GREEN TRANSIT SCHEDULER: A METHODOLOGY FOR

INTRODUCTION

The environmental impacts of transportation are significant; and, these impacts are even more significant when examined on a life-cycle basis. When examined on this basis, it is also clear that anticipated “clean” fuels and technological innovations of the future, alone, do not provide the complete solution for minimizing transportation environmental impacts or providing environ-mentally sustainable transportation systems. For example, consider “zero emitting” electric vehicles, which transfer emissions from the tailpipe to the electric utility, or the much-heralded “fuel cell,” which requires a hydrogen source that must be produced and distributed by some means. This is to say, even with cleaner fuels, other aspects of transportation system design and operation must also be addressed if overall or life-cycle environmental impacts of transportation systems are to be minimized.

From this analysis, it might be inferred that one key to minimizing the life-cycle environmental impacts of transportation is simply to minimize the transportation activity itself, since many of the direct and indirect environmental impacts are a function of, or can be attributed to, vehicle operation. While this is true conceptually, it is not feasible to implement in many circumstances, for example, in public transportation and commercial freight hauling systems that are operated because of statutory requirements or to service an anticipated demand. Typically, systems such as these utilize a fleet of vehicles—not uncommonly, a fleet comprised of different types of vehicles, e.g., having different capacities or capabilities. Here, the controllable environmental impacts of operation are affected by vehicle assignment and/or scheduling decisions. However, in a (heterogeneous fleet) system such as this, the relationship between vehicle activity, e.g., travel distance to satisfy a particular demand, and environmental impacts is situational and dependent upon vehicle parameters and the vehicle assignment including itinerary. In other words, the vehicle assignment and routing that minimizes distance or economic cost may not be the one that minimizes environmental impacts. Moreover, the environmental impacts are a function of variables in addition to travel distance alone. However, by considering these impacts to be a function of scheduling decisions, and including them in the scheduling optimization function, these impacts can be optimized (minimized) jointly with other decision variables.

The assignment or dispatching of vehicles in fleet operations entails vehicle routing, vehicle scheduling or a combination of both, following the taxonomy of Bodin and Golden (1981). And, problems such as these have been extensively studied by Operations Researchers over the years. However, there has been only very limited research to-date where environmental considerations have been included in the vehicle routing and scheduling objective function and optimization algorithm. In particular, there has been virtually no research of this type that has included environmental impacts assessed on a life-cycle basis.

In this paper, we present a methodology for optimizing vehicle routing and scheduling based on the joint optimization of cost, service, and life-cycle environmental impact parameters. We develop the methodology for a demand-responsive (also known as “dial-a-ride” [DAR]) transit system. In the U.S., the Americans with Disabilities Act requires municipal transit operators to accommodate disabled patrons. And, for a variety of reasons including safety and schedule maintenance, many municipalities have elected to do so through the provision of complementary transit (also known as paratransit), allowable under federal law, rather than by modifying existing bus fleets. While paratransit is only a small component of public transit overall, the number of miles traveled in the U.S. has doubled over the past ten years to nearly 600 million miles per year, according to the National Science and Technology Council (NSTC, 1998). And, demand for such services is expected to grow as the population ages demographically. More importantly, “high operating costs and poor management strategies that do not optimize the use of drivers and vehicles have made such services costly and less than fully responsive to their riders’ mobility needs” (NSTC). These same underlying factors would be expected to affect the environmental impacts of operation, as well, the joint optimization of paratransit cost, service, and environ-mental performance.

Transportation Environmental Impacts

At the present time, 107 areas of the U.S. are not in compliance with one or more of the Ambient Air Quality Standards established by the federal Clean Air Act, including those for carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3), lead (Pb), and particulate matter (PM-10) (United States Environmental Protection Agency [USEPA], 2002). And, a significant contributor to these air quality problems in the U.S. is transportation. According to USEPA (1999), about two-thirds of all CO emissions, and about one-third of all NOx and VOC emissions, nationwide, are attributable to transportation sources. Additionally, vehicles emit numerous toxic organic compounds, some of which are carcinogenic, including benzene, 1,3-butadiene, formaldehyde, ethyl benzene, methyl t-butyl ether (MTBE), hexane, acetaldehyde, styrene, toluene, and xylene. And, for these specific substances, highway vehicles are responsible about for one-quarter to one-half of total U.S. emissions, depending upon the pollutant (USEPA, 2000, 1996a). In addition, diesel-powered vehicles emit particulates comprised of numerous poly-cyclic and poly-aromatic hydrocarbons that are potent carcinogens, as well as ultra-fine particles that that are respiratory irritants (USEPA, 2000). Finally, the combustion of fossil fuels results in carbon dioxide and other greenhouse gas emissions; and, as of 1993, highway vehicles were responsible for about 23 percent of anthropogenic carbon dioxide emissions in the U.S. (USEPA, 1996a).

There has been substantial research investigating vehicular emissions, which are widely known to be a function of modal conditions (e.g., Hothersall and Salter, 1977). Specifically, emission rates are a function of vehicle speed, engine loading (power output), rate of acceleration or deceleration, etc., as well as mechanical factors such as carburetion and vehicle maintenance (TRB, 1995). Significant emissions also occur during engine starts as well as engine idling (CARB, 2000, 1998, 1996).

The environmental impacts of transportation are even more significant when they are examined on a life-cycle basis. Environmental life-cycle analysis (LCA) is a systematic approach and set of methods and techniques for the identification and assessment of environmental impacts and consequences over the complete life cycle of a product or process. The Society of Environmental Toxicology and Chemistry (SETAC, 1993, 1991) is generally credited for the current LCA methodological framework; and, recent ISO standards (ISO 14040 et seq.) have further formalized LCA. Moreover, the use of LCA to properly identify and characterize the environ-mental impacts and consequences of a product, process, or activity is recommended by USEPA (e.g., Keoleian and Menerey, 1994, 1993). In the case of transportation vehicles, for example, life-cycle impacts include not only those due to operation (e.g., tailpipe emissions), but also those due to vehicle production, the production of components and materials used in vehicle maintenance as well as the maintenance activity itself, and the impacts due to the “fuel cycle”—the extraction, refining, and distribution of motor fuels—to name just a few. And, the impacts in these other life-cycle stages may be significant. For example, DeLuchi (1993, 1991) found that VOC, NO2, and SO2 emissions from the “fuel cycle” to be comparable to those from the tailpipe on a normalized or “per mile” basis. Highly insightful discussions of the life-cycle stages and impacts of transportation systems are provided by USEPA (1999, 1996a), Keoleian, et al (1997), and Graedel and Allenby (1998). From these analyses, it is clear that the reduction of transporta-tion environmental impacts requires consideration of the impacts over all life-cycle stages.

Vehicle Routing and Scheduling with Environmental Considerations

There has been extensive prior research investigating and modeling the environmental impacts, primarily emissions, of vehicle operation, due in part to Clean Air Act requirements. More recently, primarily in the context of Intelligent Transportation Systems (ITS), researchers have developed combined traffic simulation/emissions models for more accurately predicting vehicle emissions based on actual (simulated) modal conditions. Descriptions of numerous traffic/ emissions models in current use may be found in FHWA (1992); USEPA (1998); Barth and Norbeck (1996, 1994); Feng, et al (1997); Shaheen, et al (1998); and Abdulhai, et al (1999).

There has also been limited prior work in the area of multi-objective network optimization, including that based on environmental impacts (tailpipe emissions), utilizing the previous models. In general, this research—including that of Tzeng and Chen (1993); Bededek (1995); SWUTC (1996); Yu (1996); Feng (1996); Kim (1995); Shaheen, et al. (1998); Benedek and Rilett (1998); Yu and Stewart (1995); and Johnston and Rodier (1999)—has focused on optimization of vehicle routing based on various traffic assignment principles and algorithms. That is, individual vehicles (representing origin-destination pairs) were assigned routings on simulated traffic networks so as to optimize particular objective functions. However, the previous research has generally been limited to optimization of specific pollutants (tailpipe emissions) individually and has not considered impacts on a life-cycle basis. More importantly, as Yu and Stewart have observed, there remains a genuine need to develop optimization models and approaches based on “a generalized cost function that includes both travel-time variables and the environmental variables.”

Insofar as the problem of fleet vehicle routing and scheduling as we have described it, i.e., where environmental impacts are included among the optimization objectives, we have found only isolated examples in the literature of prior work in this area. One example is that of Eriksson, et al. (1996), who considered the use and/or assignment of vehicles (from among two types) for the delivery of newspapers, where they identified and optimized criteria pollutant emissions on a partial life-cycle basis. Thus, in this sense, their analysis may be considered as a type of vehicle routing problem. There have also been numerous projects, utilizing ambient air quality data and other ITS technologies, to reroute traffic (either through automated traffic control or provision of information to drivers) around intra-urban areas where pollutant levels are high. (See, for example, Taylor and Herbert, 1993 and Sommerville and Bostock, 1994, respectively, for descriptions of the Advanced Transportation Telematics and APOLLON projects in Europe and Iwaoka, et al., 2000 and Yoshiura, et al., 1999 for a discussion of the Universal Traffic Management Systems 21 in Japan.) We are not aware, however, of any prior work that has provided a methodology and algorithm for the scheduling of paratransit (or other fleet) vehicles based on the joint optimization of cost, service, and environmental impact objectives—in particular, where the latter are evaluated utilizing life-cycle impact assessment (LCIA) methods.

Problem Description and Solution Approach

The objective of our research is to develop and demonstrate a methodological approach and vehicle routing/scheduling algorithm for the joint optimization of paratransit system performance including life-cycle (LCIA-based) environmental impacts (consequences). This would allow, for example, the operator of such a system to operate it in a manner that optimizes cost and service performance while simultaneously minimizing the environmental consequences of operation. We demonstrate the methodology through computer simulation of a paratransit system operation, where the modeled system is loosely based on an ACCESS Services (paratransit) provider in Los Angeles County. In order to accomplish the research objective, several developments are required and are listed below. The listing also provides a general outline of the remainder of this paper. The developments are:

1) Development of an environmental life-cycle model of paratransit operation and a life-cycle inventory (LCI) of operational environmental impacts as a function of vehicle itinerary (route/schedule) parameters;

2) Identification and quantification of the consequences of these impacts utilizing life-cycle impact assessment (LCIA) methods, as the basis of optimization;

3) Development of a multi-objective decision model with which to assess the relative desirability of alternative itineraries;

4) Translation of the decision model to an optimization model, and modification of existing DAR routing/scheduling algorithm to include the (previous) environmental consequences;

5) Simulation of paratransit operation and the vehicle scheduling algorithm.

