | Environ. Sci. Technol. 2013, 47, 3734−3742

Environmental Science & Technology

Article

Table 1. Bus Categories, Operating Costs, Emission Factors, and Global Warming Commitment fleetc a

−1

−1

−1

−1

b

category

cost ($·km )

PM2.5 (g·km )

NOx (g·km )

GWC100 (gCO2e·km )

A

B

40DO 40DB2f 40DBg 40DA 40DH 60DB 60DA 60DH 40CG

0.889 0.656 0.594 0.625 0.587 1.042 1.017 0.821 0.600

0.662 0.212 0.109 0.0244 0.0125 0.196 0.0628 0.0125 0.0168

17 22 12.3 6.83 5.2 16.3 12.2 8.97 12.4

2516 1732 1546 1590 1190 2984 2850 1860 1635

95 294 54 193 1 76 10 26 43

0 0 170 170 170 37 37 37 170

description 40 40 40 40 40 60 60 60 40

ft ft ft ft ft ft ft ft ft

old (two-stroke) diesel OxCatb baseline diesel with OxCat baseline diesel with OxCat advanced diesel with DPFd hybrid diesel with DPF baseline diesel with OxCat advanced diesel with DPF hybrid diesel with DPF CNG with OxCat

a Operating costs include fuel, propulsion-related maintenance, battery replacement for hybrids, facility maintenance, and electricity costs associated with compressing CNG (2007 U.S. dollars). b100 year global warming commitment due to CO2, CH4, and PM2.5 (i.e., BC and OC). cNumber of buses. dOxidation catalyst. eDiesel particulate filter. f1995−2001 Detroit diesel series 50. g2000−2001 Cummins ISC.

240 electric trolley buses (not considered here because they produce no primary emissions) (Table 1). Emissions Model and Operating Costs. Distance-based emissions factors and operating costs were developed for nine bus categories (Table 1 and Table S1, Supporting Information). Bus categories were developed based on the bus size, the powertrain type, the emissions control technology, and the model year and associated emissions certification level (Table S2, Supporting Information). All emissions factors were based on the Central Business District (CBD) drive cycle and developed from emissions tests of actual buses from TransLink’s fleet21 as well as published studies.22,23 Operating costs were developed from studies by TransLink and Clark et al. (Table S4, Supporting Information).24,25 Two bus fleets were considered (Table 1). Fleet A was representative of TransLink’s fleet in 2009 and fleet B was a hypothetical fleet with more modern buses. Climate Impact Indicator. The global warming commitment (GWC) of the exhaust emissions resulting from the operation of the bus fleet over a period of one day (tCO2e·day−1) was used as the indicator of climate impact.26 The GWC due to the emissions from a bus traveling one kilometer (Table 1) was estimated as

concern such as black carbon (BC) or the trade-offs between conflicting objectives in detail.20 The goal of this study was to address the above identified research gaps and limitations and to evaluate the potential of operational (in contrast to capital) control strategies to reduce the public health and climate impacts of transit systems in an integrated framework. To do this, climate and health impact indicators as well as operating cost estimates were developed and incorporated as objectives in what is herein referred to as the vehicle assignment optimization problem. The vehicle assignment problem addresses the issue of how vehicles are assigned to routes and represents one dimension of the more general vehicle scheduling problem. This study specifically explores how heterogeneity in the emission levels of different bus technologies and the exposure potential of bus routes, quantified at the intraregional scale, can be exploited by vehicle assignment optimization to minimize impacts. It also explores the implications of applying social cost−benefit analysis to evaluate trade-offs between conflicting objectives.

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MATERIALS AND METHODS

This analysis is based on a real-world case study of the transit system in Vancouver, Canada. Distance-based emissions factors, fuel consumption, and fuel and maintenance costs were estimated for diesel and CNG buses. Climate impacts of both long-lived compounds including carbon dioxide (CO2) and methane (CH4) as well as short-lived compounds including black and organic carbon (OC), both constituents of particulate matter (PM), were quantified using their estimated global warming potential (GWP). The total intake of PM2.5 emissions, calculated using the estimated intake fraction of the bus routes, was used as the public health impact indicator. Total nitrogen oxides (NOx) emissions were also considered. The estimated health, climate, and operating costs and impacts were incorporated into a vehicle assignment optimization model, and scenarios were developed to explore the implication of different optimization objectives (e.g., minimizing climate impacts). Transit System. The South Coast British Columbia Transportation Authority, commonly known as TransLink, and its operating subsidiary Coast Mountain Bus Company (CMBC) operate a fleet of approximately 1300 buses on 150 routes throughout the Metro Vancouver area (Figure S6, Supporting Information). The fleet consists predominately of diesel buses but also includes approximately 50 CNG buses and

