Abstract
Data envelopment analysis (DEA) is an analytical method for measuring, benchmarking, and improving efficiency performance. While DEA has traditionally been a deterministic ex-post approach, when operational data are not available, it can be positioned to represent an ex-ante perspective, if it is feasible to simulate production behaviors. However, there are two limitations of ex-ante DEA. First, is the representation of uncertainties associated with the contextual conditions and their impact on production. Second, is the inability to incorporate risk preferences that relate to the organizations’ attitude towards production uncertainty. This paper addresses these two gaps through a method that integrates Monte-Carlo simulations, the Subjective Expected Utility Theory, and ex-ante DEA. Our method allows to explicitly model and incorporate the uncertainties associated with the contextual variables and the production behavior, while facilitating the representation of risk preferences. We demonstrate our method through a case study that is framed around a hypothetical community evaluating Micro-Grid (MG) design alternatives. We utilize the National Renewable Energy Lab data to model the stakeholder energy demand and environmental uncertainties; and use the engineering specifications for the MG technology to populate the production possibility set. We then investigate the distribution of efficiency scores by using various stakeholder risk attitudes and find that DEA rankings are insensitive to risk preferences. The proposed method and the documented risk insensitivity are significant contributions as they allow to reposition ex-ante DEA as a nonparametric alternative to multi-criteria decision-making, which can be generalized across different application areas, including uncommon DEA applications such as engineering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Usually represented with Z variables in the DEA literature.
Also known as the “output-cubical technology” assumption.
5 k solar panels, 10 Wind Turbines, 100 MWh storage.
References
Abbas, A. E., & Howard, R. A. (2015). Foundations of decision analysis. Hoboken: Pearson Higher Ed.
Aigner, D., Knox Lovell, C. A., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1), 21–37.
Aldy, J. E., Kotchen, M. J., & Leiserowitz, A. A. (2012). Willingness to pay and political support for a US national clean energy standard. Nature Climate Change, 2(8), 596–599. https://doi.org/10.1038/nclimate1527
Amirteimoori, A., Emrouznejad, A., & Khoshandam, L. (2013). Classifying flexible measures in data envelopment analysis: A slack-based measure. Measurement, 46(10), 4100–4107. https://doi.org/10.1016/j.measurement.2013.08.019
Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10), 1261–1264. https://doi.org/10.1287/mnsc.39.10.1261
Arrow, K. J. (1971). Insurance, risk and resource allocation. In Essays in the theory of risk-bearing (pp. 134–43).
Arrow, K. J., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica: Journal of the Econometric Society, 265–90.
Arrow, K. J., & Lind, R. C. (1978). Uncertainty and the evaluation of public investment decisions. In Uncertainty in economics (pp. 403–421). Elsevier.
Australian Energy Market Operator. (2018). Initial operation of the Hornsdale power reserve battery energy storage system. https://www.aemo.com.au/-/media/Files/Media_Centre/2018/Initial-operation-of-the-Hornsdale-Power-Reserve.pdf.
Awerbuch, S. (2000). Investing in photovoltaics: Risk, accounting and the value of new technology. Energy Policy, the Viability of Solar Photovoltaics, 28(14), 1023–1035. https://doi.org/10.1016/S0301-4215(00)00089-6
Battese, G. E., & Corra, G. S. (1977). Estimation of a production frontier model: With application to the pastoral zone of Eastern Australia. Australian Journal of Agricultural Economics, 21(3), 169–179.
Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71(356), 791–799. https://doi.org/10.1080/01621459.1976.10480949
Busby, J. W., Baker, K., Bazilian, M. D., Gilbert, A. Q., Grubert, E., Rai, V., Rhodes, J. D., Shidore, S., Smith, C. A., & Webber, M. E. (2021). Cascading risks: Understanding the 2021 winter blackout in texas. Energy Research & Social Science, 77(July), 102106. https://doi.org/10.1016/j.erss.2021.102106
Chambers, R. G., Hailu, A., & Quiggin, J. (2011). Event-specific data envelopment models and efficiency analysis. Australian Journal of Agricultural and Resource Economics, 55(1), 90–106.
Chambers, R. G., & Quiggin, J. (2000). Uncertainty, production, choice, and agency: the state-contingent approach. Cambridge University Press.
Charnes, A., & Cooper, W. W. (1963). Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Research, 11(1), 18–39. https://doi.org/10.1287/opre.11.1.18
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.
Christopoulos, G. I., Tobler, P. N., Bossaerts, P., Dolan, R. J., & Schultz, W. (2009). Neural correlates of value, risk, and risk aversion contributing to decision making under risk. Journal of Neuroscience, 29(40), 12574–12583.