PARATRANSIT LIFE-CYCLE MODEL

We consider a hypothetical paratransit operation comprised of four vehicle types, including a gasoline-powered “minivan,” a CNG-powered “minivan,” and larger capacity “shuttle busses,” gasoline- and diesel-powered. We assume generic, 1998-2000 model-year “light duty” or “medium duty” vehicles for which data is available. We utilize MacLean’s (1998) life-cycle model of an automobile as the basis for our life-cycle model, although it is necessary to adapt it to the particular activity being modeled. Notably, MacLean’s LCI model combines process impacts—vehicular emissions—with those determined using aggregated (economy-wide) data, specifically, data from the Economic Input Output-Life Cycle Assessment (EIO-LCA) model developed by Lester Lave and colleagues at Carnegie Mellon University (Hendrickson, et al., 1998).

In actual paratransit operation, environmental impacts (primarily tailpipe emissions and fuel consumption) arise due to vehicle usage and are a direct function of distance traveled. However, significant operational (process) impacts also arise from other aspects of vehicle operation including engine idling and engine starts. And, these latter impacts are a function of the vehicle itinerary (i.e., vehicle scheduling decisions), but are unrelated to the vehicle travel distance (which is also a function of itinerary). The life-cycle model for the paratransit operational process is shown in Figure 1. It should be noted that when a life-cycle inventory (LCI) is developed for the process, LCI impacts are allocated on a “per mile,” “per engine start,” and “per minute idling” basis.

Vehicle running emissions are modeled utilizing the California Air Resource Board (CARB) (2000, 1998) EMFAC/Burden model. This is a regional emissions inventory model; however, we run the model including only vehicles (in the model’s database) for Southern California for the model years and generic vehicles noted before, and using the default values for all of the other model inputs. It should be noted that the results are based upon the model’s modified Federal Test Protocol drive cycle; i.e., taking into account different modal conditions. (This allows us to simulate transit using constant “average” speed, while still calculating emissions reflecting typical modal conditions.) Additionally, it is well known that the VOCs of tailpipe emissions are comprised of numerous toxins and carcinogens, such as benzene, toluene, formaldehyde, 1,3-butadiene, acetaldehyde, and others. We utilize data from the literature (e.g., USEPA, 2000; Winebrake and Deaton, 1999; Black, et al., 1998; Carslaw and Fricker, 1995; McCormick, et al., 2000; and Nylund and Lawson, 2000) to estimate these components of emissions from gasoline- as well as CNG- and diesel-powered engines. Finally, diesel emissions—in particular, the particulate and aerosol component—are known to be comprised of potent carcinogens, mostly in the form of poly-aromatic or poly-cyclic compounds. We differentiate diesel particulates (denoted as DPM-10) from particulates emitted from other sources (denoted as PM-10) in our model for this reason.

To estimate the impact (life-cycle inventories) for the other life-cycle stages, we utilize the EIO-LCA model and database available from Carnegie Mellon University, at the Green Design Initiative (2001) website at http://www.eiolca.net. Environmental impacts determined by the model include criteria pollutant, global-warming, and ozone-depleting emissions; non-renewable energy consumption; base and precious metal ore depletion; non-hazardous and RCRA waste generation; and Toxic Release Inventory (TRI) emissions. In the case of the latter, the Carnegie Mellon researchers devised an equivalency measure—based on American Conference of Governmental and Industrial Hygienists (ACGIH) Threshold Limit Values (TLVs) (Horvath, et al., 1995). The results of our life-cycle inventory analysis, with impacts summed over all life-cycle stages, are presented as Table 1 (where reported TRI emissions are on a CMU-Equivalent Toxicity basis). Details concerning the calculation and basis of these values are provided in Appendix A.

LIFE-CYCLE IMPACT ASSESSMENT BASIS

From a decision-theoretic perspective (e.g., Keeney, 1992, 1988), it is not the impacts (e.g., tailpipe pollutant emissions) per se that are the basis for concern or the appropriate basis for optimization. Rather, it is the consequences of these impacts—e.g., human health and ecological damages—that are the basis for caring and should be the optimization basis. This is also consistent with the overall SETAC (1993, 1991) LCA framework, which provides for the following LCA steps:

· Inventory. The development of a detailed listing of all material and energy inputs and outputs, including quantities, having an environmental impact;

· Classification. Identification of indicator or impact categories and assignment of inventory components to the impact categories;

· Characterization. Analysis of the impacts/impact categories in terms of human health damage, ecological damage, and resource depletion (end-point effects);

· Valuation. Assignment of relative weights or priorities to each of the end-point effects, allowing, in effect, a single “score” to be calculated and used for prioritizing alternatives.

Additionally, the SETAC framework allows for LCA to be performed at different levels of analysis, including loading (Level 1); equivalency (Level 2); toxicity, persistence, and bio-accumulation (Level 3); and exposure/effects assessment (Levels 4/5). Equivalency analysis (sometimes called “mid-point” analysis) considers only impact categories (e.g., global warming) and the potential to cause damage (e.g., global warming potential). Exposure/effects analysis (sometimes called “damage function” or “end-point” analysis) includes identification of the cause-consequence chains and considers end-point damages (e.g., human morbidity and mortality) caused by the impacts (categories) considered in the analysis. (For future reference, we denote the former analyses as providing measures of damage potential and the latter analyses as providing measures of potential damage.) An informative overview of current LCA and LCIA practice may be found in Curran (1996).

Within this overall framework, the classification, characterization, and valuation of environ-mental consequences are performed in the life-cycle impact assessment (LCIA) step of LCA. Recently, numerous LCIA suites—including models, methods, databases, and, often, companion software—for this purpose have appeared and are in common usage. (Reviews of these are provided by Jensen, et al., 1997, and Postlethwaite and de Oude, 1996.)

From both the practical and theoretical perspectives, there are many contemporaneous issues associated with these LCIA methods, such as what the results represent insofar as actual damages that may be accrued (Owens, 1999, 1997a, b; Goedkoop and Spriensma, 2000a, b; Besnainou and Coulon, 1996); which method is “best” for a particular application or analysis, since the methods do not provide data for identical sets of compounds (“stressors” in SETAC terminology) or end-point damages (e.g., Hertwich, et al., 1998; Notarnicola, et al., 1998); and the decision-theoretic validity of the valuation “formulas” that are prescribed by some of the methods (Miettinen and Hämäläinen, 1997; Seppälä, 1998; and Seppälä and Hämäläinen, 2001). Because of issues such as these, it has been suggested within the LCA technical community (Bare, et al., 2000) that LCIA results based on multiple methods (levels) of analysis might be used together to facilitate better, or, at least, more informed decision-making. For example, an analysis by Swanson, et al. (2000) found the damage indicators from several LCIA methods and levels of analysis to be complementary in nature; and, the use of data from multiple methods is intuitively appealing.

We address these issues in the next section of this paper, where we develop a decision-theoretic model. For now, what is important to understand is that the damage indicators (both mid-point and end-point) provided by the previous LCIA methodologies provide performance measures or attributes (representing environmental damages or consequences) for use in our decision and optimization models. That is, attributes are used to measure the levels of achievement of the stated objectives. We first identify the specific LCIA methods to be used, along with unit damage indicator values, for the stressors identified in the LCI (Table 1), and then consider their use as decision attributes. Finally, we use the results of the decision model (in the next main section) as the basis for specifying necessary weighting constants in the vehicle routing and scheduling objective function.

Selection of Proxy Attributes for Human Health and Ecological Damages

Shown in Tables 2 and 3 are indicator values, for the stressors listed in Table 1 (LCI), from several popular LCIA methods and/or sources: EPS (Steen, 1999a, b); Eco-Indicator (Goedkoop and Spriensma, 2000a, b); human and ecological toxicity potentials developed by Huijbregts, et al. (2000), based on the Uniform System for Evaluation of Substances (USES) LCIA model; and acidification and eutrophical potentials reported by Huijbregts (1999a). Also included in the Tables are potentials (equivalency factors) for global warming, photochemical oxidant creation, and acidification (USEPA, 1996b; CML, 2001) as well as hazard scores for human, aquatic, and terrestrial toxicity, based on USEPA’s (1994) hazard assessment methodology. The indicators were selected to include both end-point and mid-point damages, i.e., representing potential damage and damage potential, as these terms were defined previously, chosen as representative of LCA methods in current, popular use. While the final form and appearance of the decision model(s) we develop are predicated on the indicators selected, we point out that other indicators could have been utilized just as well. That is, our purpose is to provide a methodological approach for the construction and evaluation of decision models utilizing indicators from multiple LCIA methods as opposed to a prescription for a specific model.

Several important points should be noted before we proceed further. First, the values shown in the Tables, in particular, for end-point indicators such as those from the EPS and Eco-Indicator methods, are unit values and are the “raw” indicator values provided by the methodologies before application of the methodologies’ weighting or normalization factors. We develop our own weighting factors for the decision model that we develop, next. Second, as explained in the notes accompanying the Tables, we have combined the various EPS human morbidity and mortality indicators into a single constructed attribute “Calculated Disability-Adjusted Life-Years” (CDALYs) following an approach developed by Murray and Lopez (1996, reported in Goedkoop and Spriensma, 2000a). Similarly, we combined the various EPS indicators for (crop, wood, fish/meat) productive capacity losses into a similar constructed attribute “Productive Capacity Losses.” We did this at this point as a matter of convenience and based on assumed decision-maker preferences. However, as seen in the decision model presented in the next section, we would have had to perform such aggregation at some other stage of the decision model evaluation if we had not done so here. (For a discussion of constructed attributes, their use in decision analysis, and their specification and evaluation, see Keeney, 1992.) Third, we follow Owens’ (1999, 1997a, b) and Besnainou and Coulon’s (1996) view that the damage indicators provided by the previous LCIA methods provide performance indicators, albeit useful for comparative analyses, rather than precise predictions of actual damages that will be accrued. As such, following Keeney’s terminology, decision attributes defined based on these indicators are proxy attributes. Finally, it might be noticed that the stressors identified in Table 1 include certain resource consumptions (e.g., base metal) and other impacts (e.g., RCRA and solid wastes) for which data is not provided in Tables 2 and 3. The reason for this, which will be seen later, is that we use these impacts and quantities directly in the decision model; and, this is also why we have focused our attention on human health and ecological damages exclusively up to this point.

DECISION-THEORETIC BASIS AND MODEL

Because of the underlying differences and limitations in the LCIA methods above, we wish to utilize the data (damage indicators) from multiple methods and levels of analysis in our decision model, as suggested by Bare, et al. (2000). And, we develop a decision model utilizing data from multiple LCIA methods based on decision-theoretic principles. We note, however, that our objective is a decision model utilizing various LCIA damage indicators and not the de facto synthesis of a new LCIA damage assessment model. That is, we do not wish to alter the various methods’ impact categories, damage functions and indicators, and internal stressor and damage allocations.

