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Guidance for Calculating the Return on Investment in Transit State of Good Repair (2019)

Chapter: Appendix C - Model Details for Calculating Agency Costs

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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
×
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
×
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
×
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Suggested Citation:"Appendix C - Model Details for Calculating Agency Costs." National Academies of Sciences, Engineering, and Medicine. 2019. Guidance for Calculating the Return on Investment in Transit State of Good Repair. Washington, DC: The National Academies Press. doi: 10.17226/25629.
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C-1 A P P E N D I X C Model Details for Calculating Agency Costs This appendix details the asset models described in Chapter 2. These models were used to populate the set of default cost curves in the Return on Investment Calculator detailed in Chapter 4. The models are implemented in the Transit Asset Prioritization Tool (TAPT) documented in TCRP Report 172 (1). The models are described in two different reports, and this discussion integrates the materials from the two. The models were originally documented in TCRP Report 157 (2) and then modified as described in the TCRP Project E-09A Contractor’s Final Report (3). User costs are included in the model formulation but are omitted here, as user costs are calculated separately in the Return on Investment Calculator. Revenue Vehicle Model The methodology for predicting agency costs for revenue vehicles model is adapted from the FTA publication Useful Life of Transit Buses and Vans (4), with modifications to extend the approach to rail vehicles. The FTA report details a comprehensive analysis and economic model of bus and van life. Basic assumptions adapted from this report are as follows: • Vehicles deteriorate primarily as a function of accumulated mileage, which can be approximated by age if one assumes a constant annual mileage. • Transit agency costs, including rehabilitation, energy, and maintenance costs, all increase as a function of accumulated mileage (and thus, as a function of age). In addition, the probability of breakdowns (called “road calls” for buses and “failures” for rail) increases with accumulated mileage. • Practices for bus rehabilitation vary between agencies. However, a common practice is to schedule rehabilitation of specific bus components (e.g., brakes, transmission) based on component lives. Thus, in the model, rehabilitation is represented as a cost per mile that varies based on accumulated mileage rather than as a single, discrete action. Alternatively, one may specify that periodic rehabilitation is performed at a specified interval and cost. Based on these assumptions, one can predict the accumulated costs of maintaining a vehicle as its mileage increases. If user costs are added (as described in the next section), one can determine when to replace the vehicle given the objective of minimizing life-cycle transit agency and user costs. Once a vehicle exceeds its cost-

C-2 Guidance for Calculating the Return on Investment in Transit State of Good Repair minimizing replacement mileage, a transit agency and its passengers by definition spend more money to keep the vehicle in service than to replace the vehicle. The agency life-cycle cost may be expressed as follows: (C-1) where LCC life-cycle cost CP vehicle purchase cost, including the emissions cost of a new vehicle A age in years at which a vehicle is assumed to be replaced CMRt rehabilitation cost per vehicle mile at time t CMEt energy (fuel) cost per vehicle mile at time t, including cost of emissions CMMt maintenance cost per vehicle mile at time t AM annual vehicle mileage CMPt periodic rehabilitation cost incurred at time t i discount rate The following equation is used to estimate energy costs per vehicle mile (including emissions costs, if desired) as a function of lifetime mileage: (C-2) where LM lifetime mileage ke1 a constant reflecting the sensitivity of energy cost to lifetime mileage ke2 a constant set to match base year energy cost and the following equation is used to estimate maintenance costs per vehicle mile as a function of lifetime mileage: (C-3) where km1 a constant reflecting the sensitivity of maintenance cost to lifetime mileage km2 a constant set to match base year maintenance cost Defaults for values of ke1 and km1 are derived based on analysis of NTD data. The constants ke2 and km2 are set to reproduce base year values. Note the same functional form used in Equations (C-2) and (C-3) can be used to predict the occurrence of road calls and failures as a function of accumulated mileage for use in modeling user costs. The modeling of emissions costs is documented in the TCRP E-09A Contractor’s Final Report. For vehicle operations, CO2 emissions are predicted based on energy use. LMk e eekLMCME *2 1)( = LMk m mekLMCMM *2 1)( =