GWC100,b =

∑ EFb ,c ·GWP100,c c

(1)

where GWC is the global warming commitment of bus b over a 100 year time horizon (tCO2e·km−1); c are the climate forcing compounds CO2, CH4, BC, and OC; EF is the emission factor of bus category b and compound c (g·km−1); and GWP is the global warming potential for compound c over a 100 year time horizon. GWPs for both long- and short-lived, gaseous and particulate compounds were taken from the literature (Table S5, Supporting Information).15,27,28 Public Health Impact Indicator. The intake or mass of primary PM2.5 exhaust emissions inhaled by the population within 5000 m of the bus routes and resulting from the operation of the bus fleet over a period of 1 day was used as the measure of public health impact (g·day−1). Total primary emissions of PM2.5 and NOx as well as the premature mortality attributable to the intake of PM2.5 were also estimated and considered. To calculate intake, the intake fraction (iF) was estimated along each bus route. The intake fraction is a measure of exposure potential and estimates the proportion of pollutants emitted on a route that are inhaled by the population around 3735

dx.doi.org/10.1021/es304079p | Environ. Sci. Technol. 2013, 47, 3734−3742


Article

the route. Using an approach similar to that of Greco et al.,17 the average annual intake fraction was estimated for each route as ⎛C ⎞ iFr = ∑ Pz·⎜ z ⎟ ·Q ⎝ Ê ⎠

The vehicle assignment optimization problem was formulated as a binary programming problem: min /max

6

x ∈ {0, 1} (2)

z=1

k

r

(one physical bus per block) (6)

b

∑

xk ,b ≤ nb ∀ b , ∀ ts

(maximum number of buses)

k ∈ K ts

(7)

∑

xk ,b = 0

(restrict routes to specified bus lengths)

(k ,b) ∈ S

(8)

where Ψ is the objective function equal to the total intake of PM2.5 (g·day−1), the total GWC (tCO2e ·day−1), or the total emissions of compound c (g·day−1); b is the bus category; k is the block; r is the route; Υ is either the intake (I), GWC, or emission factor (EF) of bus category b and compound c on route r (g·km−1); x is the decision variable indicating if bus category b is assigned to block k; d is the total distance traveled on route r for block k; n is the total number of buses of category b in the fleet (Table 1); Kts is the set of blocks that are active at time ts; ts is the set of unique block start times; and S is the set of block (k) and bus category (b) pairs where the bus size and bus size associated with the block do not match. There were a total of 1073 blocks and 364 unique block start times. To reduce complexity, all buses were assumed to be dispatched from a single depot. In actuality, they are dispatched from seven depots. The vehicle assignment problem proposed here belongs to a class of optimization problems called generalized assignment problems which are NP-hard. It was solved using IBM ILOG CPLEX V12.4. In all cases, CPLEX was able to solve the problem to optimality (gap of 0.00%) in several seconds. Twelve scenarios (A−L) were developed to characterize the best and worst case solutions and the trade-offs between objectives for both bus fleets A and B (Table 2). In each scenario, a specific indicator (e.g., GWC) was minimized, and the percent change in the other indicators relative to the scenario in which the indicator was minimized (i.e., the best case) were estimated. The worst case scenarios were also estimated by maximizing each indicator in order to establish an upper bound. In cases were trade-offs between objectives occurred, cost−benefit analysis was explored as a method of identifying an optimal solution. Note that for presentation purposes, in some cases, the results have been expressed over a 1 year period by multiplying by 365.

