Optimal Deployment of Emissions Reduction Technologies for Construction Equipment
ABSTRACT The objective of this research was to develop a multiob- jective optimization model to deploy emissions reduction technologies for nonroad construction equipment to re- duce emissions in a cost-effective and optimal manner. Given a fleet of construction equipment emitting differ- ent pollutants in the nonattainment (NA) and near -nonattainment (NNA) counties of a state and a set of emissions reduction technologies available for installa- tion on equipment to control pollution/emissions, the model assists in determining the mix of technologies to be deployed so that maximum emissions reduction and fuel savings are achieved within a given budget. Three technologies considered for emissions reduction were des- ignated as X, Y, and Z to keep the model formulation general so that it can be applied for any other set of technologies. Two alternative methods of deploying these technologies on a fleet of equipment were investigated with the methods differing in the technology deployment preference in the NA and NNA counties. The model hav- ing a weighted objective function containing emissions reduction benefits and fuel-saving benefits was pro- grammed with C�� and ILOG-CPLEX. For demonstra- tion purposes, the model was applied for a selected con- struction equipment fleet owned by the Texas Department of
Transportation, located in NA and NNA counties of Texas, assuming the three emissions reduction technologies X, Y, and Z to represent, respectively, hydrogen enrichment, selective catalytic reduction, and fuel additive technolo- gies. Model solutions were obtained for varying budget amounts to test the sensitivity of emissions reductions and fuel-savings benefits with increasing the budget. Dif- ferent mixes of technologies producing maximum oxides of nitrogen (NOx) reductions and total combined benefits (emissions reductions plus fuel savings) were indicated at different budget ranges. The initial steep portion of the plots for NOx reductions and total combined benefits against budgets for different combinations of emissions reduction technologies indicated a high benefit-cost ratio at lower budget amounts. The rate of NOx reductions and the increase of combined benefits decreased with increas- ing the budget, and with the budget exceeding certain limits neither further NOx reductions nor increased com- bined benefits were observed. Finally, the Pareto front obtained would enable the decision-maker to achieve a noninferior optimal combination of total NOx reductions and fuel-savings benefits for a given budget.
INTRODUCTION Pollutant emissions are a serious concern for human health and for the environment1 because they can cause a range of problems to the human body (including death) and damage to trees, crops, plants, lakes, and animals. The U.S. Environmental Protection Agency (EPA) catego- rized air pollution sources as stationary and mobile. Sta- tionary sources include facilities such as oil refineries, chemical processing facilities, power plants, and other manufacturing facilities. There are federal and state air pollution control requirements for most stationary sources.2 Mobile sources are divided into two groups: on- road and nonroad. According to EPA, on-road sources are vehicles used on roads for movement of passengers or freight. They include light-duty vehicles, light-duty
IMPLICATIONS This paper describes a model that was developed to help decision-makers/fleet managers deploy emissions reduc- tion technologies to maximize the benefit of emissions re- ductions and fuel savings from their construction equip- ment fleet. The model is based on a cost-effectiveness analysis. The model was demonstrated with three different emissions reduction technologies having different opera- tional and performance characteristics. The model struc- ture is quite flexible and thus can be adapted and applied to any type of emissions reduction technologies and can be implemented on on-road and nonroad sources.
TECHNICAL PAPER ISSN:1047-3289 J. Air & Waste Manage. Assoc. 61:611–630 DOI:10.3155/1047-3289.61.6.611 Copyright 2011 Air & Waste Management Association
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trucks, heavy-duty vehicles, medium-duty passenger ve- hicles, and motorcycles. Nonroad sources consist of en- gines, aircraft, marine vessels, locomotives, and equip- ment used for construction, agriculture, transportation, and recreational purposes.3
On-road and nonroad diesel engines are responsible for emitting harmful pollutants, such as nitrogen oxides (NOx) and particulate matter (PM). On the basis of EPA’s 1999 report regarding national NOx emissions, on-road and nonroad sources contributed 34 and 22% of the na- tion’s total NOx emissions, respectively. Among the non- road sources, diesel equipment emitted 49% of NOx. Fine particulate matter (PM2.5) emissions for on-road and non- road sources were 10 and 18% of the nation’s total PM2.5 emissions, respectively, and among the nonroad sources, diesel equipment contributed 57% of PM2.5.3 These facts indicate that NOx and PM2.5 emissions from the nonroad sector, especially diesel equipment, are very significant, causing air pollution and health-related problems.4
Diesel exhaust is considered a probable human carcinogen. According to EPA, emissions from nonroad sources will continue to increase and contribute large amounts of PM and NOx. EPA’s data from 2005 indicated that nonroad engines contributed approximately 66% of the nation’s PM2.5 from all mobile sources. These non- road engine emissions affected approximately 88 million Americans living in areas violating PM2.5 air quality stan- dards. Similarly, NOx and volatile organic compound (VOC) emissions from nonroad engines were approxi- mately 36 and 37%, respectively, from all mobile sources. These two pollutants affected approximately 159 million Americans living in areas exceeding EPA’s 8-hr ozone standard.5
EPA’s 2008 National Emissions Inventory (NEI) data show that the total national NOx emissions from on-road and nonroad sources were 4,675,896 and 1,884,943 t, respectively. The same NEI data also indicate that the nonroad sources emitted approximately 29% of the total NOx emissions from the mobile sources. The share of diesel equipment was approximately 74% of NOx among the nonroad sources. Similarly, the total PM2.5 emissions from the on-road and nonroad sources were 269,454 and 116,752 t, respectively. The nonroad sources contributed approximately 66% of the total PM2.5 emissions from the mobile sources, and among the nonroad sources diesel equipment contributed approximately 66% of PM2.5 emissions.6
Construction equipment is a sector of nonroad sources. The construction industry uses more than 2 mil- lion pieces of nonroad diesel construction equipment. Most of the equipment has a long operational life—more than 25–30 yr. A report from the Clean Air Act Advisory Committee indicates that construction equipment con- tributed 32% of all mobile-source NOx emissions and 37% of PM emissions. Nonroad equipment, having less strin- gent emissions standards, emits more pollution than heavy-duty highway vehicles.7 Although stringent emis- sions standards were established for new nonroad equip- ment in 2008, most of the nonroad diesel equipment in use before 2008 will operate for many more years before retirement. EPA realized the issue with the construction equipment fleet and considered the emissions reductions
from the construction equipment fleet as an important component of an emissions control strategy.8
Various emissions reduction technologies are used to control emissions from on-road and off-road equipment in the United States. Reduced emissions is a benefit to society through improved health and to public agencies through reaching conformity, compliance, and attain- ment. However, purchasing these emissions reduction technologies is a cost to the concerned agency. Thus, it is essential for an agency to utilize their budget to install the emissions reduction technologies in a cost-effective and optimal manner, and no model has yet been developed for this purpose.
Therefore, the purpose of this study was to develop a multiobjective optimization model for optimal deploy- ment of emissions control technologies to maximize the benefit from emissions reductions and fuel savings from nonroad construction equipment located in nonattain- ment (NA) and near-nonattainment (NNA) counties. NA counties are those that failed to meet federal standards for ambient air quality, and the NNA counties are those that are at risk of violating standards although these areas currently meet federal standards.9 The model will aid the decision-maker or fleet manager to quickly decide how to choose the most appropriate emission reduction technol- ogy to be deployed and maximize the overall benefit.