The decision problem as described thus far is a classic formulation in multi-objective multi-attribute (MOMA) decision analysis, where the decision objectives include not only environ-mental damages but also cost- and service-related objectives, which we add to the model later. Numerous, theoretically rigorous methodologies such as utility theory (e.g., Fishburn, 1970, 1964; Keeney and Raiffa) or T.L. Saaty’s (1977) analytic hierarchy process (AHP) are available for such problems (see, also, Seppälä, et al., 2002.) For the problem at-hand, we assume a typical decision-maker willing to trade off accomplishment of the objectives above, consistent with current LCA practice. Moreover, the valuation formulas of current LCIA methods such as EPS and Eco-Indicator should be seen to be utility-based (e.g., Seppälä, 1998; Seppälä and Hämäläinen, 2001). Thus, to maintain consistency with current LCA practice and LCIA methods, we choose utility theory as the basis on which to develop our decision model.

Unlike most other decision methods, multi-attribute utility theory, based on the game theory of von Neumann and Morgenstern (1947), also provides a rigorous treatment of decision-maker attitude toward risk (i.e., probabilistic outcomes). (We follow the convention that “utility” models describe preferences for outcomes that are probabilistic and “value” models describe preferences for outcomes that are deterministic.) A theoretical discussion of utility theory’s axiomatic basis may be found in Luce and Raiffa (1957). Because we are considering the damage indicators provided by LCIA methods as proxy measures for actual damages (where minimization of the latter is our true or fundamental decision objective), we develop the decision model as a utility model. We also assume a decision-maker who is risk-neutral, in part, to maintain consistency with current LCIA methods. And, we assume that the other requisite conditions for a valid utility function hold (e.g., as described in Luce and Raiffa, 1957).

Basic Decision Model

We follow Keeney’s approach, overall, for the specification and hierarchical structuring of fundamental decision objectives. Following SETAC (1993, 1991), we specify the highest-level objectives as minimization of Human Health Damage, Ecological Damage, and Resource Depletion; and, we add the additional objective of minimization of Other Impacts to address those impacts from Table 1 (e.g., solid and RCRA wastes) for which consequence (damage) data is unavailable. As suggested by Bare, et al. (2000), we consider both mid-point and end-point indicators, i.e., damage potential and potential damage, for the human health and ecological categories; and, we specify these as sub-objectives. The basic decision model (objectives hierarchy) as developed thus far is shown in Figure 2, where the relationship between objectives and attributes (LCIA damage indicators from Tables 2 and 3) is also shown. In the Figure, the w_i’s are preference-based weighting or scaling constants. Additionally, we have combined Huijbregts, et al.’s (2000) various (USES-LCA-based) ecological toxic potential indicators (from Table 3) into a single constructed attribute, Eco-Toxicity Potential, following a procedure that we describe next.

Figure 2. Basic Decision Model

Aggregation of Proxy Attributes

From a theoretical perspective, there are two significant, related issues that must be addressed in order to aggregate LCIA damage indicators as decision attributes as implied in Figure 2. First, decision-maker preferences must be assessed based on actual consequences (Keeney, 1992), even though the damage indicators, as proxy attributes, provide only an imprecise measure of them (e.g., Owens, 1999, 1997a, b). Second, the underlying models from which the damage indicators are derived are not identical and consider different intermediate impact categories, damage functions, etc. That is, in order to combine damage indicators (as proxy attributes) from multiple LCIA methods, it is necessary to make factual-based judgments comparing the magnitude of actual damages represented by the respective indicators, in consideration of the methods’ underlying damage models. Ordinarily, this would not be a consideration in the combination of indicators from a single LCIA method. In our decision methodology, we address both of these issues; however, for brevity, we present only the highlights (below) as well as the final result.

We use Huijbregts, et al.’s (2000) various ecological toxicity potentials (Table 3)—specifically, their combination into a single constructed attribute, Eco-Toxicity Potential—to illustrate our overall methodological approach for aggregating proxy attributes with the above considerations in mind. Keeney (1992) provides an illuminating discussion of the problems associated with the use of proxy attributes, in particular, the need for the decision-maker to make a combination of factual-based judgments (pertaining to the levels of actual consequences associated with the proxy values) and value-based judgments (concerning the relative desirabilities of the actual consequences). This combination of judgments is problematic according to Keeney. And, he provides an approach wherein the judgments are decoupled and the factual-based judgments are made on a probabilistic basis. While Keeney’s approach could be applied to the problem at-hand, we expect many decision-makers would have difficulty elucidating the required probability distributions. Moreover, we feel the imprecision that is associated with LCIA damage indicators as predictors of actual damages is more aptly treated as vagueness than as probabilistic uncertain-ty. Specifically, we utilize (fuzzy) linguistic variables to represent the actual consequences as possible, rather than probable, outcomes, based on Zadeh’s (1978) representation of fuzzy sets as possibility distributions, where we also implicitly assume that the requisite von Neumann and Morgenstern axioms concerning probabilistic outcomes hold for possibilistic outcomes, as well.

Our overall procedure is illustrated in Figure 3; however, we note again that this procedure is also utilized in other aggregation steps when the decision model is evaluated. We calculate the unit damage indicator, Ecological Toxicity Potential (USES-ETP), denoted as D_ij, value for each substance i listed in the LCI (Table 1), as

D_ij = å_k [(w_kb_kD_ijk) / (å_kw_kb_k)], (1)

where w_k has already been normalized. The D_ijk’s are the substance- and compartment-specific USES-LCA unit damage indicators (listed in Table 2). (Notationally, the subscript “j” is used to identify damage indicators and associated decision attributes; if USES-ETP were the only damage indicator in the decision model, there would be no need for the subscript. And, the subscript “k” denotes impact categories or compartments, e.g., marine sediment. Fuzzy quantities are indicated in bold-italic typeface.)

Figures 3. Model for Evaluation of Constructed Attributes with Value

and Factual Judgments De-Coupled

Values of b_k, representing factual judgments concerning the magnitude of actual consequences associated with the compartment-specific indicators, are represented using normal, triangular fuzzy numbers representing linguistic variables. For example, the decision-maker may compare actual consequences associated with Huijbregts, et al.’s, specific potentials using linguistic variables such as “much greater,” “about the same,” etc. (See Figure 4.) Further, in Huijbregts, et al.’s methodology, toxicity potentials are calculated based on a single reference substance (1,4-dichlorobenzene). In other words, only one b_k based on 1,4-dichlorobenze is assessed for each damage compartment. Finally, following LCIA and utility theory conventions, we assume that value-based judgments, comparing consequence desirability and used to evaluate the w_k constants, can be made on a scalar basis.

Decision-Maker Preference Assumptions, Evaluation of Single-Attribute Utility Functions, and Overall Utility Equation Forms

Before we can proceed to specification of the final decision model, including aggregation of attributes based on damage indicators from multiple LCIA methods, we address some prerequisite matters concerning decision-maker preferences (assumptions) and resultant utility equation forms. First, following the convention of current LCIA methods, we assume that single-attribute (unidimensional) utility functions have a constant rate of (utility) substitution; i.e.,

Figure 4. Linguistic Variables for Damage Comparison

single-attribute utility functions are linear. For example, let D_j denote the value of (potential damage or damage attribute) attribute j. Then,

u(D_j) = - [D_j – D_j(BEST)] / [D_j(WORST) – D_j(BEST)], (2)

where D_j(WORST) and D_j(BEST) denote the “worst” and “best” values of attribute j, respectively, among the alternatives considered. Note that we have defined the utility scale such that 0 is “best” and –1 (or “about minus 1” in the case of fuzzy numbers) is “worst.” However, in our (paratransit scheduling) application we do not know the “best” and “worst” values of D_j a priori. Instead, we define reference values based on estimation of the best and worst possible scheduling scenarios. We define D_j(_BEST) = 0 and redesignate D_j(WORST) as D_jREF. Then, because of assumed linearity of the unidimensional utility function,

u(D_j) = - D_j / D_jREF. (3)

For an attribute based on a single LCIA methodology, we evaluate the attribute following the methodology’s convention. In general, attribute (D_j) values, representing “total” damage or damage potential of type j, are calculated as:

D_j = å_iI_iD_ij= å_iå_kI_iD_ijk, (4)

where I_i is the quantity of stressor i (from the LCI), D_ij is the stressor-specific unit damage indicator for stressor i and attribute (damage type) j, and D_ijk is the stressor-impact-specific unit damage indicator if such is provided by the methodology. Here, in the case of end-point or damage function LCIA methods (such as EPS and Eco-Indicator), the allocation of stressor i over the modeled impact categories and damages is performed by the methodology (and is reflected in the unit damage values, to facilitate the previous type of calculation); and, we do not alter these allocations. In the case of attributes based on mid-point or damage potential indicators (e.g., global warming potential), we allocate the stressor quantity 100 percent to each applicable impact category following USEPA (1996b, 1994).

Utility theory provides for the combination of preferences for multiple attributes (representing multiple objectives) into a single value as:

u(x₁, x₂, …, x_n) = f[u₁(x₁), u₂(x₂), …, u_n(x_n)], (5)

where the actual form of f[u_i(x_i)] is predicated upon whether certain preference independence conditions (among attributes) are met. In the case of utility functions, if the attributes X_iare additive independent (which also implies mutual utility independence among attributes), an additive utility decomposition form may be used, i.e.,

u(x_i) = å_iw_iu_i(x_i), where å_iw_i=1. (6)

That is, the preference (level) for an alternative is the simple sum of the appropriately scaled preference levels of each attribute comprising the alternative. If attributes X_i are each mutually utility independent (only), a multiplicative form may be used, i.e.,

Ku(x₁, x₂, …, x_n) + 1 = Õ_iⁿ [Kk_iu_i(x_i) + 1]. (7)

Both are special cases of the multi-linear utility function (see Keeney, 1992, for a proof),

u(x₁, x₂, …, x_N) = å_i=1 k_iu_i(x_i) + å_i=1å_j>1 k_iju_i(x_i)u_j(x_j) +

å_i=1å_j>iå_h>j k_ijhu_i(x_i)u_j(x_j)u_h(x_h) + … (8)

Because of the large number of attributes for which preference independence would have to be tested, we, instead, limit consideration to the additive and multiplicative forms as recommended by Zeleny (1982) and Keeney and Raiffa (1993), including the nesting of such forms within a larger overall model, as these forms have been shown to provide robust representations of decision-maker preferences. As a consequence, we assume attributes to be either additive or mutually utility independent (only).