(3)

I ·BMR·CR Q

b

(5)

∑ xk ,b = 1 ∀ k

where Ir,b is the intake of PM2.5 emission from a bus of category b on route r (g·km−1·day−1); iFr is the intake fraction of route r (dimensionless); and EFb is the PM2.5 emission factor of bus category b (g·km−1). The premature mortality attributable to the intake of PM2.5 was estimated as ΔM =

∑ ∑ ∑ xk ,b·Υr ,b ,c ·dr ,k]

s.t.

where iFr is the intake fraction for route r (dimensionless); Pz is the population within each zone z; C·Ê −1 is the average annual concentration to emissions ratio relating the concentration C in zone z to the unit on-route emission Ê (m−3); and Q is the population average breathing rate equal to 14.5 m3·day−1.29,30 The average annual concentration to emissions ratio (C·Ê −1) was estimated using the CALINE4 line-source dispersion model31 and one year of meteorological data in six concentric zones at distances ranging 0−50, 50−100, 100−200, 200−500, 500−1000, and 1000−5000 m from the routes.17 The population in each zone (Pz) was determined using ESRI ArcGIS 9.332 and block-level census data from the 2006 Census of Canada.33 The total intake of PM2.5 emissions resulting from a bus traveling 1 km on a route was estimated as Ir ,b = iFr ·EFb

[Ψc =

(4) −1

where ΔM is the change in mortality (deaths·year ); I is the intake of PM2.5 (g·day−1); Q is the population average breathing rate equal to 14.5 m3·day−1; BMR is the annual background all-cause mortality rate equal to 730 deaths per 100 000 people (deaths·year−1);34 and CR is the concentration response function equal to 1.0% increase in all-cause mortality per microgram per cubic meter increase in the annual average PM2.5 concentration.35,36 Vehicle Scheduling and Assignment Optimization. The goal of vehicle scheduling optimization is to find the series of trips made by a fleet of buses that minimizes an objective function subject to a set of spatial (e.g., geographical layout of the routes), temporal (e.g., timetable), and operational constraints determined in the planning process.11 The optimization solutions typically consist of a set of blocks with start and end times and locations that define the series of trips made by a single physical bus. Trips occur over a single route, but blocks may consist of trips on different routes. In a traditional vehicle scheduling problem, the objective is to minimize the number of buses and operating inefficiencies (typically defined as the nonrevenue service time or total distance traveled).11 A solution to the problem defines the value of these traditional objectives. However, within a solution there is some flexibility in terms of which bus category is assigned to which block and thus route. The effects of this flexibility on climate, health, and operating costs and impacts were explored in this study using vehicle assignment optimization. TransLink’s weekday vehicle scheduling solution for the fall of 2009 was used as the basis of this analysis, but actual bus assignments were not considered.

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RESULTS AND DISCUSSION Vehicle assignment optimization had a significant effect on exposure to PM2.5 emissions and health impacts (Table 2). For the worst case vehicle assignment solution, PM2.5 intake was more than double (107−123%) that of the best case solution. Vehicle assignments had a similar effect on total PM2.5 emissions (96−109%) and a smaller but still significant effect on NOx emissions (35−28%). In relative terms, the effect on operating costs, fuel consumption, and climate impacts (i.e., GWC) was much smaller, and the difference between the best 3736



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Table 2. Vehicle Assignment Optimization Results percent increase relative to the best case (%) [absolute value per year] scenario A B C D E F

G H I J K L

fleet

objectivea b

d

A

B

e

cost fuel GWC (climate) NOx PM2.5 PM2.5 intake (health) worst case costb fuel GWC (climate) NOx PM2.5 PMI2.5 intake (health) worst case

costb

fuel

GWC (climate)

c

1.0 best [48 ML]

c

c

c

3.0

4.1 1.6 2.3 12

best [127 ktCO2e] 3.6

best [$49M]

c

1.1 8.8 best [$45M]

c

c

1.5 12 c

c

2.2 best [42 ML]

c

c

best [110 ktCO2e]

c

c

c

c

4.8 5.8 15

c

1.0 2.9

c

2.3 9.9

NOx

PM2.5

PM2.5 intake (health)

5.7 6.9 4.7 best [930 t] 4.5 9.6 35

3.0 7.9 3.2 30 best [8.6 t] 13 109

14 19 14 42 13 best [153 g] 123

9.9 4.3 4.3 best [599 t] 4.5 6.1 28

41 43 43 26 best [2.2 t] 10 96

47 49 49 34 10 best [40 g] 107

a

For each Scenario (A−L), the listed objective was minimized. To calculate the worst case, the objectives were maximized. bOperating costs. cLess than 1%. dRepresentative of the transit agency’s bus fleet in 2009. eHypothetical more modern future bus fleet.

