Case Studies in Cross-Asset, Multi-Objective Resource Allocation (2019)

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101 A P P E N D I X Data Envelopment Analysis Overview Definition Data Envelopment Analysis (DEA) is an analytical approach that identifies the most productive “decision making unit” (“DMU”) where each DMU may require a range of inputs and produce a range of different outputs that cannot be easily compared. The approach was first formulated by Charnes, et al. (1). In their formulation, one first obtains the relative efficiency for each DMU through solving the following optimization for each DMU: subject to: In this formulation h0 is the relative efficiency for a selected DMU. For each DMU the algorithm seeks to find the set of weights that yields the maximum relative efficiency. The problem is solved considering s outputs, m inputs, and j different DMUs. The weight on each input and output should be greater than or equal to 0 and the maximum value for relative efficiency across all j DMU cannot be greater than 1. Once the relative efficiency of each DMU is established, the DMUs can be prioritized in decreasing order of relative efficiency. The basic concept behind the approach is that although we cannot make assumptions about how inputs and outputs can be valued relative to one another, we do prefer DMUs that are more efficient in achieving a given outcome. The algorithm thus seeks to define the “efficient frontier,” or set of DMUs that maximizes output per unit of input. Application to Project Prioritization When DEA is applied to project prioritization, each project is treated as a DMU, and the outputs of a project are the goal scores or utilities. Typically there is only one input: the project cost. The formulation below is equivalent to that shown above where there is only one input given these assumptions. However, here the relative efficiency is expressed as r0 rather than h0:

102 Case Studies in Implementing Cross-Asset, Multi-Objective Resource Allocation subject to: In this formulation one must determine, for each of j projects, the set of weights w (one for each of g goals) that maximizes the relative efficiency of the project, such that the maximum relative efficiency for a given set of weights is 1 for all projects and each weight is greater than or equal to 0. In this alternative formulation sij is the sore or utility of goal i of project j and cj is the cost of project j. As noted above, once the relative efficiency is established, it becomes the basis for prioritization, with projects selected in decreasing order of relative efficiency. Discussion At first glance DEA seems counterintuitive. How can the efficiency of different projects be compared if efficiency is calculated using a different set of weights for each project? However, this seemingly counterintuitive feature is a key aspect of DEA. Specifically, for each project, DEA calculates the best- case set of weights in which the project appears most attractive. In the extreme case that the project has an efficiency of 1, this occurs because the project achieves an outcome that no other project does, and thus should be prioritized highly. This outcome can result in the case that only one project yields a benefit for a certain goal. Otherwise, if even in the best possible case a project is less efficient than other projects, it is accordingly prioritized lower. For instance, a project may yield significant benefits in many goals, but if there is another project that achieves the exact outcomes at half the cost, then the relative efficiency of the project will be no greater than 0.5, as the set of available projects offers more efficient means for achieving the same outcome. Although DEA was originally developed as a way to measure organizational effectiveness, it has been used extensively for project prioritization. Sowlati et al. (2) review different variants of DEA that have been used for project prioritization and recommend defining a set of reference projects when using the algorithm for this application. As noted in Chapter 5 of this report, the authors conclude that decision makers are often better able to define representative projects to use in the algorithm than they are to try to weight achievement in different goal areas as required for alternative approaches such as the analytical hierarchy process (AHP). Defining reference projects also helps reduce the potential that addition of a single project will result in large changes in the calculation of relative efficiency of other projects. For more insights into DEA and its use for project prioritization, one should refer to the review performed by Danesh, et al. (3) and referenced in Chapter 2 of this report. In this study, the authors review over 100 different multi-criteria decision making (MCDM) methods for use in project portfolio management. The authors perform a detailed review of the eight approaches they find to be most promising, including AHP and DEA, as well as:

Data Envelopment Analysis Overview 103 • Analytic Network Process (ANP); • Dominance-Based Rough Set Approach (DSRA); • Elimination and Choice Expressing the Reality (ELECTRE); • Preference-Ranking Organization Method for Enrichment Evaluations (PROMETHEE); • Technique for Order Preference by Similarity to Ideal Solution (TOPSIS); and • VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The authors conclude that AHP and DEA are the most suitable for use in managing project portfolios. These methods meet all of the required criteria for project portfolio management defined by the authors, yield specific ranks (unlike several of the other options considered), and take less time on the part of a decision maker to use than most of the other options considered. So is the decision maker interested in implementing a multi-objective projection prioritization approach better off implementing an approach based on AHP, DEA, or something else entirely? There is no clear-cut answer to this question, and many of the challenges one faces in implementing cross-asset, multi-objective prioritization are the same regardless of the specific calculation approach one uses. Nonetheless, it seems clear that AHP and DEA represent two viable approaches. Thus, in this report, DEA is presented as alternative for supporting a prioritization approach, supplementing previous research that focused on AHP. REFERENCES 1. Charnes, A., Cooper, W.W. and Rhodes, E. “Measuring the Efficiency of Decision Making Units.” European Journal of Operational Research, Vol. 2, No. 6, pp. 429-444, 1978. 2. Sowlati, T, Paradi, J.C., and Suld, C. “Information Systems Project Prioritization Using Data Envelopment Analysis.” Mathematical and Computer Modelling. 41, 2005: 1279–1298. 3. Danesh, D., Ryan, M.J., and Abbasi, A. “A Systematic Comparison of Multi-Criteria Decision Making Methods for the Improvement of Project Portfolio Management in Complex Organizations.” International Journal of Management and Decision Making, Vol. 16, No. 3, pp. 280–320, 2017.

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 978-0-309-48099-4 9 7 8 0 3 0 9 4 8 0 9 9 4 9 0 0 0 0 N O N -PR O FIT O R G . U .S. PO STA G E PA ID C O LU M B IA , M D PER M IT N O . 88 Case Studies in Im plem enting Cross-A sset, M ulti-O bjective Resource A llocation N CH RP Research Report 921 TRB