LITERATURE REVIEW In this section, emissions estimation methodologies based on EPA’s guidelines and procedures will be discussed. Dif- ferent emissions reduction strategies such as aftertreat- ment devices, engine technologies, and fuel technolo- gies will be briefly presented. At the end of this section, several studies incorporating optimal allocation and configuration will be discussed.
Emissions Estimation Methodology EPA developed the NONROAD model for estimating pol- lutant emissions such as carbon dioxide (CO2), carbon monoxide (CO), hydrocarbon, NOx, and PM from com- pression-ignition engines. For calculating emissions from construction equipment fleets, information on the zero- hour steady-state emissions factors (EFss), transient adjust- ment factors (TAF), and deterioration factors (DF) are required. After obtaining the values for EFss, TAF, and DF, the final emissions factor (EFadj in g/hp-hr) for each pol- lutant can be calculated. The construction equipment emissions are then calculated from the adjusted emissions factor with the information on horsepower and usage hours using eq 1.10
Emissions E�g� � EFadj � horsepower � usage hours (1)
Abolhasani et al.11 compared the average emissions rates estimated from portable emissions measurement system (PEMS) data to estimates inferred from the NONROAD model. They developed and demonstrated a study design for deployment of a PEMS unit for excavators. They found that the PEMS-based emissions factors were similar in magnitude and were approximately comparable to those
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from the NONROAD model. They demonstrated the im- portance of considering intercycle variability in real- world in-use emissions to develop more accurate emis- sions inventories. It is possible to improve nonroad emissions factors and inventory models by considering such factors as intervehicle and intercycle variability.
Emissions Reduction Options Retrofit, rebuild, replace, and repower are some strategies to reduce emissions from mobile sources. “Retrofit” means installing an emissions control device on the equipment, “rebuilding” is rebuilding some core engine components of the equipment, “repowering” is replacing the older diesel engines with a newer engine, and “replac- ing” is replacing the entire older equipment or vehicle.12 The Manufacturers of Emissions Controls Association (MECA),13 Hansen,14 EPA,15 the California Air Resources Board,16 Genesis Engineering, Inc., and Levelton Engi- neering, Ltd.,17 and Lee et al.18 provide descriptions of some emissions reduction options that are briefly pre- sented in Table 1. The emissions reduction options are divided into three categories: (1) exhaust gas aftertreat- ment technologies, (2) engine technologies, and (3) fuel technologies according to Hansen14 and Genesis Engi- neering, Inc., and Levelton Engineering, Ltd.17
To formulate effective and cost-efficient emissions control strategies, it is essential to have a better under- standing of the overall effect of emissions control strate- gies on chemically interrelated important atmospheric pollutants. Luecken and Cimorelli19 used an air quality model to observe the potential effect of three emissions reductions on concentrations of ozone, PM2.5, and four important hazardous air pollutants (e.g., formaldehyde, acetaldehyde, acrolein, and benzene). Their simulations indicated the difficulty in assessing the response of toxic air pollutants to emissions reductions aimed at decreasing criteria pollutants such as ozone and PM2.5. This type of research can help air quality managers avoid strategies that may improve one pollutant but degrade air quality by increasing other pollutants.
Studies Involving Optimal Allocation and Configuration
The studies described in this section involved multiobjec- tive, mixed-integer programming, linear programming, integer programming (IP), and mixed-integer nonlinear programming. Chang and Wang20 developed and applied a multiobjective mixed-integer programming model for resolving the potential conflict between environmental
Table 1. A brief description of several emissions reduction options.
Category Example Description
Exhaust gas aftertreatment technologies
DOC Can reduce PM emissions, but the total NOx emissions remain unchanged for DOC.
Diesel particulate filter Physically traps diesel particulates and prevents their release into the atmosphere and can reduce PM emissions.
Selective catalytic reduction Capable of reducing NOx, PM, and HC emissions. Lean NOx catalysts Capable of reducing NOx emissions.
Engine technologies Engine repower and rebuild Provides NOx and PM reduction benefits. Exhaust gas recirculation Involves recirculation of a portion an engines’ exhaust
gas into its combustion chambers. Reduces NOx emissions, but increases PM, HC, and CO emissions and causes a fuel economy penalty.
Crankcase emissions control Capable of reducing PM emissions. Fuel technologies Natural gas Reduces emissions and provides a potential operating
cost savings. Biodiesel Derived from renewable sources such as vegetable
oil, animal fat, and cooking oil. Emits more NOx emissions than off-road diesel engines. Compatible for use with high-efficiency catalytic emissions– reduction technology.
Hydrogen Has low energy density in the gaseous form. Hence, if less expensive and liquefied hydrogen become readily available, then it becomes practical for use in the nonroad equipment sector.
Fuel additive Can reduce engine emissions and/or improve fuel economy. Some manufacturers claim that their products can reduce NOx, HC, PM, and/or CO emissions and can decrease fuel consumption. Some of the products might increase one or more pollutant emissions while reducing other pollutant emissions and increasing fuel efficiency.
Hydrogen enrichment HE systems create a better flame front in the engine that helps reduce emissions. Can reduce NOx and CO emissions and decrease fuel consumption.
Notes: DOC � diesel oxidation catalysts.
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and economic goals and for evaluating sustainable strat- egies for waste management in a metropolitan region. They considered four objectives: economics, noise con- trol, air pollution control, and traffic congestion limita- tions. The constraint set consisted of mass balance, capacity limitations, operation, site availability, traffic congestion, fi- nancial, and related environmental quality constraints. They performed a case study in the city of Kaohsiung in Taiwan.
Nema and Gupta21 formulated a multiobjective IP model to obtain the optimal configuration of a hazardous waste management system for transportation, treatment, and disposal of hazardous waste at a minimum cost and imposing minimum risk to the environment. The objec- tives addressed were minimization of cost, minimization of risk, and minimization of a composite objective func- tion consisting of cost and risk. The constraints consisted of mass balance of waste, allowable capacities for treat- ment and disposal technologies, and constraints related to waste-waste and waste-technology compatibility. An illustrative case example was performed to demonstrate the model’s usefulness.
Eshwar and Kumar22 used linear programming with fuzzy coefficients for optimal deployment of construction equipment. The objective was to identify the exact amount of equipment to be bought or rented to complete the project in the targeted period. The required minimum number of each type of equipment, the cost and the rent of equipment, the amount of equipment that could be hired, and the duration of service were considered as constraints. The model was able to optimally deploy equipment and was capable of successfully handling the uncertainty.
Swersey and Thakur23 developed an IP model for lo- cating vehicle emissions testing stations. The constraints used were maximum travel distance from each town to its nearest station, average waiting time at the station, max- imum hours of operations, and maximum number of lanes at each station. The station configuration that was in use had more stations than IP solutions. The IP model was able to reduce the estimated cost of the objective function by at least $3 million.
Mastsukura et al.24 proposed a mixed-integer model to minimize CO2 emissions through determining the op- timal set of ship routes and fleet of ships. Ship capacity and maximum transportation time were considered as constraints in the model. A case study was performed at the Kobe port of Japan.
Sirikitputtisak et al.25 developed a mixed-integer non- linear programming model for a multiperiod optimal en- ergy planning program. The objective function included the minimization of overall electricity costs and meeting the projected electricity demand over a span of 14 yr. Construction time, fluctuation of fuel prices, and CO2 emissions reduction target were included in the con- straints set. The program that was developed can be ex- tended to other states, provinces, or even countries.