Chung, S.-H., Lee, A.-I., Kang, H.-Y., & Lai, C.-W. (2008). A DEA window analysis on the product family mix selection for a semiconductor fabricator. Expert Systems with Applications, 35(1), 379–388. https://doi.org/10.1016/j.eswa.2007.07.011
Collopy, P. D., & Hollingsworth, P. M. (2011). Value-driven design. Journal of Aircraft, 48(3), 749–759. https://doi.org/10.2514/1.C000311
Cook, W. D., & Zhu, J. (2007). Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research, 180(2), 692–699. https://doi.org/10.1016/j.ejor.2006.03.048
Cooper, W. W., Huang, Z., Lelas, V., Li, S. X., & Olesen, O. B. (1998). Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. Journal of Productivity Analysis, 9(1), 53–79.
Cooper, W. W., Huang, Z., & Li, S. X. (1996). Chatper 13 satisficing DEA models under chance constraints. Annals of Operations Research, 66(4), 279–295. https://doi.org/10.1007/BF02187302
Daraio, C., & Simar, L. (2005). Introducing environmental variables in nonparametric frontier models: A probabilistic approach. Journal of Productivity Analysis, 24(1), 93–121. https://doi.org/10.1007/s11123-005-3042-8
Demirbas, A. (2009). Global renewable energy projections. Energy Sources Part B-Economics Planning and Policy, 4(2), 212–224. https://doi.org/10.1080/15567240701620499
Draxl, C., Clifton, A., Hodge, B.-M., & McCaa, J. (2015). The wind integration national dataset (wind) toolkit. Applied Energy, 151, 355–366.
Dyson, R. G., Allen, R., Camanho, A. S., Podinovski, V. V., Sarrico, C. S., & Shale, E. A. (2001). Pitfalls and protocols in DEA. European Journal of Operational Research, 132(2), 245–259. https://doi.org/10.1016/S0377-2217(00)00149-1
Fallah-Fini, S., Rahmandad, H., Triantis, K., & de la Garza, J. M. (2010). Optimizing highway maintenance operations: Dynamic considerations. System Dynamics Review, 26(3), 216–238.
Färe, R., & Grosskopf, S. (2013). DEA, directional distance functions and positive, affine data transformation. Omega, 41(1), 28–30. https://doi.org/10.1016/j.omega.2011.07.011
Färe, R., Grosskopf, S., Lovell, C. A. K., & Pasurka, C. (1989). Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. The Review of Economics and Statistics, 71(1), 90–98. https://doi.org/10.2307/1928055
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (general), 120(3), 253–290. https://doi.org/10.2307/2343100
Gao, J., Li, M., & Liu, H. (2015). Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making. European Journal of Operational Research, 243(1), 258–270.
Greenberg, M., Mantell, N., Lahr, M., Felder, F., & Zimmerman, R. (2007). Short and intermediate economic impacts of a terrorist-initiated loss of electric power: Case study of New Jersey. Energy Policy, 35(1), 722–733. https://doi.org/10.1016/j.enpol.2006.01.017
Hamilton, M. C., Lambert, J. H., Connelly, E. B., & Barker, K. (2016). Resilience analytics with disruption of preferences and lifecycle cost analysis for energy microgrids. Reliability Engineering & System Safety, 150(June), 11–21. https://doi.org/10.1016/j.ress.2016.01.005
Hatami-Marbini, A., Emrouznejad, A., & Tavana, M. (2011). A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making. European Journal of Operational Research, 214(3), 457–472. https://doi.org/10.1016/j.ejor.2011.02.001
Hatziargyriou, N., Asano, H., Iravani, R., & Marnay, C. (2007). Microgrids. IEEE Power and Energy Magazine, 5(4), 78–94.
Hazelrigg, G. (1998). A framework for decision-based engineering design. Journal of Mechanical Design, 120(4), 653–658. https://doi.org/10.1115/1.2829328
Hazelrigg, G. (2012). Fundamentals of decision making for engineering design and systems engineering.
Herrera-Restrepo, O., Triantis, K., Trainor, J., Murray-Tuite, P., & Edara, P. (2016). A Multi-perspective dynamic network performance efficiency measurement of an evacuation: A dynamic network-DEA approach. Omega, 60, 45–59.
Hsu, P.-L., & Robbins, H. (1947). Complete convergence and the law of large numbers. Proceedings of the National Academy of Sciences of the United States of America, 33(2), 25.