Health. PM, NOx, carbon monoxide (CO), hydrocarbons (HC), and air toxics as well as secondary pollutants including ground level ozone are all believed to play roles in causing adverse human health effects.5,40,41 In the context of heavy-duty vehicles, PM and NOx are typically the primary concerns. PM in particular has received significant attention.3,41−44 Consequentially, it was the principal focus here, as in previous studies.35,45,46 Public health impacts (i.e., intake of PM2.5 emissions) were quantified on an intraregional scale in order to account for the effects on exposure of changes in the spatial distribution of PM2.5 emissions due to different vehicle assignment solutions. This was accomplished by estimating the PM2.5 intake fraction for each bus route (eq 2). The intake fractions ranged from 5.98 to 41.4 g inhaled per million grams emitted and had a mean value of 19.2 per million (Figure S5a, Supporting Information). These values are consistent with those reported by Greco et al. for road segments in Boston, MA.17 Given the assumptions made to estimate the intake fraction in this study, the variability in the intake fractions was solely attributable to variability in the population density. Although the intake fraction provides a measure of exposure potential, it does not account for the frequency of bus service on a route and thus provides an incomplete characterization of the potential for health impacts along a route. To address this, the distance-weighted PM2.5 intake fractions (i.e., distance traveled on the route per day × intake fraction) were calculated (Figure S5c, Supporting Information). The distance-weighted intake fractions exhibited a significantly more skewed distribution than the intake fractions with a small number of very high health impact potential routes. These routes were primarily located in the more densely populated City of Vancouver (Figure S6, Supporting Information) and when minimizing health impacts would be assigned the lowest emitting buses. Scenarios E, F, K, and L show that there were differences between optimization solutions that minimized intake or exposure to PM2.5 and solutions that minimized total PM2.5 emissions (Table 2). The counterintuitive finding that exposure to PM2.5 emissions was minimized by increasing total PM2.5 emissions on the order of 10% is a direct result of differences in

and worst case solutions ranged from 3% to 15%. However, in absolute terms, the effects may be significant to transit agencies. For example, in this case study, a 1% annual increase in operating cost would translate into approximately $0.5 million. It is unlikely that transit agencies operate their fleets at the extreme, worst case (actual vehicle assignments were not considered in the study), so the real-world benefits would likely be smaller than expressed by the relative difference between the best and worst case solutions. However, these scenarios provide a useful characterization of the potential benefits that may be derived from vehicle assignment optimization in reducing health, climate, and operating costs and impacts. Optimization Objectives. The climate and health impacts of bus emissions were the primary focus of this study. Operating costs were also estimated but may vary between agencies. Labour costs were assumed to be unaffected by changes in bus assignments and were therefore not considered. Further, given the operational scope of this study, capital financing costs were assumed to be sunk costs and were therefore also not considered. Climate. CO2, CH4, and nitrous oxide have long been identified as greenhouse gases that contribute to global climate change.28 More recently, the climate forcing role of short-lived compounds such as the PM constituents BC, OC, and sulfate (SO4) has received wider attention.20,28,37−39 Of these compounds, only CO2, CH4, and BC were found to be significant contributors and therefore were included in the analysis (Table S6, Supporting Information). All other species combined accounted for less than 0.5% of the total GWC on a per kilometer basis. Further, BC accounted for less than 3% of the total GWC for all buses except the older two-stroke diesel buses in the 40DO category. However, if a shorter time horizon was used to estimate the GWP (e.g., 20 instead of 100 years), BC would make up a more significant fraction of the total GWC. For all bus categories, CO2 was responsible for a minimum of 90% of the total GWC on a per kilometer basis. Thus, the focus of previous studies on the climate impacts of CO2 and CH4 and the omission of other climate forcing compounds such as BC would appear to be warranted for modern transit buses, assuming a 100 year time horizon. 3737



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Figure 1. Scatter plots of the total distance traveled on a block and the intake fraction of the block. Each point represents a specific block and is color coded by bus category. The scatter plots show the bus-block assignments for fleet A and the scenarios that minimized (a) climate impacts, (b) total emissions of PM2.5, and (c) health impacts.