From the above discussion and the objectives structure of Figure 2, our intended direction may be inferred. Namely, let the following denote decision sub-objectives (with associated attributes):

H º Human Health Damage

E º Ecological Damage

R º Resource Depletion

O º Other Impacts

HD º Human Health Potential Damages

HP º Human Health Damage Potential

ED º Ecological Potential Damages

EP º Ecological Damage Potential.

Then, from the objectives structure in Figure 2, we define utility functions such that:

u(itinerary) = f[u_H(H), u_E(E), u_R(R), u_O(O)], (9)

where

u_H(H) = f[u_HD(HD), u_HP(HP)] (10)

u_E(E) = f[u_ED(ED), u_EP(EP)], (11)

and where these individual utility functions are evaluated utilizing the damage indicators (as attributes) shown in Figure 2.

Following current LCIA practice, we assume the highest-level attributes of Equation 9 to be additive independent. In simple terms, additive independence implies that the preference order for alternatives is dependent only on the values and associated uncertainties of the attributes individually and not in combination. (See Keeney, p. 134, for a more precise and technical definition.) And, we also see this assumption as reasonable for the aggregation of attributes within the individual damage potential and potential damage utility functions, i.e., evaluation of u_HP(HP), u_HD(HD), u_EP(EP), and u_ED(ED).

However, current LCIA practice does not provide guidance insofar as the combination of damage potential and potential damage attributes. Here, we provide for the possibility (although not necessity) that a decision-maker’s preference for the values of one set of attributes is not independent of the values and uncertainties (technically, as lotteries, or in this case, as possibility distributions) involving the other set of attributes. And, we assume only the weaker condition of mutual utility independence.

The result of these assumptions is that we may specify a decision model of overall form:

u(itinerary) = w_Hu_H(H) + w_E u_E(E) + w_R u_R(R) + w_Ou_O(O), where (12)

u_H(H) = w_HDu_HD(HD) + w_HPu_HP(HP) +

(1-w_HD-w_HP) u_HD(HD)u_HP(HP), (13)

u_E(E) = w_EDu_ED(ED) + w_EPu_EP(EP) +

(1-w_ED-w_EP)u_ED(ED)u_EP(EP), (14)

where w_H + w_E + w_R + w_O = 1, all other terms are as defined previously, and where equations for evaluation of u_R(R), u_O(O), u_HD(HD), u_HP(HP), u_ED(ED), and u_EP(EP) remain to be defined.

Finally, we note one important point concerning the utility functions above and assessment of scaling constants. Because of certain assumed preference conditions (decision-maker risk neutrality and additive independence among attributes within each of the HD, HP, ED, EP, R, and O damage domains), utility functions and value functions (i.e., based on deterministic outcomes) assessed over these domains must be coincident. Specifically, since we are also assuming a decision-maker who is risk-neutral, where u(x) ~ v(x), a utility function (u[x]) assessed over an additive value function (v[x]) must also be additive. This means that if we were assessing preferences for an actual decision-maker, once we have determined that the decision-maker is risk-neutral, we can assess preferences based on deterministic outcomes (rather that lotteries involving uncertain outcomes) and induce utility functions over the assumed (linear) value functions. Similarly, it allows us to combine utility functions and value functions directly. Had these preference conditions not been the case, we would have had to assess utility functions based on uncertain outcomes or estimated the functions from assessed value functions and assessment of the decision-maker’s risk tolerance. (Procedures for both may be found in Keeney and Raiffa, 1993) Additionally, we note one important distinction between value and utility functions: value functions provide cardinal measures, while utility functions provide only ordinal measures, insofar as strength of preference (Keeney, 1992). That is, differences of utility values do not have cardinal meaning.

Evaluation of End-Point Damage-Based Utility Functions, u_HD(HD) and u_ED(ED)

As seen in Figure 2, we evaluate the end-point damage-based utility functions, u_HD(HD) and u_ED(ED), based upon the damage indicators provided by the EPS and Eco-Indicator LCIA methodologies. However, the problem that arises is that the two methods, even though generally considering the same stressors and impact categories, do not assign the stressors identically to the same impact categories, as is more clearly seen in Figures 5a and 5b. Hn.

Hence, the resultant indicators, e.g., for species loss (NEX and PDF, respectively), are not comparable measures. In other words, decision-maker factual judgment insofar as the magnitude of actual damages represented by each proxy measure for each stressor is necessary. However, if we followed the methodologies’ conventions and aggregated damage indicators across stressors (Equation 4) first before calculating utility values (Equation 3), the differences between the two methods would be masked by the aggregation and there would be no basis on which to make the necessary factual judgments.

A direct solution to this problem may be found by combining Equations 3 and 4. Specifically, it should be seen (in the case of damage indicators from a single LCIA method) that

u(D_j) = - [å_iI_iD_ij / D_jREF] = å_iu(D_ij), (15)

where u(D_ij) = - I_iD_ij / D_jREF. and D_ij is the stressor-specific unit damage indicator for stressor i, as before. This is true because of the assumed linear single-attribute utility function, the linear manner in which the methods combine stressor- and impact-specific damage indicator values, and the way that D_jREF has been defined. The quantity u(D_ij) may be thought of as a “partial utility value,” attributable to stressor i, and where the utility value (of an alternative) taking into account all stressors is the sum of the partial utility values. Thus, to combine indicators from multiple (EPS and Eco-Indicator) methods, we follow an approach similar to that previously utilizing linguistic-based factual judgments. (We also adjust the “spread” of the fuzzy variables to reflect the relative degree of imprecision associated with the methodologies. In this case, because the indicators and methods provide less imprecise indicators than before, we use narrower “spreads.”) Let A_Xl denote a decision attribute (X Î HD, ED damage domains, l = 1, 2, …) and a_Xli be the value of A_Xlfor stressor i. Then:

u_Xli(a_Xli) = - å_j{I_iå_k[(D_ijk)(b_Xlijk)] / D_j(REF)}, " D_jÎ A_Xl (16)

where the b_Xlijk values are normalized values representing factual judgments as to the relative significance (in terms of actual damages) associated with each damage indicator D_ijk, evaluated for each damage type j and stressor i. For example, Human Health Potential Damage is evaluated based on one attribute A_HD1 (l = 1), which, in turn, is evaluated utilizing the EPS CDALY and Eco-Indicator DALY damage indicators (e.g., D_j=1 and D_j=2). Values of b_HD1ijk are ascribed for each stressor i and impact category k (global warming, human toxicity, oxidant creation; k=1, 2, 3). Assumed values of b_HD1ijk are provided in Table 4 to illustrate the process. Finally, the partial utility values are then aggregated over all stressors as:

u_Xl(a_Xl) = å_iu_Xli(a_Xli), for X = HD, ED. (17)

Values of u_HD(HD) and u_HP(HP) and then calculated simply as:

u_X(X) = å_lw_Xlu_Xl(a_Xl), l = 1, 2, … ; å_lw_Xl = 1; for X=HD, ED. (18)

In the above calculations, it should be seen that we are aggregating fuzzy quantities, in the calculation of utility values, as fuzzy weighted averages, i.e., as r = (å_l=1^L w_lu_l(A_l) / (å_l=1^L w_l). (See, for example, Klir and Yuan [1995].)

Evaluation of Mid-Point Damage-Based Utility Functions, u_HP(HP) and u_EP(EP)

The procedure for evaluation of the mid-point-based damage potential utility functions, u_HP(HP) and u_EP(EP), is more or less similar to the previous procedure with certain exceptions. From Figure 2, the two constructed attributes, Human Toxicity Damage Potential (based on the damage indicators USES HTP and EPA-HHHRF) and Eco-toxicity Damage Potential (based on the damage indicators USES-ETP, EPA-THRF, and EPA-AHRF) are first evaluated. In the first case, because both indicators provides measures of the same type of damage potential (human health), only factual judgments are required and partial utility values may be calculated using Equation 16. In the latter case, both value- and factual-based judgments are required, since the indicators represent different types of damage potentials. In this case:

u(a_Ej) = - å_k {[h_Eke_Ek (DP_jk / DP_jk(REF))] / [å_kh_Eke_Ek]}, (19)

where h_Ek and e_Ek are value- and factual-based weighting constants, respectively (e.g., as in Figure 3). Single-attribute utility values for all other lowest-level attributes, u(a_Xj), evaluated based on a single damage indicator, may be evaluated following Equation 3. Utility values for the decision attributes B_X, where X = HP, EP, are evaluated as

u_X(B_X) = å_j{[c_Xjd_Xju(a_Xj)] / [å_jc_Xjd_Xj]}, (20)

where c_Xj and d_Xj are value- and factual-based weighting constants, respectively. (Values of c_Xj and h_Ek are normalized because of the assumed linear-additive decomposition form. Normalized values of e_Ek and d_Xj may also be used; however, it should be seen in Equations 19-20 that it is the product, e.g., å_jc_Xjd_Xj, that is normalized in the calculation itself.)

The most important difference in this case is that the value- and factual-based scaling constants are not assessed for each stressor i. Rather, they are ascribed based upon the impact category, as it is assumed that the equivalency factors on which the damage indicators are based take into account stressor-specific differences.

Evaluation of Resource Depletion and Other Impacts Utility Functions, u_R(R) and u_O(O)

Utility values for Resource Depletion and Other Impacts objectives (attributes) are calculated directly from the LCI quantities (Table 1). In the case of the latter, we do this because of the lack of readily available consequence data, and, in the case of the former, because of the lack of consensus damage measures within the LCA community (e.g., Guinee and Heijungs, 1995; Hertwich, 1996). (However, this does not obviate entirely the need for the decision-maker to consider the consequences of these impacts, i.e., in the assessment of weighting constants.) We also assume that the attributes comprising the Resource Depletion and Other Impacts objectives to be additive (and mutually utility) independent, allowing simple, linear-additive utility functions to be defined for each. Following the previous nomenclature:

u_R(R) = å_jw_Rj u(D_j), " D_jÎ R, å_jw_Rj = 1 (21)

u_O(O) = å_jw_Oj u(D_j), "D_jÎ O, å_jw_Oj = 1 (22)

u(D_j) = – (D_j / D_j(REF)), D_j(REF) ³ max[D_j] among alternatives (23)

D_j = å_iI_i D_ij, " D_jÎ R, " D_jÎ O; D_ij= 1 if D_j Î {R, O}, 0 otherwise. (24)

It should be seen in the above that D_ijin this case is a dummy variable used to maintain consistency of nomenclature and to provide for the use of damage indicators other than stressor quantity in the decision model, if desired. Finally, we note that the utility functions above are, technically, value functions, as there is no uncertainty of outcome involved.