MODEL FORMULATION Figure 1 shows a flowchart of the overall approach that involves several steps ranging from development of the model to proposing a deployment plan of emissions con- trol technologies. This model, which incorporates net
present worth of benefits and costs, is an improved ver- sion of the model formulated by Bari.26 The process be- gins with conceptualizing the model through incorporat- ing the objectives, constrains, and required data. The subsequent steps are testing and refinement of the model. The final step is the output of the model that will provide a deployment plan prescribing a mix of emissions reduc- tion technologies for deployment.
The objective of this optimization model is to maxi- mize the emissions reduction and fuel savings for a given nonroad construction equipment fleet. The constraint set consists of relevant economic, operational, and technical constraints. Table 2 summarizes the definition of the ma- jor variables used in the model. The set C is defined as the set containing the NA and NNA counties, indexed by c. The set nc is the total number of counties in consider- ation. The set E is the set of different categories of con- struction equipment indexed by e, and the set ne is the total categories of construction equipment for consider- ation. The set nce is the total number of equipment of category e located in county c, and each piece of equip- ment is indexed by i. Set P represents the set of different pollutants indexed by p, and np denotes the total number of pollutants to consider.
Set T represents the set of emissions reduction tech- nologies indexed by t, and nt is the total number of emissions control technologies to consider. Em denotes
Figure 1. Flowchart of the overall approach.
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the emissions from a particular piece of equipment. Cp represents the cost of the pollutant p, and Rpt is the emissions reduction efficiency of technology t for pollut- ant p. The variable I represents a binary variable having a value of 0 or 1. If a particular technology is selected for a piece of equipment, then the value of I will be 1; other- wise it will be zero.
The set AP is the analysis period for each piece of equip- ment during which retrofit costs could be incurred or ben- efits received, and AP is indexed by �. For an equipment of category e located in county c, the corresponding analysis period would be �c,e,i. For the net present worth analysis, the interest rate r was considered to be 3%.27 For simplicity, it was assumed that the usage hour and fuel consumption for each piece of equipment as well as operation and mainte- nance costs for each technology will remain constant for each year within the analysis period.
Similarly, the benefits obtained from emissions re- duction and fuel savings for each piece of equipment will remain constant for each year within the analysis period. The cost of emissions per pollutant p from the ith equip- ment of category e located in county c is Emc,e,i,pCp. If technology t is applied on that particular piece of equip- ment, the emissions reduction benefit will then be Emc,e,i,pCpRp,tIc,e,i,t. The final expression of the present worth value of total emissions reductions over a period of �c,e,i for each piece of equipment is
�� � AP�c � C�e � 1 ne �i � 1
nc,e �p � 1 np �t � 1
nt �Emc,e,i,pCpRp,tIc,e,i,t�
� ��1 � r��c,e,i � 1r�1 � r��c,e,i � (2) Henceforth, the second factor of the above expression is denoted by �c,e,i so that
�c,e,i � ��1 � r��c,e,i � 1r�1 � r��c,e,i � (3) The fuel consumption of a piece of equipment is denoted by Fc,e,i, the fuel efficiency of technology t is FEt, and the cost of fuel per gallon is CF. If the technology selected causes a fuel penalty, then the value of FEt will be nega- tive. Therefore, the expression for fuel savings is Fc,e,iCF- FEtIc,e,i,t. The final expression of the present worth value of the total fuel savings over a period of �c,e,i for each piece of equipment is
�� � AP�c � C�e � 1 ne �i � 1
nc,e �t � 1 nt ��c,e,iFc,e,iCFFEtIc,e,i,t� (4)
Objective Function Two objectives were considered: (1) maximization of emissions reduction and (2) maximization of fuel savings. The final expression of the weighted objective function consisting of emissions reduction benefits and fuel sav- ings is shown in eq 5.
Maximize Z �
W1 � � � AP
� c � C
� e � 1
ne � i � 1
nc,e � p � 1
np � t � 1
nt
��c,e,iEmc,e,i,pCpRp,tIc,e,i,t�
� W2 � � � AP
� c � C
� e � 1
ne � i � 1
nc,e � t � 1
nt
��c,e,iFc,e,iCFFEtIc,e,i,t�
(5)
In eq 5, W1 and W2 are the weights associated with the emissions reduction benefits and the benefit from fuel savings, respectively, such that W1 � W2 � 1. Note that W1 and W2 can be assigned any values between 0 and 1 to represent the contribution of emissions reduction and fuel saving benefits, respectively.
Model Constraints For formulation of constraints, information about the type of emissions reduction technologies (e.g., retrofit, fuel addi- tive, etc.) is necessary. For the model presented here, it is assumed that three technologies (labeled as X, Y, and Z) are available for use. Further, assume that X and Y correspond to some retrofit type of technology and Z represents a fuel additive that is injected into the fuel system. The purchase and installation cost of emissions reduction technology t is denoted by Ct and the operation and maintenance cost are represented by Comc,e,i,t. The purchase and installation costs associated with emissions reduction technology t is then CtIc,e,i,t, and the operation and maintenance costs are Comc,e,i,tIc,e,i,t. The expression for the budget constraint is presented in eq 6, in which the first and second terms represent the purchase and installation costs and the oper- ation and maintenance costs, respectively, incurred for ret- rofit technologies and the third term is the cost associated with the fuel additive.
Table 2. Nomenclature of the variables used in the model.
Variable Definition
C Set of NA and NNA counties nc Total number of counties E Set of different categories of construction equipment ne Total categories of construction equipment nc,e Total number of equipment of category e in county c P Set of different pollutants np Total number of pollutants T Set of emissions reduction technologies nt Total number of emissions reduction technologies Em Emissions from a piece of equipment Cp Cost of pollutant p Rp,t Emissions reduction efficiency of technology t for pollutant p I Binary variable AP Set of analysis periods for each piece of equipment Fc,e,i. Fuel consumption of a piece of equipment CF Cost of fuel per gallon FEt Fuel efficiency of technology t Ct Cost associated with technology t Comc,e,i,t Operation and maintenance costs of technology t for each
piece of equipment ruc,e,i Remaining usage hours of a piece of equipment Ue,i Expected usage hours of a piece of equipment rac,e,i Remaining age of a piece of equipment Ae,i Expected age of a piece of equipment
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� c � C
� e � 1
ne � i � 1
nc,e � t � 1
�nt � 1�
CtIc,e,i,t
� � � � AP
� c�C
� e � 1
ne � i � 1
nc,e � t � 1
�nt � 1�
��c,e,iComc,e,i,tIc,e,i,t�
� � � � AP
� c � C
� e � 1
ne � i � 1
nc,e
��c,e,iC3Ic,e,i,t� � Budget �$�
(6)
To understand the criteria of selecting a piece of equip- ment eligible for being retrofitted, Texas Department of Transportation (TxDOT) officials were consulted. Through consultation with TxDOT, which is known to own the largest construction equipment fleet in the United States, it was found that a piece of equipment should have a remaining age and remaining usage hours of at least half of its expected age and expected usage hours before dis- posal for retrofitting. The remaining usage hours and the expected usage hours at disposal of a piece of equipment are represented by ruc,e,i and Ue,i, respectively. Similarly the remaining age and the expected age at disposal of a piece of equipment are represented by rac,e,i and Ae,i, respectively. The constraints for remaining usage hours and remaining age are presented in eqs 7 and 8. Note that the coefficient of 0.5 used in eqs 7 and 8 can be changed to suit the policy of a given equipment fleet manager.
ruc,e,i � 0.5Ue,i (7)
�c � 1 to nc, e � 1 to ne, i � 1 to nce�
rac,e,i � 0.5Ae,i (8)
�c � 1 to nc, e � 1 to ne, i � 1 to nce�
The combination of technologies, such as X (t � 1) with Z (t � 3) and Y (t � 2) with Z (t � 3), is possible (as indicated by experts’ guidelines) whereas researchers considered that X and Y technologies are mutually exclusive and not deployed to- gether. These constraints are shown in eqs 9 and 10.