assignments had less of an effect on climate impacts and operating costs (Tables 1 and 2). Note that this also applies to capital investments (i.e., adopting new technologies would have a more significant effect on health compared to climate impacts). For example, if the transit agency upgraded its current fleet (fleet A) to the more modern fleet B, health impacts would be decreased by 71%, but climate impacts would only be decreased by 13% (Table 2). The total distance traveled by each bus category can vary. A transit agency must have enough buses to meet the schedule at peak demand. During nonpeak periods, fewer buses are required and operated. Which bus categories serve these periods impacts the distance they travel. Thus, the difference between peak and off-peak periods influences the distance traveled by the various bus categories. The relationship between the route intake fractions and the total distances traveled on the routes has important implications for the differences between the scenarios in which total emissions and exposure (i.e., intake) are minimized. If the ranking of the routes based on the total distance and the intake fraction were the same (i.e., positively correlated), there would be no difference in the assignment solutions for the two scenarios, but the relative change in exposure would be greater than the relative change in the total emissions as a result of the positive correlation. If, on the other hand, the rankings were the opposite (i.e., negatively correlated), the assignment solutions would differ, and there would be a trade-off between the two scenarios and thus regional versus intraregional scale approaches. In this study, distances and intake fractions were weakly negatively correlated (r = −0.19), which resulted in the trade-off between scenarios that minimized total PM 2.5 emissions and those that minimized PM2.5 intake (Figure 1 and Table 2). Multiobjective Optimization. The results in Table 2 show that there were trade-offs between minimizing operating costs, climate impacts, and health impacts. For example, in scenario C, minimizing climate impacts (GWC) resulted in a 14% increase in health impacts (PM2.5 intake), and in scenario I, it resulted in a 49% increase. Similarly, in scenarios A and G, minimizing operating costs resulted in 14% and 47% increases in health impacts, respectively. Thus, transit agencies that optimize their operations based on operating costs and/or climate impacts alone, a potentially common practice, may unintentionally increase health impacts, by as much as 49% in the case of fleet B. This finding highlights the need to consider

the intake fractions and the distance traveled between routes. It demonstrates that minimizing total emissions does not guarantee that exposure and health impacts are minimized. These results also quantitatively show the difference between regional and intraregional scale approaches to estimating exposure and corroborate previous findings that show regional scale approaches lead to negatively biased estimates.5,16,47 Optimization. Visualizations of the vehicle assignment optimization solutions are shown in Figure 1. These figures show graphically how different optimization objectives and heterogeneity in the emissions factors, distance traveled, and intake fractions impact the assignment of bus categories to blocks and thus routes. For example, a comparison of Figure 1a and b shows that the blocks served by 40CG and 40DB buses were swapped in order to meet the two different objectives (i.e., climate and health). The distinct bands and clustering show how the blocks are prioritized with respect to the objectives. The shift from vertical bands (Figure 1a,b) to angled bands in the case of optimizing for PM 2.5 intake (Figure 1c) demonstrates graphically how the intake fraction and exposure impacts the optimization results. Operational optimization strategies fundamentally rely on heterogeneity (Figure 1). In the case of vehicle scheduling and assignment optimization, variability must exist in the emission factors associated with the bus categories and either the total distance all buses in a category travel or the intake fraction (i.e., exposure potential) of the bus routes for any change in impacts or costs to be possible. For example, if a bus fleet was composed of a single bus category, impacts and costs would be constant regardless of changes in vehicle assignments. Thus, the optimization results and the magnitude of the potential benefits are dependent on the characteristics of a specific transit system and in the case of health impacts the population density of a region (Figure S9, Supporting Information). Distinct bus categories arise from adoption of new bus technologies by transit agencies. These technologies have primarily reduced pollutants that impact health (as opposed to those that impact climate) and thus resulted in significant variability of emissions associated with health impacts within fleets. For example, in this study, PM2.5 emission factors were found to vary by over an order of magnitude between bus categories. This heterogeneity was responsible for the significant effect of vehicle assignment on health impacts (Table 2). Variability in the emission factors of other pollutants such as CO2 were significantly smaller, and as a result, vehicle 3738



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Figure 2. Relationship between health and operating and climate costs for (a) fleet A and (b) Fleet B. The change in the minimum health impact is expressed as a function of the sum of the operating and climate costs assuming a value of $25 per tCO2e. Actual vehicle assignment solutions occur anywhere on or above the curve. Bottom and left axes show the change in absolute value, and top and right axes show the corresponding percent change.