Evaluation of Value- (Preference-) Based Weighting Constants

We assume that value- (preference-) based scaling constants, representing the relative desirabilities of the attributes (as consequences), can be assessed on a scalar basis, following LCIA and utility theory practice. Techniques for the elicitation of decision-maker preference may be found in Pöyhönen and Hämäläinen (1997) as well as Keeney and Raiffa (1993). Importantly, these constants are relative to, and must be assessed based upon, the range of outcomes (i.e., the reference values) considered (Keeney, 1992). Also, importantly, the scaling constants (w_k’s) must be evaluated utilizing preference, i.e., u(x) values as opposed to attribute (x) values, in order to identify points of preference indifference. Keeney and Raiffa (1993) provide a rigorous approach for the assessment of scaling constants. Procedurally, their approach entails the comparison of changes of attribute values (e.g., Dx₁ and Dx₂) and corresponding changes of utility values, i.e., Du₁(Dx₁) and Du₂(Dx₂), to find values of Dx₁ and Dx₂ such that Du₁(Dx₁) = Du₂(Dx₂) (from which weighting constants can be calculated), where the consequence scales are normalized scales.

Calculation of Itinerary (Environmental) Utility Function Values and Defuzzification of Results

For any itinerary, the transit distance, engine idling time, and number of engine starts can be determined. (Engine idling and starts occur at nodes, following an assumed paratransit service/ operational policy. This is discussed later.) LCI impacts for an itinerary are calculated by multiplying the previous quantities by the unit impact factors provided in Table 1 for the applicable vehicle type. Damage indicator (attribute) values are calculated by multiplying the resultant impact quantities by the unit damage indicator values provided in Tables 2 and 3 (i.e., Equation 4). And, the itinerary utility value (Equation 12) is calculated utilizing the utility relationships described in the Sections 4.2 through 4.6.

From the various equations, it should be seen that certain of the calculated intermediate quantities are (normal, triangular) fuzzy numbers. However, because fuzzy numbers cannot be ranked or ordered as scalar numbers can, they must be defuzzified on some basis. As a general rule, because the fuzzy number (set) contains distributional information, we do not defuzzify calculated values until after the final calculation, to avoid loss of this information. (For a discussion of fuzzy arithmetic calculations, as well as defuzzification algorithms, see, for example, Klir and Yuan, 1995.) For this purpose, we use the common Center of Area (COA) defuzzification algorithm, which returns the support (x- or abscissa) value of the centroid of the fuzzy possibility distribution, i.e., x_c = (x₁ + x₂ + x₃) / 3, where x₁, x₂, and x₃ are the x- values of the vortices. In the case of a triangular fuzzy number (a, b, c), it should be seen that the x- values correspond to the quantities a, b, and c, respectively.

Decision Model Translation for Use in Optimization – Calculation of “Unit Partial Utility Values”

Using the decision model just presented, the utility value of an itinerary (in terms of environ-mental consequences) may be calculated based upon the transit distance, engine idling (minutes), and number of engine starts resultant of the itinerary. In terms of the utility calculation, these variables are independent variables (notwithstanding the fact that there are a function of the itinerary itself). And, rather than performing all of the previous calculations repeatedly, it is desirable to transform the model from a decision model to an optimization model, i.e., based on the previous independent variables:

u(itinerary) = f(Distance, Idling, Engine Starts, Vehicle Type). (25)

From the previous equations, it should readily be seen that if the calculated single-attribute utility value for any damage indicator (attribute D_j) is –x for one mile of travel, it will be –2x for two miles of travel, etc., because of the linearities that exist in the calculation of damage values and single-attribute utility functions. Similarly, the same result will hold for the LCI quantities expressed in “per minute engine idle” and “per engine start” units. Further still, the utility functions u_HD(HD), u_HP(HP), u_ED(ED), u_EP(EP), U_R(R), and U_O(O) are also each evaluated utilizing linear-additive combinations of the respective, single-attribute utility functions, i.e., the u(D_j)’s, from which they are evaluated. The point is that these functions can be evaluated once for each vehicle type and each vehicle operational unit, i.e., a mile of travel, a minute of engine idling, and an engine start. And, Equations 12-14 (for calculating the itinerary utility value) may then be evaluated directly from these unit quantities together with the known number of respective units, i.e., miles of transit, minutes idling, and number of engine starts. Illustrative values of these “unit partial utility factors,” calculated based upon values of factual- and value-based weighting constants that we have assumed for a hypothetical decision-maker, are provided in Table 5. Details of the calculation of these values are provided in Appendix B. Values of assumed decision-maker weighing constants may be found in Appendix C.

PARATRANSIT OPERATION, MODELED SYSTEM AND MULTI-OBJECTIVE SCHEDULING ALGORITHM, AND EXPERIMENTAL DESIGN

In general, paratransit service is provided “door-to-door”; that is, the client is picked up at a requested location and transported to a desired location. In this regard, service is similar to taxi service. However, unlike taxi service, ridesharing (combining multiple, non-related clients having non-identical origins and destinations) is allowed. Moreover, increasing ridesharing is seen as key to improving productivity (Dessouky and Adam, 1998a). Also in general, two types of service requests are provided for: advance requests and same-day (“ASAP” or “immediate”) requests. Planned vehicle routes (itineraries) for advance requests typically are determined in advance. However, the planned routings must then be modified dynamically and in real-time to accommodate same-day or “ASAP” requests. The latter task, called dispatching, may be facilitated with the aid of certain ITS technologies, such as automatic vehicle location (AVL) and geographic information systems (GIS). Because of clients’ physical disabilities, specially equipped vehicles—in particular, those than can accommodate wheelchair-bound patrons—are utilized. It should be noted, however, that not all clients are necessarily wheelchair-bound, and that paratransit fleets are often composed of multiple vehicle types for this reason.

Paratransit providers must comply with certain standards, including those prescribed in regulations as well as in contractual terms. For example, the provider may be penalized (e.g., by the transportation authority) if the provider refuses “appropriate” service requests or misses agreed upon time windows (for example, +/- 15 or 20 minutes of the agreed upon time). Conversely, the provider may receive performance incentives based on service and economic performance, e.g., productivity and utilization of resources. In practice, ride requests are assigned to vehicles in a manner that minimizes an objective function comprised of cost and service performance objectives. (See, for example, Chira-Chavala, 1999 and Dessouky and Adam, 1998a.)

Paratransit Vehicle Scheduling

The paratransit (DAR) optimization problem is a problem in combinatorial optimization and is a combined vehicle routing and scheduling problem as described before. Following the taxonomy of Psaraftis (1980) and Jaw, et al. (1986), the paratransit problem of interest is “many-to-many” (origins and destinations), multi-vehicle, and having time windows. Specific cases of the problem include static (advance reservation) scheduling and dynamic (immediate service) dispatching. There may also be additional constraints, including service constraints (e.g., maximum ride times), vehicle capacity, as well as precedence and other logical constraints. Numerous algorithms for DAR routing and scheduling have been developed and reported in the literature, generally for simplified versions of the real-world problem. Overall, the algorithms (where time windows are assumed) can be dichotomized based upon whether they are for the static or dynamic case, for single- or multiple-vehicle systems, and exact or heuristic.

Early research to develop scheduling algorithms was generally based on the construction and solution of minimum spanning trees and/or Traveling Salesman Problem (TSP) tours. Psaraftis (1983, 1980), for example, provides both exact and heuristic solutions for the single vehicle case, for both static and dynamic requests, where, in the case of the latter, the tour was reoptimized every time a new request was received. Stein (1978) provided an analytical examination of both single- and multi-vehicle fleets, considering both the static and dynamic cases. He proposes a two-step approach of clustering or partitioning of requests followed by individual tour construction. However, his focus was on optimal partitioning versus solution of the resultant TSP problem. More recently, Ioachim, et al. (1995) modeled the problem as a pick-up and delivery problem with time windows (PDPTW), which they solve in several steps. However, their solution, too, involves the solution of a resultant TSP problem, which they solve by a column generation method.

While exact solutions to the TSP problem are available (e.g., based on Hamiltonian cycles), the problem is NP-hard, meaning that the number of iterations that must be performed increases non-polynomially with the size of the problem. For this reason, heuristic scheduling algorithms are generally utilized in practice; and, two areas of development are of particular note. The first is the development of “insertion” algorithms (e.g., Jaw, et al., 1986; Madsen, et al., 1995; Toth and Vigo, 1997), where requests are tentatively inserted into existing vehicles’ schedules on some heuristic basis, with the preferred insertion being the one that minimizes the objective function of interest. These algorithms can be used to construct initial vehicle itineraries for static requests as well as to modify them dynamically. The second development of note is the development of post-insertion optimization procedures (e.g., Gendreau, et al., 1994, 1992), applicable to itineraries constructed using insertion-type as well as other algorithms.

Modeled Paratransit System and Operation

In the modeled paratransit system, service is provided on a “24/7” basis through the use of shifts. Modeled vehicles can accommodate certain numbers of wheelchair and “regular” patrons, where the capacity of each is fixed. And, the fleet is comprised of different types and sizes of vehicles—with each vehicle type having specific capacities for each type of patron as well as specific (non-identical) economic costs of service and environmental impacts. Two types of requests are provided for: “immediate” and “advance,” where the latter are those received in excess of five hours before the requested pick-up time. Advance requests are scheduled at the beginning of the shift (the first shift on which they could be serviced.) That is, “skeleton” itineraries are created based on the advance requests. Immediate requests are scheduled when received. In our model, transit speed is deterministic and is the same for all vehicles (28 mph, the average transit speed in Los Angeles). However, loading and unloading times are stochastic. It is assumed that the position and status of all vehicles is known at all times; and, the scheduling of immediate requests takes into account the vehicles’ actual statuses.

Time windows are applied to pick-up times (only); and, “maximum ride time” is imposed as a feasibility constraint to prevent excessive ride times (drop-off times) due to indirect routing. For a pickup, the “on-time” window is defined as -x/+y minutes of the requested (assigned) pick-up time, where the “late” window (y) is different for immediate and advance requests. This is a “soft” window, meaning service will proceed no matter how late the vehicle arrives. The “early” window, which is the same for both types of requests, is a “hard” window. If a vehicle arrives before the window (before –x minutes), the vehicle waits and service begins at the “early” window, i.e., -x minutes of the requested pick-up time. Monetary penalties are applied if the vehicle arrives at the pick-up location early or late, i.e., outside of the on-time window. In the modeled system, all vehicles originate and return to a central depot. Overtime is not allowed; and, vehicles must return to the depot by the end of the shift.