�t � 1 nt Ic,e,i,t � 2 (9)
�c � 1 to nc, e � 1 to ne, i � 1 to nce�
�t � 1 2 Ic,e,i,t � 1 (10)
�c � 1 to nc, e � 1 to ne, i � 1 to nce�
Another requirement was that the fuel additive, such as Z (t � 3), must be deployed for all or none of the equipment within a county because fuel is generally supplied for all equipment within a county from a common fuel depot. Thus the fuel additive constraint is shown in eq 11.
Ic,e,i � 1,t � 3 � Ic,e,i � 2,t � 3 � · · · � Ic,e,i,t � 3 � c,e (11)
Therefore, the final optimization model is an IP model. The objective function is expressed by eq 5, which is
subjected to the constraints expressed in eqs 6–11. The model result will be a deployment plan of emissions con- trol technologies with a view to maximize the emissions reduction and fuel-savings benefits depending on the val- ues of W1 and W2. Most IP problems, such as the one presented here, are combinatorial and NP-hard and there- fore not easily solvable. The model was programmed and solved with Visual C�� and ILOG CPLEX. The model formulation is quite general and can be upgraded and expanded to include emissions reduction options other than NOx and the other set of emissions reduction tech- nologies and can be applied to on-road and nonroad sources in excess of nonroad construction equipment fleet.
CASE STUDY For demonstration purposes, the model was solved con- sidering three main categories of construction equipment (e.g., graders, loaders, and excavators) from TxDOT’s con- struction equipment fleet assuming that the three emis- sions reduction technologies labeled previously as X, Y, and Z, represent, respectively, hydrogen enrichment (HE), selective catalytic reduction (SCR), and fuel additive (FA) technologies. The selected technologies HE, SCR, and FA have different operational and performance characteris- tics. FA is very inexpensive with low emissions reduction efficiency and providing no fuel economy. HE is moder- ately expensive with moderate emissions reduction effi- ciency and leading to better fuel economy. SCR is the most expensive technology with the highest emissions reduction efficiency, but it is coupled with a fuel penalty. These three emissions reduction technologies were se- lected because their different operational characteristics would enable testing the adaptability of the model and data for these technologies were readily available.
Texas has 254 counties, of which 20 counties are designated as NA and 3 counties are designated as NNA counties by EPA. Figure 2 presents the Texas districts in the 8-hr ozone NA and NNA counties.9 Federal funding will be at risk if Texas violates the air quality standards established by the Federal Clean Air Act and regulated by EPA. For this reason, the Texas Commission on Environ- mental Quality, TxDOT, and their local partners have focused most of their emissions reduction programs on these NA areas.28
TxDOT has one of the largest construction equip- ment fleets in the United States and they own and operate approximately 3200 pieces of nonroad diesel equip- ment.18 Their construction equipment fleet consists of graders, loaders, excavators, pavers, rollers, trenchers, cranes, and off-highway tractors. They have prepared a well-organized database of their nonroad fleet containing different characteristics of equipment such as horse- power, fuel consumption, model year, age, usage hours, and location of the equipment, etc. This database was helpful in estimating the emissions from the construction equipment fleet using EPA’s procedure as previously mentioned.
According to EPA’s 2008 NEI data, the total NOx emissions from on-road and nonroad sources were 354,370 and 131,566 t, respectively, in Texas; nonroad sources accounted for 27% of the total NOx emissions
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from the mobile sources in Texas.6 The Texas Transporta- tion Institute (TTI) estimated the total NOx emissions from TxDOT’s diesel construction equipment fleet to be 461 t over fiscal years 2005–2007 for a total of 3170 pieces of diesel construction equipment in Texas.18 NOx is a precursor of ozone, which is responsible for adverse health effects such as respiratory problems. Therefore, a priority for TxDOT is to reduce NOx emissions from their large diesel construction equipment fleet, especially equipment located in NA and NNA counties.
The three main categories of diesel construction equipment—graders, loaders, and excavators—were se- lected for the study because these were the highest NOx- emitting pieces of equipment of TxDOT’s equipment fleet. The average NOx emissions from graders, loaders, and excavators over fiscal years 2005–2007 were 146.1, 116.6, and 56.3 t, respectively, resulting in a total of 319 t of NOx from these three categories of equipment.18 NOx emissions from graders, loaders, and excavators consti- tuted approximately 69% of the total 461 t of NOx emis- sions mentioned above. The remaining categories of equipment other than these three were considered as “other” categories in the analysis for estimating the
amount of technology Z required for deployment in a county. According to TxDOT, all pieces of equipment in a county were fueled from a common diesel tank located in that county. Therefore, technology Z had to be deployed for all of the pieces of equipment located in a particular county (i.e., either the entire county receives Z or it does not receive it at all). The total amount of Z required for a county was estimated based on the amount of diesel re- quired for the remaining or other categories of equipment in addition to graders, loaders, and excavators.
Data Requirement and Collection Emissions Reduction Technologies. Data regarding the three different emissions reduction technologies were collected through communications with different technology ven- dors, questionnaire surveys, telephone interviews, and e- mails. The main purpose of the questionnaire survey was to acquire information regarding the characteristics and prop- erties of the technologies, their availability, the different costs associated with them, requirements, fuel economy, and emissions reduction efficiencies. Because no reliable data were available regarding the effectiveness of the emis- sions control technologies, the data provided by the vendors
Figure 2. NA and NNA counties in Texas.
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had to be used. However, the model is general enough to be upgraded easily after better emissions reduction efficiency data are available.
The combinations of X with Z and Y with Z were considered in the model. The combined NOx reduction efficiencies were estimated based on consultation with the vendors of X and Y. The vendor of X mentioned that the combination of X and Z systems will have an additive effect in NOx reduction efficiency, with the combined NOx reduction efficiency being 41.8%. Consultation with the vendor of Y revealed that the NOx reduction effi- ciency due to the combination of Y and Z systems will not be additive, but it will have a combined effect with a combined efficiency of 81.16%. The vendor of Y men- tioned that Y was not applicable for equipment having a horsepower of less than 100. The cost of technology Y and size of the components made the system impractical to retrofit on such a small mobile engine.
According to the vendors, technology X has a war- ranty up to 4545 hr of operation and technology Y has a life of 5 yr. Using the 4545 operation hours for every piece of equipment in the NA and NNA counties, researchers found that the technology life of X calculates out to be greater than 5 yr for every piece of construction equip- ment in the study. The lifetime of technology Y is the limiting factor. Therefore, the maximum value that �c,e,i can have is 5 yr in this study. Some of the equipment had a remaining age of less than 5 yr before disposal, and some of the equipment had already reached or exceeded the age for disposal. Under the circumstances, the follow- ing conditions were considered to determine the value of �c,e,i for each piece of equipment:
(1) If the remaining age is � 5 yr, then �c,e,i � 5 yr. (2) If 0 � the remaining age is � 5 yr, then �c,e,i � the
remaining age. (3) If the remaining age is � 0 yr, then �c,e,i � 1 yr.