exponentially as a result of the highly skewed distance-weighted intake fraction distribution (Figure S5c, Supporting Information). Vehicle assignment optimization would result in cobenefits (i.e., health and climate impacts and operating costs would decrease) if a transit agency’s actual vehicle assignment solution were above the curve or on the curve and to the right of the asterisk. Note that solutions do not exist below the curve. Figure S12 (Supporting Information) and Figure 2 provide a more complete picture of the results in Table 2, which may be deceiving given the nonlinear relationships shown in these figures. The optimal, minimum social cost solution must lie at some point on the Pareto frontier. The circles in Figure 2 indicate the optimal social cost solutions assuming a value of a statistical life (VSL) of $7.7 million 2007 U.S. dollars (2007 USD), which corresponds to the central estimate recently used by the United States Environmental Protection Agency (USEPA) and other researchers.36 If either the VSL or mortality estimates increased, the optimal solution would shift right along the curve, approaching the minimum health impact solution (asterisk). If the value of the climate impacts increased, the shape of the curve would approach the shape in Figure S12 (Supporting Information), and the optimal solution would shift left along the curve, approaching the minimum climate impact solution (cross). Note however, that at $25 per tCO2e, the climate costs represent less than 7% of the operating cost (Table 1). Therefore, the magnitude or value of the climate impacts would have to increase substantially before climate impacts would significantly affect the optimal solution (Figures S13 and S14, Supporting Information). Thus, the primary trade-off in vehicle assignment and scheduling optimization is likely between health impacts and operating costs. Operating, health, and climate impacts made up 71%, 24%, and 5%, respectively, of the total social cost ($71 million·year−1) of the optimal solution for fleet A and 87%, 8%, and 5%, respectively, of the total social cost ($53 million·year−1) for fleet B. Although the operating costs dominate the total social cost, it is the rate of change of the costs with respect to one another that influences the optimization results. Thus, the exponential increase in health impacts as operating and climate costs approached their minimum value meant that the optimal

multiple objectives. Trade-offs between operating costs and climate impacts were much smaller because fuel consumption significantly influences both of these objectives. With respect to objectives involving total emissions or costs, trade-offs between objectives (e.g., minimizing GWC and PM2.5) only occur if there are trade-offs in the emission factors or costs between bus categories (i.e., one bus category has a higher GWC emission factor than another bus category but a lower PM2.5 emission factor). If trade-offs between bus categories do not exist, any objective can be used to find the optimal assignment solution, and optimization would always result in cobenefits. However, this is not the case when considering exposure. As previously discussed, the relationship between the total distances traveled on a route and the intake fraction also plays a role in determining whether there are trade-offs. Trade-Offs and Optimal Solutions. If trade-offs exist between objectives, the objectives must be expressed in a common measure in order to identify an optimal vehicle assignment solution. Social cost−benefit analysis, in which costs and benefits are monetized, is one possible approach that has been widely used in the assessment of impacts of vehicle emissions.36,46,48,49 As a result, its implications were explored here. Figure S12 (Supporting Information) and Figure 2 show the change in the minimum health impact (PM2.5 intake) as a function of the change in the climate impact (GWC) and the sum of the operating and climate costs, respectively. Climate impacts were valued at $25 per tCO2e based on the offset price set by the Pacific Carbon Trust in the Province of British Columbia.50 Because operating costs and climate impacts are highly correlated, the shape and features of the curves in Figure S12 (Supporting Information) and Figure 2 are nearly identical. Note however, that as there are three objectives in Figure 2, the curves are in reality surfaces. Operating and climate costs were combined to simplify the presentation. Pareto optimal solutions, where there are trade-offs between health impacts and climate impacts and operating costs, occur on the segment of the curves between the cross and asterisk (i.e., the Pareto frontier). For both fleets, trade-offs only occurred as climate impacts and operating costs approached their minimum value, at which point health impacts increased 3739



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quantitatively evaluate the implications and costs of how, for example, buses are actually allocated to depots. Implications. Evolution in bus technologies, particularly with respect to controlling pollutants that impact health, such as PM, and capital investments by transit agencies in these technologies have resulted in the potential for large differences in emission factors within transit bus fleets. Operational optimization strategies such as vehicle assignment and scheduling optimization can exploit this heterogeneity and minimize the climate and health impacts as well as operating costs of transit systems with minimal capital expenditure. It is important to emphasize that capital and operational control strategies are complementary and that transit agencies should pursue both types of control strategies. Operational control strategies ultimately offer transit agencies a way to maximize the benefits of their capital investments. The magnitude of the benefits of operational optimization are dependent on heterogeneity in the emission factors of the bus fleet, as well as characteristics of the transit system and the region. The greater the heterogeneity, the greater the potential benefits. For example, by considering exposure at the intraregional scale, the optimization was able to exploit variability in the exposure potential between bus routes arising from variability in the population density and achieve greater reductions in health impacts. An important secondary finding of this study was that regional scale approaches are biased and underestimate exposure by 10−13% compared to intraregional scale approaches (Table 2). In general, the benefits of operational optimization would be greatest for large heterogeneous bus fleets that operate in regions where there is significant variably in the population density. This study showed that, in relative terms, vehicle assignment had a much greater effect on health impacts than either climate impacts or operating costs. Thus, there is a particular need to reduce the uncertainties associated with estimating and valuing health impacts. Although it is difficult to identify an optimal solution with certainty, unless there are significant biases in the model or the relative value of the impacts, it is unlikely that the optimization would lead to grossly nonoptimal solutions. Finally, a GIS-based tool was developed to automate the intake fraction calculation, which is likely the most complex step. This tool reduces the barriers to implementing the operational optimization approaches discussed in this study.