Service requests are generated randomly and are not known a priori. Request parameters—including origin and destination locations, requested pick-up times, call-in times, and number and type of patron (wheelchair and non-wheelchair)—are random variables, where the distributional parameters that are used are based on actual data provided by ACCESS Services, Inc., and reported in Dessouky and Adam (1998a, b). Experimental values of these and the previous parameters are provided in Table 6.

Simulated vehicle operation is governed by certain service polices. First, vehicles depart service nodes as soon as service (loading/unloading) is completed and proceed to the next scheduled node, unless the last service node is also the last node on the itinerary. In this case, they wait at the last service node (which must be a destination node), either until another request is received or until such time that the vehicle could depart and return to the depot at the end of the shift. Additionally, vehicles en route between service nodes are not rerouted dynamically. Finally, insofar as engine idling and starting, drivers allow the engine to idle during loading and unloading. Similarly, drivers allow the engine to idle at pick-up nodes if the vehicle must wait (because the vehicle is early) and there are passengers already on-board. (This is done for passenger comfort, e.g., to allow operation of the vehicle’s air conditioner or heater as well as other devices.) On the other hand, if the vehicle arrives at a pick-up node early and there are no passengers already on board, the driver is assumed to turn off the vehicle’s engine and restart it at the time boarding begins. (These considerations do not apply to drop-off nodes, as unloading begins immediately when the vehicle arrives at the node.)

Simulation Model and Model Verification/Validation

To simulate operation of the modeled system, we developed an event-based simulation program written entirely in Microsoft^® Visual Basic^TM 6.0, where “events” include the scheduling of a service request and the arrival of a vehicle at a service node (because of stochastic loading/unloading times). In execution, the program constructs planned itineraries, which are converted during the course of the simulation to executed itineraries as a result of “events.” That is, when an event occurs, the affected vehicle’s itinerary—specifically, planned times subsequent to the event time—may be affected and are modified accordingly. The model makes extensive use of data files, recording all aspects of vehicle itineraries (times and node sequences) as well as request-related service data. These files are used for the calculation of simulation statistics and were used significantly for debugging and model verification. Additionally, the program includes extensive error traps, which were also used for model verification.

To validate the model and program, we compared the simulation results to those of a similar model—based on the same overall request, service, and experimental parameters and paratransit system—and insertion algorithm previously reported by Dessouky and Adam (1998a). For validation purposes, we ran the model with the environmental parameters and values set to zero, and utilizing the same request data (file) as Dessouky and Adam. We then compared the results based on the key performance measures reported by Dessouky and Adam previously. (The measures include those reported in Section 6.)

Basic Real-Time Scheduling Heuristic

We adapt Dessouky and Adam’s (1998a) scheduling objective function to the modeled service policies and penalties described above. Specifically, their algorithm is an implementation of Jaw, et al.’s (1986) parallel insertion algorithm. And, based on the modeled system, we define the objective function based on the weighted summation of three itinerary-related costs: 1) transit cost (based on itinerary distance), 2) lateness penalty (if the vehicle arrives at the pick-up location after the on-time window), and 3) earliness penalty (if the vehicle arrives at the pick-up location before the on-time window).

Modification to Include Environmental Impacts

We next modify the previous heuristic to include environmental impacts. Although we have not stated this explicitly before, we use utility (theory) as the basis for aggregating economic costs and environmental consequences, as they are in different units and there is no consensus approach or data by which to monetize all environmental consequences. Our objective function is of the form:

maximize u(service of requests) = w_Cu(economic cost) +

w_Eu(environmental impact). (27)

Let {R} be the set of requests for service to be scheduled and r_i be the i^th request for service. The provision of service (for request r_i) incurs both an economic cost (denoted as CS_i) and an “environmental cost” (denoted as EC_i). The scheduling objective, generally speaking, is to minimize the combined values of CS_i and EC_i over {R}, i.e., maximize å_i_{ÎR u}(CS_i, EC_i). (The utility values are calculated as disutility, i.e., negative values; thus, the objective is to maximize these values.)

Applying the same (additive independence) preference assumptions as before, the objective is:

maximize å_i_ÎRu(CS_i, EC_i) = å_i_ÎR[w_CSu(CS_i) + w_ECu(EC_i)]. (28)

Let CS_ij* denote the total economic cost of all vehicles’ itineraries (i.e., as Equation 26) after insertion of r_i into vehicle j’s itinerary; and let EC_ij* denote the environmental system “cost” of all vehicles’ itineraries after insertion of r_i into vehicle j’s itinerary. The basis for evaluation of EC_ij* and u(EC_ij*) was discussed earlier. We calculate u(CS_ij*) also utilizing reference values as before, i.e., u(CS_ij*) = - CS_ij* / CS_REF, where CS_REF is the estimated “worst” system cost for the operational period.

An exact solution to this problem would require that either all r_i were known a priori or that all vehicles’ itineraries were reoptimized after each new request was received. And, since neither are feasible or practical, our optimization is heuristic and based on optimizing each request individually:

maximize u(CS_ij*, EC_ij*) = maximize [w_CSu(CS_ij*) +

j j

w_ECu(EC_ij*)] for "r_iÎ{R}. (29)

Finally, before leaving this topic, we note one additional point that was alluded to earlier. We assume that utility functions have only ordinal quality, even though under certain circumstances value functions, having cardinal quality, could be induced as described earlier. And, we do this so that our methodology is not predicated on any particular preference condition, i.e., decision-maker risk neutrality. Because of this, we cannot evaluate insertion costs (as utility values) on a marginal basis. Moreover, because the environmental utility function is non-linear and utility values are relative to the scale on which consequences are evaluated, the alternative that is “best” based on individual vehicle itinerary environmental impacts and associated scales may not, necessarily, be the “best” alternative when evaluated based upon system-wide environmental impacts and scales. And, it is the system-wide impacts of operation, rather than the impacts of any particular vehicle, that is the basis for caring, i.e., the preference basis. Thus, we determine the “best” insertion based on “total system” utility value, evaluated including all in-service vehicles and itineraries, for each request scheduled.

Experimental Design

Values of experimental and other cost/service parameters are provided in Table 6; and, we only briefly discuss the experimental design here in terms of its purpose and overall strategy. Our primary purpose is to demonstrate that, through our methodology and the consideration of environmental parameters in the vehicle routing and scheduling process (i.e., algorithm), the overall environmental impacts of the operation can be substantially reduced. Additionally, we would like to demonstrate that this can be accomplished without equally substantial increases in operating “cost”—which we measure in units of utility as well as dollars and travel distance.

Because the system is stochastic and the variables used to measure system performance are random variables, we utilize the method of independent replications (e.g., Law and Kelton, 1991; Pritsker and O’Reilly, 1999) to reduce the variance of the simulation results. In the simulation program itself, because of the way that service requests are generated and the way the vehicle-shifts are accounted for, the transient effects that would be otherwise be expected to occur at system (simulation) start-up and shut-down have been eliminated. This is to say, we simulate paratransit operation as a terminating system; and, we can replicate single 24-hour operating periods with minimal transient effects that would affect the outcome.

We consider several fleet composition scenarios, where the fleet is comprised of at least two or more vehicle types (from the types in Table 1). And, we also consider the case of a homogeneous fleet. For each scenario, we compare the results—in terms of “cost” and environmental impact—based on scheduling using our algorithm versus those where only economic costs are considered (as in current paratransit scheduling algorithms). We also simulate various levels of system loading (by adjusting the number of available vehicles, since the number of requests per period is constant). Specifically, we would expect to find greater environmental improvement in a system having “surplus” vehicles (including “environmentally friendlier” ones) available. And, we also investigate the effect of varying the weighting constants in the objective function (Equation 29). All scenarios utilize the same sets of service requests.

EXPERIMENTAL RESULTS

Simulation results, for the fleet compositions and fleet sizes (representing different levels of system loading) simulated, are provided in Tables 7 through 11. In the tables, the first row of each composition-size combination (shown in boldface) represents the “baseline,” that is, based on the scheduling algorithm (objective function) considering only economic costs. And, the rows immediately below each “baseline” case are results based on the new algorithm including environmental impact (Equation 29). We first consider the effects of the new algorithm in terms of service performance and then in terms of cost and environmental performance.

As seen in Table 7, together with the vehicle utilization results from Table 9, the three loading levels simulated represent cases of surplus capacity (surplus vehicles available), adequate capacity (all or most available vehicles utilized), and capacity shortage (unscheduled requests). It should also be observed that ridesharing (defined as the number of requests served divided by the number of trip starts) remains relatively constant over all cases and environmental weights, while vehicle utilization increases as capacity relative to demand decreases. In the case of the latter, this represents the elimination of “slack.” This is further evidenced by the trend of increasing mean pick-up delay and decreasing on-time performance. However, taken together, we interpret the constancy of ridesharing as indicating ridesharing is primarily governed by the service and operational policies and constraints, together with the spatial and temporal distribution of requests, rather than by other factors such as capacity. Overall, it should be seen from Table 7 that the effect of increasing environmental weight in the objective function is to increase pick-up delays and decrease on-time performance.

The effects of the new algorithm in terms of cost and environmental performance may be seen in Table 8, as well as in Tables 10 and 11 comparing life-cycle environmental impacts. (From the regulatory perspective, in particular for Southern California, the criteria and other pollutant air emissions [Tables 10a and 11] represent the most significant impacts identified in the LCI [Table 1]. Moreover, when examined by life-cycle stage, up to one-half or more of the total life-cycle emissions, depending upon pollutant, are attributable to vehicle operation, service and maintenance, and fuel refining and distribution—all of which would be expected to occur in the Southern California region.) From Table 8, it should be immediately seen that the most significant improvement in terms of environmental impact (as utility value) relative to the “baseline”—both alone and relative to marginal cost increase—occurs at the smallest environmental weighting factor. That is, while further environmental improvement may (or may not) be possible, it comes with increasing marginal cost. Moreover, from Table 7, the service impacts are the least affected. Thus, we believe many decision-makers would find this case (w_ENV=0.125) to represent the best marginal “trade-off.” And, we consider only this case in the remaining discussion.

Overall, the greatest environmental improvement (in terms of utility value and specific pollutants) is seen to occur in Case I, the heterogeneous fleet comprised of four types of vehicles. (This is also our primary case of interest.) And, improvement occurs at all three levels of system loading. For example, in the “best” (surplus vehicle) case, as measured in utility values, environmental performance is improved by about 33 percent while cost is increased by only about 4 percent. However, all Case I improvements (considering only the “baseline” and w_ENV=0.125 cases and based on utility value) are statistically significant at the 95 percent (a=0.05) confidence level.⁽^{1, 2)} Moreover, for this case, the apparent, slight cost increases for the first two loading levels are not statistically significant at the same confidence level.