The second and third conditions mentioned above are valid only for Z deployment because the remaining age requirement for X or Y deployment is greater than 5 yr for all of the pieces of equipment being considered in the fleet.
The cost of diesel per gallon was incorporated into the model to consider the fuel savings or fuel penalty resulting from the installation of emissions reduction technology on a piece of equipment. The cost of diesel used in this study was $2.216/gal on the basis of a May 2009 diesel price.29 Table 3 summarizes the data regarding
the selected emissions reduction technologies used in this research.
Air Pollution Damage Cost. The damage cost of NOx was obtained from the Highway Economic Requirements Sys- tem (HERS) model30 developed for the Federal Highway Administration. It was designed to simulate improvement selection decisions on the basis of the relative benefit-cost merits of alternative improvement options. The HERS model uses damage costs for different pollutants. The pollutants are CO, VOCs, NOx, sulfur dioxide, PM2.5, and road dust. The estimates were derived from the study performed by McCubbin and Delucchi.31 The damage cost of NOx used in the HERS model was $3,625/t, which was calculated from the total annual costs from health and property damages.
First, the total amount of each pollutant emitted an- nually by highway vehicles was calculated. The damage cost of each pollutant in dollars per ton was then derived by dividing the total annual cost from health and prop- erty damages by the respective pollutant emitted annu- ally. These values are assumed to provide acceptable esti- mates of damage costs for each pollutant.30 The damage cost for NOx (i.e., $3,625) was used in this research for calculating NOx reduction benefits.
Burris and Sullivan32 identified a potential method- ology for obtaining the incremental societal costs and benefits from a variable pricing project. They applied the methodology to the QuickRide high occupancy/toll lanes in Houston, TX. They considered vehicular pollutant emissions to estimate the benefits and costs of the project. They obtained the monetary values of emissions from research conducted by Delucchi33 and Small and Ka- zimi.34 These two works based the cost of emissions on the cost of healthcare for treatment of diseases related to motor vehicle emissions. Table 4 shows the NOx costs obtained from different studies.
Analysis Scheme For a given budget, TxDOT’s preference is to allocate the available budget first in the NA counties for deploying the emissions control technologies, and then spend the re- maining budget in the NNA counties. The construction fleet database revealed that approximately 77% of the fleet was in the NA counties, with the remaining 23% in the NNA counties. As previously mentioned, TxDOT sug- gested that the criteria regarding the remaining age and remaining usage hours should be at least equal to 50% of its expected age and expected usage hours, respectively, before considering a piece of equipment to be retrofitted. The data regarding the usage hours and the age at disposal
Table 3. Data regarding selected emissions reduction technologies.
Technology X Y Z
Purchase and installation cost ($) 8400 17100c 18e
Operation cost ($) – 0.25d – Maintenance cost ($) 100a 0.75d – Dosage rate (mL) – – 4.25f
Fuel efficiency (%) 8b 1 – NOx reduction efficiency (%) 36 80 5.8 NOx combined reduction efficiency (%) 41.8 81.16
g –
Notes: aPer year; bAfter 240 hr of operation; cWithin 101–300 hp; dPer hour; ePer gallon of Z; fPer gallon of diesel; gOn the basis of consultation with the vendor for Y.
Table 4. Cost of NOx obtained from different studies.
Pollutant
HERS Model30
($/t)
Delucchi33 Small and Kazimi34 and Levinson36
($/t)aLow ($/t) High ($/t)
NOx 3,625 1,445 (1.59) 21,180 (23.34) 1,210 (1.33)
Notes: Values in parentheses are in $/kg as obtained from the studies. aValues obtained by Small and Kazimi as modified by Levinson.
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of a piece of equipment were obtained from TxDOT. Ap- proximately 25% of TxDOT’s equipment had sufficient remaining age and remaining usage hours to satisfy the requirement.
Two different approaches were followed in obtaining the model solution. The first approach will be called “method 1,” in which all of the technologies (i.e., X, Y, and Z) are optimally deployed only in the NA counties at the first stage. In the second stage, the same technologies are deployed in the NNA counties with the remaining budget, if any. The second approach will be called “method 2,” in which all of the technologies (i.e., X, Y, and Z) are optimally deployed in the NA counties along with the de- ployment of technology Z only in the NNA counties at the first stage. Then X and Y are deployed in the NNA counties in the second stage. Method 1 strictly follows the guidelines provided by TxDOT. Method 2 has been proposed as an alternative and was found to be a better option for deploy- ment of emissions reduction technologies.
For both methods, the objective function consisted of two weighted-objectives: (1) maximizing NOx reduction and (2) maximizing fuel savings subject to the constraints expressed in eqs 6–11. Technology X results in fuel sav- ings whereas technology Y causes a fuel penalty. For the weighted objective function expressed by eq 5, five pairs of values for W1 and W2 were selected for each method (1 and 2) chosen for deployment of emissions reduction technologies. This produced five cases designated as A, B, C, D, and E for each method. Table 5 shows the values used for W1 and W2 used in this study for five different cases for each method (1 and 2). Table 6 summarizes the analysis scheme, and Figure 3 presents the flowcharts for methods 1 and 2.
RESULTS AND DISCUSSION This section presents the model application results pre- scribing a mix of technologies to be deployed for emis- sions reduction on construction equipment. Two alterna- tive approaches or methods have been tested, each having five options (A, B, C, D, and E) producing 10 cases. In the analyses, cases 1C and 2C, having weights of W1 � 0.5 and W2 � 0.5, respectively, for NOx reduction and fuel- savings benefits in the weighted objective function were considered as the base cases. Comparison between the base case (i.e., cases 1C and 2C) and the other cases (i.e., A, B, D, and E) of the respective methods for total NOx reduction and total combined benefits are analyzed and discussed. Next, comparisons between method 1 and method 2 for the respective cases are shown, followed by an analysis of the benefit-cost (B-C) ratio for both methods.
In the following discussion, total NOx reduction means reduction of NOx emissions from the equipment fleet located in NA and NNA counties. Combined fuel savings is defined as the fuel saved from the equipment fleet located in NA and NNA counties using the emissions reduction technologies. The total combined benefits in- clude the NOx reduction benefits and the fuel savings in the NA and NNA counties from installing emissions con- trol technologies.
Table 7, a and b, present a summary of the intra- and intermethod comparison of the different cases, represent- ing the deployment options of emissions reduction tech- nologies in terms of total NOx reductions and the total combined benefits. The first and the second part of Table 7a show the comparison of various cases for NOx reduc- tions with that of the respective base cases under method 1 and method 2, respectively. The third part of Table 7a presents the comparison between corresponding cases in methods 1 and 2. Table 7b contains a similar comparison of cases from the two methods in terms of the total combined benefits. Table 7, a and b, clearly show which case performs better in the different budget ranges to- gether with the corresponding ranges of NOx reductions and combined benefits. The intra- and intermethod com- parisons of various cases are discussed in the following paragraphs.
Figure 4 shows the variation of the total combined benefits for methods 1 and 2 with increasing the budget.
Table 5. Value of W1 and W2 for different cases.
Cases
Weights Associated with Benefits for
NOx Reduction, W1 Fuel Savings, W2
1A and 2A 1 0 1B and 2B 0.7 0.3 1C and 2C 0.5 0.5 (base case) 1D and 2D 0.3 0.7 1E and 2E 0 1
Table 6. Analysis scheme.