social cost solutions did not correspond with the minimum operating cost solutions. Uncertainties. With respect to single objectives, systematic uncertainties (i.e., biases), rather than the magnitude of the uncertainties, are likely to affect the optimization and could potentially lead to nonoptimal vehicle assignments that increase impacts. For example, the emissions model used in this study is not sensitive to road grade. Thus, emissions and the resulting impacts on uphill routes were likely systematically underestimated, which could have resulted in a nonoptimal vehicle assignment. The magnitude of the uncertainties are more significant when considering multiple objectives. While there are numerous sources of uncertainty, the dominant sources are likely those associated with the estimation of health and climate damages and their valuations (e.g., monetization). For example, estimates range from $0.95−21.4 million (2007 USD) for VSL, $11−100 (2007 USD· tCO2e−1) for the cost of carbon, and 0.3−2.0% increase in all-cause mortality per microgram per cubic meter for CR.35,51−53 To bound the possible effects of this uncertainty as well as the impacts of different methods of evaluating trade-offs, the Pareto frontiers were estimated. They show, for example, that, in relative terms, the optimal solution for fleet B is more sensitive to how trade-offs are made than for fleet A (Figure 2). Further, a sensitivity analysis using the ranges listed above showed that the optimal solutions were most sensitive to variables (VSL and CR) used to estimate health costs (Figures S13 and S14, Supporting Information). Optimal solutions were tightly clustered when carbon costs were varied. The optimal solution significantly deviated from the minimum health impact solution only when health impacts were valued at their extreme lowest valuations due to the exponential shape of the Pareto frontiers. Thus, at least with respect to health impacts, the optimization results are likely significant despite the large uncertainties. Nevertheless, it is difficult to fully understand the effect of uncertainty on the results without out a formal analysis, which was beyond the scope of this study but warrants future consideration. Assumptions and Limitations. The vehicle scheduling problem has not traditionally addressed the problem of how vehicles are assigned to routes, but methods have been developed that deal with this issue.54,55 Although these were not explicitly considered in this study due to the complexity of specifying and solving such problems,54 the vehicle assignment problem proposed in this study provides a lower bound on the potential benefits of solving the more complex vehicle scheduling problem (i.e., it understates the potential benefits). The vehicle scheduling problem should be able to exploit additional flexibility in the way routes are linked to form blocks. While the vehicle assignment problem proposed here is not appropriate for initial operational planning because it requires an existing scheduling solution (i.e., blocks) as an input, it can be applied to any bus fleet already in operation. All buses were assumed to originate from a single depot; however, in actuality, they originate from multiple depots. This simplification means that some vehicle assignment solutions may be inconsistent with the way in which the transit agency distributes buses across its depots and could violate constraints on the total number of buses at a specific depot or result in additional deadhead (nonrevenue service) trips. There may also be other operational constraints (e.g., requiring accessible buses on specific routes) that were not captured in this analysis. Thus, the vehicle assignment optimization problem formulated here represents the ideal case and provides a baseline from which to

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ASSOCIATED CONTENT

S Supporting Information *

Detailed description of methods; histograms of the intake fractions and distance-weighted intake fractions; map of the bus routes; influence diagram of the factors affecting the optimization; sensitivity analysis; detailed discussion of the assumptions and limitations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a scholarship from the Natural Sciences and Engineering Research Council of Canada, a 3740



Article

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Doctoral Fellowship from the University of British Columbia, and grants from the U.S. National Science Foundation Centre for Climate and Energy Decision Making at Carnegie Mellon University (SES-0949710), Auto21, and TransLink. We are especially grateful to TransLink and Coast Mountain Bus Company.

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