Ipakchi, A., & Albuyeh, F. (2009). Grid of the future. IEEE Power and Energy Magazine, 7(2), 52–62.
Just, R. E., & Pope, R. D. (2001). The agricultural producer: Theory and statistical measurement. Handbook of Agricultural Economics, 1, 629–741.
Karvetski, C. W., & Lambert, J. H. (2012). Evaluating deep uncertainties in strategic priority-setting with an application to facility energy investments. Systems Engineering, 15(4), 483–493. https://doi.org/10.1002/sys.21215
Kaufman, N. (2014). Why is risk aversion unaccounted for in environmental policy evaluations? Climatic Change, 125(2), 127–135. https://doi.org/10.1007/s10584-014-1146-8
Keeney, R. L. (1996). Value-focused thinking: Identifying decision opportunities and creating alternatives. European Journal of Operational Research, 92(3), 537–549.
Kumbhakar, S. C., Ghosh, S., & Thomas McGuckin, J. (1991). A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. Journal of Business & Economic Statistics, 9(3), 279–286.
Lampe, H. W., & Hilgers, D. (2015). Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA. European Journal of Operational Research, 240(1), 1–21. https://doi.org/10.1016/j.ejor.2014.04.041
Lasseter, R. H., & Paigi, P. (2004). Microgrid: A conceptual solution. In 2004 IEEE 35th annual power electronics specialists conference (IEEE Cat. No.04CH37551) (Vol. 6, pp. 4285–4290) https://doi.org/10.1109/PESC.2004.1354758
Meeusen, W., & van Den Broeck, J. (1977). Efficiency estimation from Cobb–Douglas production functions with composed error. International Economic Review, 18(2), 435–444. https://doi.org/10.2307/2525757
Merton, R. C. (1975). Optimum consumption and portfolio rules in a continuous-time model. In Stochastic optimization models in finance (621–661). Elsevier.
Moschini, G., & Hennessy, D. A. (2001). Uncertainty, risk aversion, and risk management for agricultural producers. In Handbook of agricultural economics, (Vol. 1, pp. 87–153). Agricultural Production. Elsevier. https://doi.org/10.1016/S1574-0072(01)10005-8
Mozumder, P., Vásquez, W. F., & Marathe, A. (2011). Consumers’ preference for renewable energy in the Southwest USA. Energy Economics, 33(6), 1119–1126.
Nauges, C., O’Donnell, C. J., & Quiggin, J. (2011). Uncertainty and technical efficiency in Finnish agriculture: A state-contingent approach. European Review of Agricultural Economics, 38(4), 449–467. https://doi.org/10.1093/erae/jbr014
Nordhaus, W. D. (2008). A question of balance: Weighing the options on global warming policies. Yale University Press. http://books.google.com/books?hl=en&lr=&id=qgeoZDu5SbQC&oi=fnd&pg=PR7&dq=david+nordhaus+question+of+balance&ots=gIcQtqJydV&sig=umdbv76K5TINU009scWgkFUh8NU
Nozick, R. (1994). The nature of rationality. Princeton University Press.
NREL. (2016). Energy analysis—Energy technology cost and performance data. http://www.nrel.gov/analysis/tech_lcoe_re_cost_est.html
O’Donnell, C. J., Chambers, R. G., & Quiggin, J. (2010). Efficiency analysis in the presence of uncertainty. Journal of Productivity Analysis, 33(1), 1–17. https://doi.org/10.1007/s11123-009-0143-9
O’Donnell, C. J., & Griffiths, W. E. (2006). Estimating state-contingent production frontiers. American Journal of Agricultural Economics, 88(1), 249–266.
Olesen, O. B., & Petersen, N. C. (1995). Chance constrained efficiency evaluation. Management Science, 41(3), 442–457. https://doi.org/10.1287/mnsc.41.3.442
Oxford Dictionary. (2019). Performance | definition of performance in English by Oxford Dictionaries. Oxford Dictionaries | English. 2019. https://en.oxforddictionaries.com/definition/performance
Paradi, J. C., & David Sherman, H. (2014). Seeking greater practitioner and managerial use of DEA for benchmarking. Data Envelopment Analysis Journal, 1(1), 29–55.