Environmental improvements (as utility value) are also seen to result in Case II (heterogeneous fleet comprised of two vehicle types) at all system loading levels. And, all improvements are statistically significant at the 95 percent confidence level. (See Notes 1 and 2.) Finally, for the homogeneous fleet case (Case III), while Table 8 indicates very slight environmental (utility value) improvement at all three system loading levels, the improvement is not statistically significant.

Insights into the scheduling effects of the new algorithm may be obtained from the data in Table 9, where the most obvious effect is the shifting of vehicle selection, i.e., from “dirtier” to “cleaner” vehicles. And, this is seen to occur (in the heterogeneous fleet cases) at all system loading levels. Additionally, it should be seen that average distance and total number of vehicles utilized appear to decrease with increasing environmental objective weight—up to a certain point. This would be expected to be associated with increasing pick-up delays; and, this is seen to occur from Table 7. Finally, the number of engine starts and controllable (waiting) engine idling also appear to decrease slightly with increasing environmental objective weight.

____________

(1) We calculate the confidence interval for x = m₁ - m₂, i.e., the difference of means, where m_j » E(X_j). However, in our simulation, we used the same sets of requests for each simulated case; and X_1j and X_2j would, therefore, not be expected to be independent. (However, n₁ = n₂.) Because of this, we use the “standard” paired-t confidence interval, defining Z_j = X_1j – X_2j, where the Z_j’s are assumed to be IID. (We calculate Z_j using the results of individual replications, which are not reported in this paper, where X_1j is the “baseline” case where w_ENV =0 and X_2j is the case where w_ENV =0.125.) Then, E(Z_j) = x. And, the 100(1-a) confidence interval for Z_MEAN is Z_MEAN ± t_{n-1, 1-}_a_/2 [Var(Z_MEAN)]^½, where Var(Z_MEAN) = {å_j=1^J [Z_j – Z_MEAN]² }/ n(n-1). (See, for example, Law and Kelton.) That is, we are relying on the Central Limit Theorem to imply that the coverage probability will be near 1- a. However, according to Law and Kelton, the parametric approach is robust in this case, as any skewness in the underlying distributions will be eliminated upon subtraction. And, finally, we make the claim that differences in environmental performance (as utility value) are statistically significant if zero does not fall within the confidence interval. The calculated 95 percent confidence intervals for x, for the three cases (I, II, III) and fleet sizes, are:

Case Variable 210 Veh. 180 Veh. 150 Veh.

I u(env) [0.1399, 0.1626] [0.0676, 0.0835] [0.0274, 0.0356]

I u(cost) [-0.0118, -0.0053] [-0.0098, -0.0038] [-0.0092, 0.0117]

II u(env) [0.0123, 0.0218] [0.0050, 0.0108] [0.0013, 0.0055]

II u(cost) [-0.0080, -0.0007] [-0.0112, 0.0004] [-0.0230, 0.0100]

III u(env) [-0.0018, 0.0065] [-0.0009, 0.0047] [-0.0025, 0.0027]

III u(cost) [-0.0074, 0.0000] [-0.0109, -0.0015] [-0.0119, 0.0067]

(2) In order to perform the above comparisons, we must assume that differences of utility value have cardinal meaning, which is contrary to the point made earlier. In the case at-hand, utility functions do have cardinal meaning, as they were induced over valid value functions. However, in general, this may not be the case. Unfortunately, the only other way around this dilemma would be to calculate differences based on absolute quantities, i.e., pollutant emissions individually. We did this for the case of NO_x emissions, because these emissions are a concern (precursor to smog and ozone formation) and we assume them to be “representative.” And, we calculated paired-t confidence intervals as described in Note 1. We found the differences (e.g., Tables 10 and 11) to be statistically significant for all Case I and Case II fleet size scenarios. Differences for Case III were found not to be statistically significant except for the 210 vehicle scenario.

CONCLUSIONS AND RECOMMENDATIONS

In this research, we developed a methodology for the combined routing and scheduling of fleet vehicles where environmental impacts, assessed using environmental life-cycle impact assessment (LCIA) methods, have been included in the scheduling algorithm and optimization objective function. And, we demonstrated the methodology for a demand-responsive (“Dial-a-Ride” or paratransit) transit application, where both vehicle cost and environmental impact parameters were assumed based upon generic classes of vehicles and literature data. Through simulation, we showed that substantial environmental performance improvements (emissions reductions) can be achieved for heterogeneous fleets, at various loading levels, with only minimal negative impacts on operational cost and service performance, which was our primary objective. (In the case of a homogeneous fleet, the environmental improvements were minimal and not statistically significant.) While we considered only certain specific heterogeneous fleet compositions, we believe the results are generalizable to other heterogeneous fleet compositions that might have been modeled based upon observed algorithm effects. Additionally, we note that the specific results are based upon the arbitrary allocation of vehicles (types) to the service shifts that were modeled. In other words, on those shifts where additional vehicles were available (because they were not on-duty at the time), further environmental impact reductions may have been possible through different “mixes” of allocated vehicle types. (It should be seen that there are trade-offs insofar as vehicle operating cost, environmental impact, and capacity. And, the “best” fleet composition is not, necessarily, a fleet comprised exclusively of the lowest-cost or “cleanest” vehicles available.)

The environmental impacts of fleet vehicle operation are influenced by many controllable and non-controllable variables and, of course, are a function of parameters specific to the specific vehicles and vehicle types comprising the fleet. One of these controllable variables is vehicle assignment including routing and scheduling. And, while our results can only be generalized so far, we believe they are adequate to demonstrate, for the generalized heterogeneous fleet case, that opportunities for reducing environmental impacts are available through vehicle routing and scheduling decisions, and that environmental performance can be jointly optimized with other operational (e.g., cost and service) objectives. We also note that the emissions data we used vary dramatically as a function of different driving patterns and cycles. We did not study the changes in driving cycle in this study.

The South Coast Air Basin (including Los Angeles County) is the only region in the country designated by USEPA as being in “extreme” non-attainment with the Clean Air Act Ambient Air Quality Standard (AAQS) for ozone. The area is also designated in the lesser category of “serious” non-attainment with the AAQS for particulates (PM-10). Moreover, a 1999 study by the SCAQMD (2002) found that up to 90 percent of the carcinogenic risk in the South Coast Basin due to air quality is attributable to mobile sources, primarily from diesel particulates and air toxics. We have shown that, in certain circumstances, all of these can potentially be reduced. (In the case of ozone, this is achieved through reduction of its precursors, NO_x and VOCs.)

The methodology that we developed could be incorporated into existing paratransit scheduling software, although to do so, we would recommend the modifications discussed in the “Implementation” section. Moreover, the SCAQMD, under Regulation XXII (“Mobile Source Emissions Mitigation Programs”), provides funding for mobile source emissions mitigation projects where the emissions reductions are “real,” “surplus,” “quantifiable,” and meet other criteria. That is, it is within the realm of possibility that SCAQMD funding might be obtainable by a paratransit provider, in conjunction with a paratransit scheduling software provider, to incorporate emissions reduction into paratransit scheduling software.

IMPLEMENTATION

We envision the benefits of this research to be as follows:

1) We believe the primary benefit of this research is that it dispels the notion, for the case of a heterogeneous fleet, that environmental impacts (whether life-cycle based or based simply on criteria pollutant emissions) are solely a function of travel distance and are not affected by vehicle routing and scheduling decisions. While we see this research as being exploratory in some regards, as there has been virtually no prior research in this area, we hope that the results provide impetus to others to investigate potential applications, benefits, and limitations of the methodology.

2) We developed the methodology taking into account life-cycle environmental impacts and utilizing rigorous decision-theoretic methods. As noted above, the methodology could be incorporated into existing paratransit scheduling software. To facilitate this, we suggest:

a) Limitation of impacts considered to criteria and air toxic pollutants, as these are of greatest concern in the South Coast Air Basin. (Additionally, global warming gases such as carbon dioxide could be included based on current legislation.) Moreover, while consideration of environmental impacts over all transportation life-cycle stages is required in order to achieve environmentally sustainable transportation systems, there are many jurisdictional and regulatory barriers that make this “systems approach” difficult to implement at the present. Therefore, we would suggest further limitation of impacts considered to tailpipe emissions.

b) If limited to the above impacts, manufacturers’ FTP certification data should readily be available and allow specification of emissions based on actual data for actual vehicle makes and models (e.g., as user input).

c) The purpose of the decision model developed herein was to facilitate specification of weighting constants in the routing/scheduling objective function for the environ-mental impacts, e.g., tailpipe emissions as a function of vehicle itinerary, although this was perhaps obscured by the fact that the objective function was specified based on utility rather than emissions values. Nonetheless, an objective function could alternatively have been specified of the form å_iw_iI_i, where I_i are the emissions of interest and w_i are preference-based weighting constants. In the case of the latter, less formal and rigorous methods are available for determining or specifying these; and, we suggest use of these methods in any implementation of the methodology.