Model Details for Calculating Agency Costs C-3 Default values for converting energy use are 0.0111 tons per gallon of diesel fuel and 0.0008 tons per kilowatt hour. Emissions costs associated with the production of replacement vehicles may also be included in the vehicle replacement cost, if desired. Age-Based Asset Model The age-based model can be used to predict life-cycle costs for any transit asset other than a revenue vehicle. The model predicts the probability of asset failure using a Weibull distribution. This distribution defines the survival curve that shows the probability the asset will fail as the asset ages. As failure becomes more likely over time, the relative benefit of replacing the asset before it reaches a specified age threshold tends to increase. Costs included in the calculation include periodic replacement, maintenance, and additional agency costs incurred in the event of an asset failure. Using the Weibull distribution, the cumulative probability of asset failure is given by the following equation: (C-4) where: f(t) cumulative probability of asset failure t asset age in years k shape parameter scale parameter One way to determine the shape and scale factors is to solve for these given information about asset survival ages. Models from FTA’s TERM can be used to estimate these. The shape and scale parameters are calculated from the survival ages as follows: (C-5) (C-6) where: A50 the age to which 50 percent of the assets are expected to survive A25 the age to which 25 percent of the assets are expected to survive In the enhanced age-based model, annual asset maintenance cost is assumed to increase exponentially over an asset’s life: (C-7) where: mt maintenance cost in year t

C-4 Guidance for Calculating the Return on Investment in Transit State of Good Repair k0 a parameter based on average maintenance costs experienced for the asset k1 a parameter reflecting the rate at which maintenance costs increase with asset age. The model allows for specification of emissions cost or other costs, as well. Like maintenance costs, these other costs are assumed to increase exponentially over time. For an asset that is replaced at age A (either because it fails in year A or because A is the age at which the asset is replaced if it does not fail before then), the present value of maintenance and other annual costs between time t=0 and t=A is calculated as follows: (C-8) where: A the age at which the asset is replaced CA the present value of maintenance costs and other costs for the asset over the A years of its life mt maintenance and other costs in year t of the asset’s life i discount rate Based on this model, the annualized life-cycle cost for an asset can be calculated based on the following equation for determining the NPV of all future costs for the asset depending on asset replacement policy: (C-9) where: A the age at which the asset will be replaced (if it does not fail beforehand) NA the present value of all future costs under the policy of replacing the asset at age A. It is assumed that the asset is replaced at time t = 0 and all future costs are discounted back to that time. R replacement cost if the asset does not fail F cost of an asset failure (including the cost to replace the asset) Pt probability that the asset will fail in year t Ct present value of maintenance and other costs over the life of an asset that fails in year t CA present value of maintenance and other costs over the life of an asset that is replaced at age A i discount rate The second term in the above equation (i.e., the summation from t=1 to A) accounts for the possibility that the asset will fail before it reaches age A. The terms in that summation are the probability that the asset will fail in year t times the present value of

Model Details for Calculating Agency Costs C-5 costs that would be incurred if the asset failed in that year. These costs include the present value of maintenance and other annual costs, discounted value of the extra cost that is incurred due to asset failure, and the present value of all costs that would be incurred when and after the asset is replaced at time t, which is NA/(1+i)t. The third term in the above equation accounts for the possibility that the asset will survive to age A and then be replaced. It is the probability of the asset surviving times the present value of costs that would be incurred in this case. These costs include the present value of maintenance and other annual costs plus the present value of all costs incurred when and after the asset is replaced at time A, which is NA/(1+i)A. Solving the above equation for NA, we obtain (C-10) NA can be converted to an annualized cost by applying the discount rate i, i.e., (C-11) where: ACA the annualized cost of a policy in which assets are replaced at age A if they do not fail before then. The net benefit associated with replacing an asset now versus the alternative of replacing the asset a year from now can be approximated as the difference between the expected cost of keeping the asset in place an additional year and the annualized life- cycle cost under an optimum asset replacement policy: (C-12) where: Bt net benefit of replacing an asset at age t relative to keeping the asset in place for an additional year P(t+1|t) probability that the asset will fail by time t+1 given that it has survived to time t R replacement cost if the asset does not fail F cost of an asset failure (including the cost to replace the asset) ct+1 maintenance and other costs in year t+1 of the asset’s life annualized life-cycle cost with an optimum asset replacement policy Condition-Based Asset Model Like the age-based model, the condition-based model can be used to predict life-cycle costs for any transit asset other than revenue vehicles, provided data are available