Approach Options Cases
Method 1 (In the first stage deploy X, Y, and Z in NA counties; in second stage, deploy same technologies in NNA counties with remaining budget, if any)
Different combinations of two weighted objectives (i.e., NOx reduction and fuel savings; see Table 5)
1A, 1B, 1C, 1D, and 1E
Method 2 (In the first stage, deploy X, Y, and Z in NA counties and Z in NNA counties; in second stage, deploy X or Y on any given equipment in the NNA counties with remaining budget, if any)
2A, 2B, 2C, 2D, and 2E
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These combined benefits result in the first year of deploy- ing the emissions reduction technologies. The total com- bined benefit is composed of the benefits from the total NOx reductions and total fuel savings. As expected, the total benefit generally increases with an increasing bud- get. However, method 1 shows that there are some drops in the total benefit as the budget increases. For example, B1 has a larger budget than B2, but the figure shows that the overall benefit for budget B1 is less than budget B2. This is the result of the deployment pattern chosen by TxDOT (i.e., giving priority to NA counties over NNA counties). The NA counties receive expensive technology such as X or Y in budget B1; therefore, less money is available for the NNA counties. Thus, the benefits for the NA counties rise but the benefits for NNA counties de- crease, and as a result, the overall benefits decrease. How- ever, in budget B2, the NA counties do not receive similar amounts of the expensive technology (such as X or Y) because the budget is insufficient and hence a larger bud- get amount is available for the NNA counties. This causes the overall benefit for B2 to be greater than B1. Therefore, method 2 was proposed to improve the deployment pat- tern and prevent the benefit decreases observed in method 1. In method 2, benefits are obtained even with a small increase in investment through deploying Z in the NNA counties at the first stage. Note that unlike method
1, method 2 does not depend on large investment amounts to realize benefits.
To present the sensitivity of the NOx reductions and combined benefits with budgets, graphs of total NOx re- ductions and total combined benefits are plotted for bud- gets ranging from approximately $500 to $1,500,000. The model solutions were developed for budgets up to $1,500,000 because NA and NNA counties receive the maximum possible units of X, Y, and Z coverage up to this budget amount; thereafter, NOx reductions and the total combined benefits remain constant with further invest- ment increases.
Comparison of Cases with the Base Case under Method 1
Figure 5, a and b, present the total NOx reductions and total combined benefits, respectively, for all five cases in method 1. Comparisons of the cases in method 1 with the base case 1C are presented in the following paragraphs with reference to Table 7, a and b, and Figure 5, a and b.
Case 1A versus Case 1C. A comparison between case 1A and case 1C for the total NOx reductions indicated that case 1C had greater NOx reductions than case 1A for budgets ranging from $90,000 to $120,000, $180,000 to
Figure 3. Flowcharts of methods 1 and 2.
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Table 7a. Comparison of cases for total NOx reductions.
Comparison Type Cases Compared Budget Range ($) Outcome Range of Total
NOx Reduction (t)
Comparison of cases with the base case under method 1
1A vs. 1C 90–120,000; 180,000–300,000; 900,000–1,200,000 1C 1A 0.0038–3.12 Remaining budgets 1A�1C 0–2.47
1B vs. 1C 500–100,000 1B�1C 0–1.72 180,000–300,000 0.67–2.35 600,000–1,500,000 0–0.78 150,000–170,000 1C 1B 1.3–1.6 400,000–500,000 0.51–2.48
1C vs. 1D 500–50,000 1C�1D 0–3.12 80,000–110,000 0–3.70
150,000–180,000 0.2–2.65 300,000–1,500,000 0.28–5.74 Remaining budgets 1D 1C 0.12–1.96
1C vs. 1E Entire budget range 1C 1E 0.57–51.51 Comparison of cases with the base case
under method 2 2A vs. 2C 60,000–70,000 2A 2C 0.01–0.15
90,000–700,000 0.04–0.98 900,000–1,200,000 0.08–0.80
2B vs. 2C Entire budget range 2B�2C 0–0.86 2C vs. 2D 90,000–1,150,000 2C 2D 0.39–18.30 2C vs. 2E Entire budget range 2C 2E 0.60–51.51
Comparison of corresponding cases under methods 1 and 2
1A vs. 2A 500–500,000 2A 1A 0.03–2.73 800,000–1,150,000 1A�2A 0–0.084
1B vs. 2B 500–500,000 2B 1B 0.03–3.05 800,000–1,500,000 1B�2B 0–0.11
1C vs. 2C 500–200,000 2C 1C 0.03–3.50 400,000–1,500,000 1C 2C 0–0.30
1D vs. 2D 500–600,000 2D 1D 0.03–3.75 800,000–1,150,000 1D�2D 0–0.66
Table 7b. Comparison of cases for total combined benefits.
Comparison Type Cases Compared Budget Range ($) Outcome Range of Total
Combined Benefit
Comparison of cases with the base case under method 1
1A vs. 1C 130,000–200,000; 400,000–1,200,000 1C�1A $0–11,100 Remaining budgets 1A�1C $0–6,800
1B vs. 1C 110,000–190,000 1C 1B $320–8,865 400,000–1,500,000 $30–9,855
Remaining budgets 1B�1C $0–3,740 1C vs. 1D 500–50,000 1C�1D $0–9,770
80,000–110,000 $0–9,950 150,000–180,000 $3,260–6,620 300,000–600,000 $2,750–13,570
1,100,000–1,500,000 $1,005–3,660 Remaining budgets 1D 1C $125–7,910
1C vs. 1E Entire budget range 1C 1E $1,950–152,470 Comparison of cases with the base case
under method 2 2A vs. 2C 500–1,000,000 2C�2A $0–3,970
1,140,000–1,500,000 $0–100 1,100,000–1,130,000 2A 2C $10–40
2B vs. 2C 500–1,000,000 2C�2B $0–1,480 1,160,000–1,500,000 $0–100 1,100,000–1,150,000 2B 2C $10–170
2C vs. 2D 90,000–1,150,000 2C 2D $1,605–55,970 2C vs. 2E Entire budget range 2C 2E $2,040–152,470
Comparison of corresponding cases under methods 1 and 2
1A vs. 2A 500–900,000 2A 1A $90–8,675 1B vs. 2B 500–1,000,000 2B 1B $90–9,110
1,140,000–1,190,000 $15–110 1C vs. 2C 500–200,000 2C 1C $90–9,485
400,000–1,500,000 1C�2C $0–170 1D vs. 2D 500–900,000 2D 1D $90–11,330
1,000,000–1,500,000 1D�2D $0–1,300
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$300,000, and $900,000 to$1,200,000, respectively. The minimum and maximum differences in NOx reductions within these budget ranges were 0.0038 and 3.12 t, respectively. Case 1A had either equal or greater NOx reductions than case 1C for the remaining budget amounts. The maximum difference in NOx reductions came to approximately 2.47 t within the remaining budget amounts.
Comparing the total combined benefits of cases 1A and 1C shows that case 1C had equal or higher benefits than that of case 1A for budgets ranging from $130,000 to $200,000 and $400,000 to $1,200,000. The maximum difference of total benefits in these budget ranges was approximately $11,100. For the remaining budget amounts, case 1A had either equal or greater total com- bined benefits than case 1C, with a maximum difference of approximately $6,800.