DISCLAIMER ……………………………………………………………………………………………………...	ii

ABSTRACT ………………………………………………………………………………………………………...	ii

LIST OF FIGURES AND TABLES ………………………………………………………………………………	iv

DISCLOSURE ……………………………………………………………………………………………………...	v

ACKNOWLEDGEMENT …………………………………………………………………………………………	v

INTRODUCTION ………………………………………………………………………………………………….	1

TRANSPORTATION ENVIRONMENTAL IMPACTS ………………………………………………...	2
VEHICLE ROUTING AND SCHEDULING WITH ENVIRONMENTAL CONSIDERATIONS ……..	3
PROBLEM DESCRIPTION AND SOLUTION APPROACH …………………………………………..	4

PARATRANSIT LIFE-CYCLE MODEL ………………………………………………………………………...	4

LIFE-CYCLE IMPACT ASSESSMENT BASIS ………………………………………………………………...	6
SELECTION OF PROXY ATTRIBUTES FOR HUMAN HEALTH AND ECOLOGICAL DAMAGES …………………………………………………………………….………...	7

DECISION-THEORETIC BASIS AND MODEL ……………………………………………………………….	8
BASIC DECISION MODEL ……………………………………………………………………………...	9
AGGREGATION OF PROXY ATTRIBUTES ……………………………………………………….…	10
DECISION-MAKER PREFERENCE ASSUMPTIONS, EVALUATION OF SINGLE-
ATTRIBUTE UTILITY FUNCTIONS, AND OVERALL UTILITY EQUATION FORM …………….	11
EVALUATION OF END-POINT DAMAGE-BASEDUTILITY FUNCTIONS ………………………..	15
EVALUATION OF MID-POINT DAMAGE-BASED UTILITY FUNCTIONS ………………………..	16
EVALUATION OF RESOURCE DEPLETION AND OTHER IMPACTS UTILITY FUNCTIONS …...	16
EVALUATION OF VALUE- (PREFERENCE-) BASED WEIGHTING CONSTANTS ………………	17
CALCULATION OF ITINERARY (ENVIRONMENTAL) UTILITY FUNCTION
VALUES AND DEFUZZIFICATION OF RESULTS …………………………………………………...	17
DECISION MODEL TRANSLATION FOR USE IN OPTIMIZATION—CALCULATION
OF “UNIT PARTIAL UTILITY VALUES” ……………………………………………………………..	18

PARATRANSIT OPERATION, MODELED SYSTEM AND MULTI-OBJECTIVE
SCHEDULING ALGORITHM, AND EXPERIMENTAL DESIGN …………………………………………...	18

PARATRANSIT VEHICLE SCHEDULING …………………………………………………………….	19
MODELED PARATRANSIT SYSTEM AND OPERATION …………………………………………...	20
SIMULATION MODEL AND MODEL VERIFICATION/VALIDATION …………………………….	21
BASIC REAL-TIME SCHEDULING HEURISTIC ……………………………………………………..	21
MODIFICATION TO INCLUDE ENVIRONMENTAL IMPACTS …………………………………….	22
EXPERIMENTAL DESIGN ……………………………………………………………………………...	23

EXPERIMENTAL RESULTS …………………………………………………………………………………….	23

CONCLUSIONS AND RECOMMENDATONS …………………………………………………………………	26

IMPLEMENTATION ……………………………………………………………………………………………...	27

APPENDIX

A. VEHICLE LIFE-CYCLE IMPACT ASSESSMENT BASIS ………………………………….	42
B. VEHICLE (PARTIAL UNIT) UTILITY FACTOR BASIS …………………………………...	62
C. VALUES OF ASSUMED DECISION-MAKER SCALING CONSTANTS ………………….	80

REFERENCES ……………………………………………………………………………………………………..	84

FIGURES	PAGE

1. Paratransit Operation Life-Cycle Model …………………………………………..	5
2. Basic Decision Model ……………………………………………………………...	9
3. Model for Evaluation of Constructed Attributes with Value and Factual Judgments Decoupled ………………………………………………...	11
4. Linguist Variables for Damage Comparison ………………………………………	12
5a. Combined Fundamental and Means-Ends Network for Health Damages ………...	28
5b. Combined Fundamental and Means-Ends Network for Ecological Damages …….	28

TABLES

1. Life-Cycle Inventory for Modeled Vehicle Types ………………………………...	29
2. LCIA Equivalency and Hazard Ranking Factors ………………………………….	30
3. LCIA Damage Function Indicators by Impact Category ………………………….	31-32
4. Normalized Values of b_Xlijk Used in Evaluation of Human Health and Ecological Damage Potential ………………………………………….	33
5. Unit Partial Utility Values Used in Simulation ……………………………………	34
6. Values of Selected Simulation and Experimental Parameters …………………….	35
7. Comparison of Service Performance Results for Simulated Cases ……………….	36
8. Scheduling Algorithm Results—Cost and Environmental Performance ………….	37
9. Comparison of Results Affecting Environmental Performance …………………...	38
10a. Scheduling Algorithm Results—Life-Cycle Criteria and Other Pollutant Air Emissions …………………………………………………………...	39
10b. Scheduling Algorithm Results—Other Life-Cycle Impacts ………………………	40
11. Comparison of Life-Cycle Emissions—Percentage Change in Average Daily Emissions Due to New Scheduling Algorithm ……………………	41

Table 1. Life-Cycle Inventory for Modeled Vehicle Types
Impact	LD Gasoline-Powered “Minivan”			LD CNG-Powered “Minivan”			MD Gasoline-Powered “Shuttle Bus”			MD Diesel-Powered “Shuttle Bus”
	g/mile	g/min.	g/start	g/mile	g/min.	g/start	g/mile	g/min.	g/start	g/mile	g/min.	g/start
NMOG (VOC)	0.4445	0.3041	0.2417	0.5600	0.0140	0.0092	0.6419	0.5189	0.5486	0.9862	0.1380	0.0940
Methane	0.0087	0.0526	0.0160	6.5400	0.3589	0.2480	0.0310	0.0749	0.0370	0.0176	0.0054	0.0037
Formaldehyde	0.0013	0.0088	0.0067	0.0180	0.0099	0.0068	0.0060	0.1450	0.0168	0.0519	0.0160	0.0109
1,3-Butadiene	0.0003	0.0018	0.0013				0.0012	0.0029	0.0034	0.0021	0.0006	0.0004
Acetaldehyde	0.0003	0.0018	0.0013	0.0020	0.0001	0.0001	0.0012	0.0029	0.0034	0.0104	0.0032	0.0022
Toluene	0.0060	0.0352	0.0276				0.0243	0.0587	0.0674	0.0041	0.0013	0.0009
Benzene	0.0021	0.0123	0.0097				0.0085	0.0205	0.0237	0.0021	0.0006	0.0004
Methyl t-Butyl Ether	0.0042	0.0176	0.0149				0.0128	0.0309	0.0377
SO_x (SO₂)	1.083	0.068	0.046	0.928	0.005	0.003	1.203	0.121	0.054	1.077	0.083	0.057
NO_x (NO₂)	1.088	0.189	0.408	1.714	0.145	0.0992	2.176	0.323	1.383	4.593	0.359	0.244
CO	3.025	6.248	2.959	2.669	0.036	0.0249	6.048	12.403	9.244	2.018	0.332	16.042
GWP (CO₂ / CO₂-equiv.)	867.2	154.0	104.3	936.2	32.3	22.2	1302.1	273.1	121.6	860.2	73.8	50.1
PM-10	0.148	0.009	0.006	0.1466	0.023	0.0151	0.188	0.016	0.007	0.116	0.009	0.006
Diesel PM-10 (DPM-10)										0.0601	0.0230	0.0156
TRI air emissions	0.042	» 0	» 0	0.044	» 0	» 0	0.038	0.001	» 0	0.041	» 0	» 0
Non-renew. energy use (units in Mjoules)	7.488	0.982	0.668	7.024	0.069	0.047	13.135	1.760	0.786	6.968	1.050	0.710
Fuel use (in gasoline eq.) (Units in gallons)	0.0498	0.0125	0.0086	0.0454	0.0010	0.0007	0.0889	0.0223	0.0100	0.0387	0.0157	0.0107
Base-metal ore depletion	66.682	0.520	0.354	71.280	0.037	0.025	60.119	0.929	0.415	65.804	0.553	0.376
Prec.-metal ore depletion	12.724	0.076	0.052	13.615	0.005	0.004	11.385	0..137	0.061	12.554	0.082	0.055
RCRA Wastes	1.466	0.051	0.035	1.525	0.004	0.002	1.468	0.092	0.041	1.428	0.055	0.037
Non-recycled solid waste	4.800			5.560			5.190			6.82

Table 2. LCIA Equivalency and Hazard Ranking Factors
Stressor	GWP (2)	POCP (3)	Acidification Potential (4)	Eutrophication Potential (4)	Human Health Hazard Ranking Factor (1)	Terrestrial Hazard Ranking Factor (1)	Aquatic Hazard Ranking Factor (1)
CO₂	1	0			0	0	0
CO	3	0.270			4.8	0	0
NO_x	0	0.028	0.7	1.0	12.3	0	0
PM-10	0	0			0	0	0
(NM)VOC	11	0.64			17.8	0.5	32.5
SO_x	0	0.048	1.0		3.6	0	0
1,3-Butadiene	11	0.85			43.8	1.8	46.8
Formaldehyde	11	0.52			70.2	12.6	28.2
Toluene	11	0.64			12.2	0	24.0
Benzene	11	0.22			38.7	0	25.2
Acetaldehyde	11	0.64			27.0	3.3	19.5
Methane	24.5	0.006			0	0	0
Methyl t-Butyl Ether (MTBE)	11	0.175			1.2	1.2	1.2
DPM-10	0	0			37.0	0	71.2
(1) Hazard ranking values from USEPA (1994). DPM-10 value based on anthracene. VOC value based on xylene (mixed isomers). Values for CO, NO_x, SO_x estimated on LC₅₀. (2) GWP values taken from Steen (1999a). (3) POCP values taken from CML (2001). VOC value based on toluene. (4) Acidification and eutrophication values taken from Huijbregts (1999) and USEPA (1996b).

Table 3. LCIA Damage Function Indicators by Impact Category
Stressor	Impact Category and Indicator Type and Value
	Global Warming				Human Toxicity
	Global Warming				Toxicity	Oxidant Formation	Carcinogenic Effects	Respiratory Effects	Toxic Potential
	EPS-CDALY	Eco-DALY	EPS-Prod.Cap.	EPS-NEX	EPS-CDALY	EPS-CDALY	Eco-DALY	Eco-DALY	USES-HTP
CO₂	1.30E-6	2.10E-7	-3.97E-2	1.26E-14
CO	3.91E-6		-4.05E-2	3.78E-14	1.44E-8			7.31E-7
NOx	-4.34E-6		3.45E-3	-1.08E-13	1.43E-4	8.28E-8		8.91E-5	1.2E+0
PM-10	-4.34E-6		3.45E-3	-1.08E-13	5.42E-4			3.75E-4	9.6E-2
(NM)VOC

GREEN TRANSIT SCHEDULER: A METHODOLOGY FOR

Mansour Rahimi

Maged Dessouky

DISCLAIMER

ABSTRACT

LIST OF FIGURES AND TABLES ………………………………………………………………………………

ACKNOWLEDGEMENT …………………………………………………………………………………………

PARATRANSIT OPERATION, MODELED SYSTEM AND MULTI-OBJECTIVE

CONCLUSIONS AND RECOMMENDATONS …………………………………………………………………

IMPLEMENTATION ……………………………………………………………………………………………...

APPENDIX

REFERENCES ……………………………………………………………………………………………………..

LIST OF FIGURES AND TABLES

ACKNOWLEDGEMENT

INTRODUCTION

Figure 2. Basic Decision Model

Figures 3. Model for Evaluation of Constructed Attributes with Value

and Factual Judgments De-Coupled

Table 1. Life-Cycle Inventory for Modeled Vehicle Types

Impact

LD Gasoline-Powered “Minivan”

LD CNG-Powered

MD Gasoline-Powered

MD Diesel-Powered