Peng, F. Z., Li, Y. W. & Tolbert, L. M. (2009). Control and protection of power electronics interfaced distributed generation systems in a customer-driven microgrid. In 2009 IEEE power energy society general meeting (pp. 1–8). https://doi.org/10.1109/PES.2009.5275191
Peykani, P., Mohammadi, E., Saen, R. F., Sadjadi, S. J., & Rostamy-Malkhalifeh, M. (2020). Data envelopment analysis and robust optimization: A review. Expert Systems, 37(4), e12534. https://doi.org/10.1111/exsy.12534
Ross, A. M., Hastings, D. E., Warmkessel, J. M., & Diller, N. P. (2004). Multi-attribute tradespace exploration as front end for effective space system design. Journal of Spacecraft and Rockets, 41(1), 20–28.
Ruggiero, J. (1998). Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research, 111(3), 461–469.
Saastamoinen, A. (2015). Heteroscedasticity or production risk? A synthetic view. Journal of Economic Surveys, 29(3), 459–478.
Sadjadi, S. J., & Omrani, H. (2008). Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies. Energy Policy, 36(11), 4247–4254.
Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16–20.
Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers & Mathematics with Applications, 24(8), 259–266. https://doi.org/10.1016/0898-1221(92)90203-T
Sengupta, M., Xie, Yu., Lopez, A., Habte, A., Maclaurin, G., & Shelby, J. (2018). The national solar radiation data base (NSRDB). Renewable and Sustainable Energy Reviews, 89(June), 51–60. https://doi.org/10.1016/j.rser.2018.03.003
Serra, T., & Lansink, A. O. (2014). Measuring the impacts of production risk on technical efficiency: A state-contingent conditional order-m approach. European Journal of Operational Research, 239(1), 237–242. https://doi.org/10.1016/j.ejor.2014.05.020
Shankar, S., & Quiggin, J. (2013). Production under uncertainty: A simulation study. Journal of Productivity Analysis, 39(3), 207–215. https://doi.org/10.1007/s11123-012-0281-3
Shin, J., Woo, JongRoul, Huh, S.-Y., Lee, J., & Jeong, G. (2014). Analyzing public preferences and increasing acceptability for the renewable portfolio standard in Korea. Energy Economics, 42(March), 17–26. https://doi.org/10.1016/j.eneco.2013.11.014
Soshinskaya, M., Crijns-Graus, W. H. J., Guerrero, J. M., & Vasquez, J. C. (2014). Microgrids: Experiences, barriers and success factors. Renewable and Sustainable Energy Reviews, 40(December), 659–672. https://doi.org/10.1016/j.rser.2014.07.198
Sueyoshi, T. (2000). Stochastic DEA for restructure strategy: An application to a Japanese petroleum company. Omega, 28(4), 385–398. https://doi.org/10.1016/S0305-0483(99)00069-9
Szabó, S., Jäger-Waldau, A., & Szabó, L. (2010). Risk adjusted financial costs of photovoltaics. Energy Policy, Large-Scale Wind Power in Electricity Markets with Regular Papers, 38(7), 3807–3819. https://doi.org/10.1016/j.enpol.2010.03.001
Szajnfarber, Z., Grogan, P. T., Panchal, J. H., & Gralla, E. L. (2020). A call for consensus on the use of representative model worlds in systems engineering and design. Systems Engineering, 23(4), 436–442. https://doi.org/10.1002/sys.21536
Tanrioven, M. (2005). Reliability and cost-benefits of adding alternate power sources to an independent micro-grid community. Journal of Power Sources, 150(October), 136–149. https://doi.org/10.1016/j.jpowsour.2005.02.071
“Tesla Powerpack.” (2017). https://www.tesla.com/powerpack
The Army Senior Energy Council. (2009). Army energy security implementation strategy. Washington, DC.
Toloo, M. (2009). On classifying inputs and outputs in DEA: A revised model. European Journal of Operational Research, 198(1), 358–360. https://doi.org/10.1016/j.ejor.2008.08.017
Tom, S. M., Fox, C. R., Trepel, C., & Poldrack, R. A. (2007). The neural basis of loss aversion in decision-making under risk. Science, 315(5811), 515–518.
Topcu, T. G., & Mesmer, B. (2015). Customer, commercial, and government value functions for electric vehicle system design. In IIE annual conference. proceedings, 959. Institute of Industrial and Systems Engineers (IISE).