Case 1B versus Case 1C. Comparisons between case 1B and case 1C for total NOx reductions indicated that the total NOx reductions for case 1B were equal to or greater than those of case 1C for budgets ranging from $500 to $100,000, $180,000 to $300,000, and $600,000 to $1,500,000. The difference in NOx reductions ranged from approxi- mately 0 to 1.72 t, 0.67 to 2.35 t, and 0 to 0.78 t, respectively. Case 1C exceeded case 1B in terms of total NOx reductions for budgets ranging from $150,000 to $170,000 and $400,000 to $500,000, with the corre- sponding NOx reductions varying from approximately 1.3 to 1.6 t and 0.51 to 2.48 t, respectively.
Case 1C exceeded case 1B for total combined benefits for budgets ranging from $110,000 to $190,000 and $400,000 to $1,500,000, with the difference in the total combined benefits varying from approximately $320 to $8,865 and $30 to $9,855, respectively. For the remaining budget amounts, case 1B was either equal to or greater than case 1C in terms of total combined benefits, having a max- imum difference of approximately $3,740 of total benefits.
Case 1C versus Case 1D. Case 1C was compared with case 1D and the results indicated that case 1C was equal to or greater than Case 1D for total NOx reductions for budgets ranging from $500 to $50,000, $80,000 to $110,000,
$150,000 to $180,000, and $300,000 to $1,500,000. The difference in total NOx reductions ranged from approxi- mately 0 to 3.12 t, 0 to 3.70 t, 0.2 to 2.65 t, and 0.28 to 5.74 t, respectively. For the remaining budget amounts, case 1D exceeded case 1C for total NOx reductions, with the corresponding differences in NOx reductions varying from approximately 0.12 to 1.96 t.
For the total combined benefits, case 1C was equal to or greater than case 1D for budgets ranging from $500 to $50,000, $80,000 to $110,000, $150,000 to $180,000, $300,000 to $600,000, and $1,100,000 to $1,500,000. The differences in total benefits within these budget ranges varied from approximately $0 to $9,770, $0 to $9,950, $3,260 to $6,620, $2,750 to $13,570, and $1,005 to $3,660, respectively. For the remaining budget amounts, case 1D exceeded case 1C for total combined benefits, with the differences in total benefit varying from approximately $125 to $7,910.
Case 1C versus Case 1E. Case 1C had greater total NOx reductions than case 1E for the entire budget range of $500–1,500,000, with the difference in NOx reductions varying from approximately 0.57 to 51.51 t. Similarly, for total combined benefits, case 1C exceeded case 1E for the entire budget range, with the difference in total combined benefits ranging from approximately $1,950 to $152,470.
Comparison of Cases with the Base Case under Method 2
Figure 6, a and b, show the total NOx reductions and total combined benefits for method 2. On the basis of these figures and Table 7, a and b, comparisons of different cases under method 2 with base case 2C are presented in the following paragraphs.
Case 2A versus Case 2C. A comparison of total NOx reduc- tions between case 2A and case 2C revealed that case 2A exceeded case 2C in terms of NOx reductions for budgets ranging from $60,000 to $70,000, $90,000 to $700,000, and $900,000 to $1,200,000. The differences in total NOx
Figure 4. Total benefits for different budgets in methods 1 and 2 in the first year of deployment.
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reductions in these budget ranges varied from approxi- mately 0.01 to 0.15 t, 0.04 to 0.98 t, and 0.08 to 0.80 t, respectively. For the remaining budget amounts, there was no difference between the two cases.
Case 2C was equal to or better than case 2A for total combined benefits for budgets ranging from $500 to $1,000,000 and $1,140,000 to $1,500,000. The differences in the total combined benefits in these budget ranges varied from $0 to $3,970 and $0 to $100, respectively. Case 2A showed greater combined benefits than case 2C, with the difference in the total combined benefits ranging from $10 to $40 for the budget ranging from $1,100,000 to $1,130,000.
Case 2B versus Case 2C. Case 2B had equal or greater total NOx reductions than case 2C for the entire budget range of
$500–1,500,000. The difference in total NOx reductions varied from approximately 0 to 0.86 t within that budget range.
Case 2C had equal or greater total combined benefits than case 2B for the budget ranges of $500–1,000,000 and $1,160,000–1,500,000. The differences in total combined benefits in these budget ranges were approximately $0– 1,480 and $0–100, respectively. However, case 2B had greater total combined benefits than case 2C for budgets ranging from $1,100,000 to $1,150,000, with the differ- ence in the total combined benefits in the range of ap- proximately $10–170.
Case 2C versus Case 2D. The total NOx reductions and the total combined benefits for case 2C were greater than those
0
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Case 1D (W1=0.3,W2=0.7)
Case 1E (W1=0,W2=1)
(a)
(b)
Figure 5. NOx reductions and benefits obtained by method 1: (a) total NOx reductions, and (b) total combined benefits.
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for case 2D for the budget ranging from $90,000 to $1,150,000. The corresponding differences in total NOx re- ductions and total combined benefits varied from approxi- mately 0.39 to 18.30 t and approximately $1,605 to $55,970, respectively. For the remainder of the budget amounts, total NOx reductions and total combined benefits were equal for both of the cases.
Case 2C versus Case 2E. In terms of total NOx reductions and total combined benefits, case 2C was better than case 2E for the entire budget range of $500–1,500,000, with the corresponding differences ranging from ap- proximately 0.60 to 51.51 t and approximately $2,040 to $152,470, respectively.
Comparison between Corresponding Cases of Methods 1 and 2
This section presents a comparison between method 1 and 2 for the respective cases. Figures 7a–7h show the graphical comparison of the corresponding cases of the two methods in terms of total NOx reductions and total combined benefits for both methods. Table 7, a and b, show summaries of the comparisons for total NOx reduc- tions and total combined benefits, respectively.
Case 1A versus Case 2A. Figure 7a and Table 7a show that case 2A performs better than case 1A at certain budget ranges. Case 2A exceeded case 1A in terms of total NOx reductions for budgets ranging from $500 to $500,000 and
Total NOx Reduc�on
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Case 2B (W1=0.7,W2=0.3)
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Case 2D (W1=0.3,W2=0.7)
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Case 2D (W1=0.3,W2=0.7)
Case 2E (W1=0,W2=1)
(a)
(b)
Figure 6. NOx reductions and benefits obtained by method 2: (a) total NOx reductions, and (b) total combined benefits.
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the difference in total NOx reductions varied from approx- imately 0.03 to 2.73 t in that budget range. For the remain- ing budget amounts, case 1A had equal or greater NOx reduction benefits than case 2A for a budget ranging from $800,000 to $1,150,000, with NOx reduction differences in the range of approximately 0–0.084 t.
Similarly, Figure 7b and Table 7b show that case 2A had greater total combined benefits than case 1A for the budget ranging from $500 to $900,000 with the differ- ence in total combined benefits ranging from approxi- mately $90 to $8,675. For the remainder of the budget amounts, the differences between the two cases were negligible.
Case 1B versus Case 2B. Referring to Figure 7c and Table 7a for total NOx reductions and Figure 7d and Table 7b for total combined benefits, cases 1B and 2B show a similar pattern as described previously for cases 1A and 2A. Case 2B exceeded case 1B for total NOx reductions for the budget ranging from $500 to $500,000, and the differ- ences in total NOx reductions varied from approximately 0.03 to 3.05 t in that budget range. For the remaining budget amounts, case 1B had equal or greater NOx reduc- tions than case 2B, with the difference in NOx reductions ranging from approximately 0 to 0.11 t for the budget range of $800,000–1,500,000.