C-6 Guidance for Calculating the Return on Investment in Transit State of Good Repair characterizing the asset’s condition. This model approximates the condition of an asset using a Markov Decision Process. This approach is commonly used for pavement and bridge management systems and is well-documented in the literature. To apply the approach, it is necessary to define a set of condition states and a set of rehabilitation/replacement actions for each state. For each state there is, by definition, a “do-minimum” action and potentially other rehabilitation/replacement actions. It is also necessary to specify the cost for each action and the probability of transition from one state to another given an action is taken. This transition probability matrix thus specifies predicted deterioration (the probability of transition given the “do-minimum” action is performed) and action effectiveness. Once a Markov Decision Process has been defined, a linear program can be formulated and solved to determine what actions, if taken on an asset, will minimize costs over time. The primary output of the model is the recommended rehabilitation/replacement policy, which specifies what action to perform based on the condition of the asset. The model also predicts annualized costs assuming the policy is followed as well as the future life- cycle cost for each condition state/action combination if a given action is performed in the next period and the optimal policy is followed subsequently. The benefit of performing an action is the savings that will result from performing the action relative to deferring action for one year (performing the “do-minimum” action). If this difference is non-zero, it is more cost effective to perform the action than to defer work. The PI is calculated by dividing this benefit by the action cost. Default models have been developed for a range of assets using condition states and deterioration data from FTA’s TERM Lite, using the five-point condition scale defined in this system. To develop a new model for an asset one must define the condition states and actions for the asset, transit agency and user costs associated with each action, and the transition probability matrix for the asset. In formulating the problem, it is necessary to describe the optimal stationary policy for the asset—that is, the optimal set of actions to take in each condition state—using Bellman’s optimality equation: (C-13) where LCC*(x) minimum life-cycle cost for asset in state x a optimal action to perform in state x Cx,a cost of taking action a in state x probability of transition from state x to state y given action a is performed     + += ∑ y a yxax a yLCCP i CxLCC )( 1 1 )( *,, * min a yxP ,

Model Details for Calculating Agency Costs C-7 Although Equation C-13 is a dynamic equation, it can be formulated and solved as a linear program. Once the optimal policy has been determined, the life-cycle cost for an asset in state x given action a is performed in the next period can be specified as follows: (C-14) Note this equation assumes that following the next period, the optimal policy is followed. Thus, the difference between LCC(x|a) and LCC*(x) represents the additional cost incurred if action a is followed rather than the optimal action. Likewise, the benefit B of performing an action relative to deferring action for one decision period (typically one year) is the difference between the life-cycle costs for the do-minimum action and the selected action. Implementation of the Asset Models One has two options for using the models described here in the Return on Investment Calculator described in Chapter 4. One option is to obtain results using the models in TAPT and then enter the results directly in the Return on Investment Calculator. The second option is to enter baseline values for agency costs and the average asset age by asset class for each year of the analysis. In the latter case, a set of default cost curves are used to scale the base costs in proportion to asset age. The research team populated these default cost curves using TAPT defaults and then scaled the results such that the value equals 100 for an age of 0 years. References 1. Robert, W., V. Reeder, K. Lawrence, H. Cohen, and K. O’Neil. TCRP Report 172: Guidance for Developing a Transit Asset Management Plan. Transportation Research Board of the National Academies, Washington, D.C., 2014. 2. Spy Pond Partners, LLC; KKO & Associates, LLC; H. Cohen; and J. Barr. TCRP Report 157: State of Good Repair: Prioritizing the Rehabilitation and Replacement of Existing Capital Assets and Evaluating the Implications for Transit. Transportation Research Board of the National Academies, Washington, D.C., 2013. 3. Robert, W., V. Reeder, K. Lawrence, H. Cohen, and K. O’Neil. “Guidance for Developing the State of Good Repair Prioritization Framework and Tools: Research Report.” Contractor’s Final Report for TCRP Project E-09A. 2014. 4. Booz Allen Hamilton Inc. Useful Life of Transit Buses and Vans. Technical Report FTA VA-26-7229-07.1. 2007. ∑++= y a yxax yLCCPi CaxLCC )( 1 1 )|( *,,

Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation

TRA N SPO RTATIO N RESEA RCH BO A RD 500 Fifth Street, N W W ashington, D C 20001 A D D RESS SERV ICE REQ U ESTED ISBN 978-0-309-48087-1 9 7 8 0 3 0 9 4 8 0 8 7 1 9 0 0 0 0

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Transit state of good repair (SGR) is a critical area within the U.S. transit industry. All transit agencies, large or small, regardless of region of the country or modes operated, face challenges in maintaining their physical assets in good repair, and many are in a situation where the funds available for rehabilitating and replacing existing capital assets are insufficient for achieving SGR.

The TRB Transit Cooperative Research Program's TCRP Research Report 206: Guidance for Calculating the Return on Investment in Transit State of Good Repair addresses transit agency, user, and social costs and benefits of SGR investments. The report presents an analysis methodology that utilizes and builds upon previous research performed through the Transit Cooperative Research Program (TCRP) presented in TCRP Reports 157 and 198. The guidance (presented in Chapter 3) walks through the steps for calculating the ROI for a potential investment or set of investments.

A key product of the research is a spreadsheet tool intended for transit agency use. It is discussed in Chapter 4.

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