Topcu, T. G., & Mesmer, B. L. (2018). Incorporating end-user models and associated uncertainties to investigate multiple stakeholder preferences in system design. Research in Engineering Design, 29(3), 411–431. https://doi.org/10.1007/s00163-017-0276-1
Topcu, T. G., Triantis, K., Malak, R., & Collopy, P. (2020). An interdisciplinary strategy to advance systems engineering theory: The case of abstraction and elaboration. Systems Engineering, 23(6), 673–683. https://doi.org/10.1002/sys.21556
Topcu, T. G., Triantis, K., & Roets, B. (2019). Estimation of the workload boundary in socio-technical infrastructure management systems: The case of Belgian railroads. European Journal of Operational Research, 278(1), 314–329. https://doi.org/10.1016/j.ejor.2019.04.009
Torre, W. V., Bartek, N., & Washom, B. (2012). The San Diego regional experience in developing microgrids, a collaboration between utility and a local university. In Power and energy society general meeting, 2012 IEEE, 1–2. IEEE. http://ieeexplore.ieee.org/abstract/document/6345525/
UK Department of Environment. (n.d). “Renewable Energy | Annex 1 Wind Energy: Spacing of Turbines | Planning Portal.” Draft PPS 18. Retrieved October 11, 2016, from http://www.planningni.gov.uk/index/policy/policy_publications/planning_statements/pps18/pps18_annex1/pps18_annex1_wind/pps18_annex1_technology/pps18_annex1_spacing.htm
U.S. Energy Information Administration. (2019). “Electric Power Monthly.” Government. Washington, DC. https://www.eia.gov/electricity/data/state/
Ustun, T. S., Ozansoy, C., & Zayegh, A. (2011). Recent developments in microgrids and example cases around the world—A review. Renewable and Sustainable Energy Reviews, 15(8), 4030–4041. https://doi.org/10.1016/j.rser.2011.07.033
Von Neumann, J., & Morgenstern, O. (2007). Theory of games and economic behavior (60th anniversary commemorative edition). Princeton University Press.
Wang, H.-J., & Schmidt, P. (2002). One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. Journal of Productivity Analysis, 18(2), 129–144. https://doi.org/10.1023/A:1016565719882
Wang, Y.-M., & Chin, K.-S. (2011). The use of OWA operator weights for cross-efficiency aggregation. Omega, 39(5), 493–503. https://doi.org/10.1016/j.omega.2010.10.007
Wegener, M., & Amin, G. R. (2019). Minimizing greenhouse gas emissions using inverse DEA with an application in oil and gas. Expert Systems with Applications, 122(May), 369–375. https://doi.org/10.1016/j.eswa.2018.12.058
Wei, G., Chen, J., & Wang, J. (2014). Stochastic efficiency analysis with a reliability consideration. Omega, 48, 1–9.
Wu, J., Yin, P., Sun, J., Chu, J., & Liang, L. (2016). Evaluating the environmental efficiency of a two-stage system with undesired outputs by a DEA approach: An interest preference perspective. European Journal of Operational Research, 254(3), 1047–1062. https://doi.org/10.1016/j.ejor.2016.04.034
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183–190. https://doi.org/10.1109/21.87068
Yager, R. R., & Alajlan, N. (2014). On characterizing features of OWA aggregation operators. Fuzzy Optimization and Decision Making, 13(1), 1–32.
Yang, H., & Pollitt, M. (2009). Incorporating both undesirable outputs and uncontrollable variables into DEA: The performance of Chinese coal-fired power plants. European Journal of Operational Research, 197(3), 1095–1105. https://doi.org/10.1016/j.ejor.2007.12.052
Zahedi-Seresht, M., Jahanshahloo, G.-R., & Jablonsky, J. (2017). A robust data envelopment analysis model with different scenarios. Applied Mathematical Modelling, 52(December), 306–319. https://doi.org/10.1016/j.apm.2017.07.039
Zahedi-Seresht, M., Khosravi, S., Jablonsky, J., & Zykova, P. (2021). A data envelopment analysis model for performance evaluation and ranking of DMUs with alternative scenarios. Computers & Industrial Engineering, 152(February), 107002. https://doi.org/10.1016/j.cie.2020.107002
Zhang, X., Huang, G. H., Lin, Q., & Hui, Y. (2009). Petroleum-contaminated groundwater remediation systems design: A data envelopment analysis based approach. Expert Systems with Applications, 36(3, Part 1), 5666–5672. https://doi.org/10.1016/j.eswa.2008.06.136
Zhao, Y., Triantis, K., Murray-Tuite, P., & Edara, P. (2011). Performance measurement of a transportation network with a downtown space reservation system: A network-DEA approach. Transportation Research Part E: Logistics and Transportation Review, 47(6), 1140–1159. https://doi.org/10.1016/j.tre.2011.02.008
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Topcu, T.G., Triantis, K. An ex-ante DEA method for representing contextual uncertainties and stakeholder risk preferences. Ann Oper Res 309, 395–423 (2022). https://doi.org/10.1007/s10479-021-04271-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-021-04271-1