Figure 7d and Table 7b show that case 2B had greater total combined benefits than case 1B for budgets ranging from $500 to $1,000,000 and $1,140,000 to $1,190,000, with the total combined benefits difference ranging from approximately $90 to $9,110 and $15 to $110, respec- tively. For the remaining budget amounts, the differences between both of the cases were very negligible.
Case 1C versus Case 2C. Figure 7e and Table 7a show that case 2C had greater NOx reductions than case 1C for budgets ranging from $500 to $200,000, with the corresponding difference in NOx reductions varying from approximately 0.03 to 3.50 t. For the remaining budget amounts, case 1C had greater NOx reductions than case 2C for budgets rang- ing from $400,000 to $1,500,000, with the difference in NOx reductions ranging from 0 to 0.30 t.
Figure 7f and Table 7b indicate that case 2C had greater total combined benefits than case 1C for budgets varying from $500 to $200,000, with the difference in total combined benefits ranging from approximately $90 to $9,485. Case 1C had equal or greater total combined benefits than case 2C for budgets ranging from $400,000 to $1,500,000, with the difference in total combined ben- efits varying from approximately $0 to $170.
Case 1D versus Case 2D. Figure 7g and Table 7a show that case 2D exceeded case 1D in terms of total NOx reductions for the budget ranging from $500 to $600,000, with the difference in total NOx reductions varying from approxi- mately 0.03 to 3.75 t. For the budget ranging from $800,000 to $1,150,000, case 1D had equal or greater NOx reduction benefits than case 2D and the corresponding difference in NOx reductions ranged from approximately 0 to 0.66 t.
For total combined benefit, Figure 7h and Table 7b show that case 2D had greater combined benefits than case 1D for the budget ranging from $500 to $900,000, with the difference in total combined benefits varying from approx- imately $90 to $11,330. Case 1D was equal to or greater than case 2D for the remaining budget amounts ($1,000,000– 1,500,000), with the differences in the total combined ben- efits ranging from approximately $0 to $1,300.
Case 1E versus Case 2E. Cases 1E and 2E were the same in terms of deploying emissions reduction technologies. Both cases focus on maximizing fuel savings (W1 � 0 and W2 � 1) only. The cases do not focus in maximizing NOx reductions because W1 � 0. Thus, with W1 � 0 and W2 � 1, both methods produced the same deployment pattern. Therefore, there was no difference between the cases. Figure 7i shows the total NOx reductions and total com- bined benefits for cases 1E and 2E.
The discussion of the intra- and intermethod com- parison of different cases shows that there were differ- ences in total combined benefits among the cases. Often the difference in benefits was negligible or small, ranging from approximately $1 to $330. At times, the difference in the total combined benefits was high, ranging from approximately $1,000 to $152,500. The differences in the range of overall benefits between any two cases, for the intra- and intermethod comparison, varied from $1 to $152,500. The differences were primarily dependent on the available budget, emissions, horsepower, usage hours, fuel consumption, distribution of the equipment, and the total number of NA and NNA counties.
The graphs of combined benefits for cases 2A–2D ap- peared to be parallel, showing a similar increasing trend. Thus, both of the objectives, NOx reductions and fuel savings, were equally beneficial and made the showed graphs for cases 2A–2D follow almost similar paths and directions (Figure 6b).
Figures 7a–7h show that the method 2 cases have higher NOx reductions and higher total combined bene- fits than the method 1 cases for certain budget ranges, clearly showing that the method 2 graphs lie above the method 1 graphs. Method 2 cases prevented the benefit drops, which occurred in the method 1 cases for total NOx reductions and total combined benefits. The method 2 graphs for total NOx reductions and total combined ben- efits increased upward without any drop in NOx reduc- tions or benefits with the increased budget amounts.
In method 1, NA counties consume most of the available budget, leaving less available for NNA coun- ties and thus sometimes lowering the overall benefits. However, in the same situation, the overall benefit could be increased by also spending a portion of the investment in the NNA counties. In method 1, after all of the equipment in the NA counties are supplied with Z, because Z is least expensive, depending on the avail- able budget, X or Y can then be deployed on the equip- ment. If the available funding is not sufficient for de- ploying X, Y, or both in the NA counties, the remaining budget is assigned to the NNA counties and leads to increased overall benefits.
By increasing the budget (in the same situation), after the available funding is just sufficient to deploy X, Y, or both in the NA counties, all of the funding is assigned in
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Volume 61 June 2011 Journal of the Air & Waste Management Association 625
the NA counties and the NNA counties may receive less, or nothing, compared with the previous situation. This causes the NOx reductions and the overall benefits to drop compared with the previous situation.
The method 2 concept was developed to overcome the situation observed in method 1. In method 2, NOx reductions and benefits are realized even with a small investment increase by deploying Z in the NNA counties
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Figure 7. Comparison between cases: (a) total NOx reductions (case 1A vs. case 2A), (b) total combined benefits (case 1A vs. case 2A), (c) total NOx reductions (case 1B vs. case 2B), (d) total combined benefits (case 1B vs. case 2B), (e) total NOx reductions (case 1C vs. case 2C).
Bari et al.
626 Journal of the Air & Waste Management Association Volume 61 June 2011
in the first stage. Deploying Z in the NNA counties in the first stage prevents the drop in NOx reductions and com- bined benefits, which were observed in method 1 with increasing the budget.
Comparison of B-C Ratio of Methods 1 and 2 Figures 5b and 6b show that total combined benefits increase with increasing the investment under methods 1 and 2. The initial steep portion of the graphs (up to investment of approximately $100,000) indicates a higher B-C ratio for all cases except cases 1E and 2E. The B-C ratio is greater than 1 for investments up to $100,000 for both methods. In method 1, the B-C ratio varied from approx- imately 3.97 to 1 with investments up to $100,000. For budgets exceeding $100,000, the B-C ratio shows a de- creasing trend, with the B-C ratio dropping from approx- imately 1 to 0.18. These B-C ratio values hold true on the average for all method 1 cases except case 1E. However, method 2 showed a higher B-C ratio, which ranged from approximately 4.15 to 1 for investments up to $100,000. Thereafter, the B-C ratio dropped from a value of approx- imately 1 to 0.18 for investments greater than $100,000. This is generally true for all method 2 cases except case 2E. For cases 1E and 2E, benefits started to accrue around a
budget of $10,000 and the B-C ratio varied from 0.54 to 0.19 for budgets exceeding $10,000.
Identification of the Pareto Front The rationale for this analysis is that providing decision- makers with the Pareto front/Pareto optimal solutions will assist them in determining the tradeoffs needed when se- lecting one candidate optimal solution versus others. Win- ston and Venkataramanan35 defined Pareto optimal solu- tions as follows: “a solution (call it A) to a multiple-objective problem is Pareto optimal if no other feasible solution is at least as good as A with respect to every objective and strictly better than A with respect to at least one objective.” A related definition is “a feasible solution B dominates a fea- sible solution A to a multiple-objective problem if B is at least as good as A with respect to every objective and is strictly better than A with respect to at least one objective.” The set of all noninferior (not dominated) solutions is called the Pareto front.
Figure 8a shows the feasible solution sets for all cases in both methods. From these solution sets, the dominated/inferior points were identified and re- moved. The remaining solution set is the collection of noninferior solutions. Figure 8b presents the noninfe- rior solution sets for all cases in methods 1 and 2. Table
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