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Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis

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  • Anna Labijak-Kowalska

    (Poznań University of Technology)

  • Miłosz Kadziński

    (Poznań University of Technology)

Abstract

We consider the problem of measuring the efficiency of decision-making units with a ratio-based model. In this perspective, we introduce a framework for robustness analysis that admits both interval and ordinal performances on inputs and outputs. The proposed methodology exploits the uncertainty related to the imprecise data and all feasible input/output weight vectors delimited through linear constraints. We offer methods for verifying the robustness of three types of outcomes: efficiency scores, efficiency preference relations, and efficiency ranks. On the one hand, we formulate mathematical programming models to compute the extreme, necessary, and possible results. On the other hand, we incorporate the stochastic analysis driven by the Monte Carlo simulations to derive the probability distribution of different outcomes. The framework is implemented in R and made available on open-source software. Its use is illustrated in two case studies concerning Chinese ports or industrial robots.

Suggested Citation

  • Anna Labijak-Kowalska & Miłosz Kadziński, 2023. "Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis," Operational Research, Springer, vol. 23(1), pages 1-34, March.
    • Handle: RePEc:spr:operea:v:23:y:2023:i:1:d:10.1007_s12351-023-00755-z
    DOI: 10.1007/s12351-023-00755-z
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    1. K S Park, 2007. "Efficiency bounds and efficiency classifications in DEA with imprecise data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 533-540, April.
    2. Jie Wu & Yafei Yu & Qingyuan Zhu & Qingxian An & Liang Liang, 2018. "Closest target for the orientation-free context-dependent DEA under variable returns to scale," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(11), pages 1819-1833, November.
    3. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.
    4. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    5. Aparicio, Juan & Cordero, Jose M. & Ortiz, Lidia, 2019. "Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    6. Bohlool Ebrahimi & Mehdi Toloo, 2020. "Efficiency bounds and efficiency classifications in imprecise DEA: An extension," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(3), pages 491-504, March.
    7. Chen, Lei & Wang, Ying-Ming, 2020. "DEA target setting approach within the cross efficiency framework," Omega, Elsevier, vol. 96(C).
    8. Kao, Chiang & Liu, Shiang-Tai, 2009. "Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks," European Journal of Operational Research, Elsevier, vol. 196(1), pages 312-322, July.
    9. F. Hosseinzadeh Lotfi & G. R. Jahanshahloo & M. Khodabakhshi & M. Rostamy-Malkhlifeh & Z. Moghaddas & M. Vaez-Ghasemi, 2013. "A Review of Ranking Models in Data Envelopment Analysis," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-20, July.
    10. A. Hadi‐Vencheh & R. Kazemi Matin, 2011. "An application of IDEA to wheat farming efficiency," Agricultural Economics, International Association of Agricultural Economists, vol. 42(4), pages 487-493, July.
    11. Kadziński, Miłosz & Tervonen, Tommi, 2013. "Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements," European Journal of Operational Research, Elsevier, vol. 228(1), pages 169-180.
    12. Salvatore Corrente & Salvatore Greco & Roman Słowiński, 2017. "Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by n-point intervals," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 127-157, June.
    13. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    14. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    15. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    16. Ciomek, Krzysztof & Ferretti, Valentina & Kadzinski, Milosz, 2018. "Predictive analytics and disused railways requalification: insights from a Post Factum Analysis perspective," LSE Research Online Documents on Economics 85922, London School of Economics and Political Science, LSE Library.
    17. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    18. M C Gouveia & L C Dias & C H Antunes, 2008. "Additive DEA based on MCDA with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 54-63, January.
    19. Yongjun Shen & Elke Hermans & Tom Brijs & Geert Wets, 2013. "Data Envelopment Analysis for Composite Indicators: A Multiple Layer Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 739-756, November.
    20. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    21. Widiarto, Indra & Emrouznejad, Ali, 2015. "Social and financial efficiency of Islamic microfinance institutions: A Data Envelopment Analysis application," Socio-Economic Planning Sciences, Elsevier, vol. 50(C), pages 1-17.
    22. Bohlool Ebrahimi & Madjid Tavana & Andreas Kleine & Andreas Dellnitz, 2021. "An epsilon-based data envelopment analysis approach for solving performance measurement problems with interval and ordinal dual-role factors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1103-1124, December.
    23. Kadziński, Miłosz & Labijak, Anna & Napieraj, Małgorzata, 2017. "Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports," Omega, Elsevier, vol. 67(C), pages 1-18.
    24. Tervonen, Tommi & van Valkenhoef, Gert & Baştürk, Nalan & Postmus, Douwe, 2013. "Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 224(3), pages 552-559.
    25. Joe Zhu, 2014. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 1, pages 1-9, Springer.
    26. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2003. "Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)," European Journal of Operational Research, Elsevier, vol. 147(1), pages 117-127, May.
    27. Zhu, Joe, 2003. "Imprecise data envelopment analysis (IDEA): A review and improvement with an application," European Journal of Operational Research, Elsevier, vol. 144(3), pages 513-529, February.
    28. William W. Cooper & Kyung Sam Park & Gang Yu, 2001. "An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 49(6), pages 807-820, December.
    29. Lahdelma, Risto & Salminen, Pekka, 2006. "Stochastic multicriteria acceptability analysis using the data envelopment model," European Journal of Operational Research, Elsevier, vol. 170(1), pages 241-252, April.
    30. Zhu, Joe, 1996. "Robustness of the efficient DMUs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 90(3), pages 451-460, May.
    31. Risto Lahdelma & Pekka Salminen, 2001. "SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making," Operations Research, INFORMS, vol. 49(3), pages 444-454, June.
    32. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    33. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    34. Azadi, Majid & Farzipoor Saen, Reza, 2013. "A combination of QFD and imprecise DEA with enhanced Russell graph measure: A case study in healthcare," Socio-Economic Planning Sciences, Elsevier, vol. 47(4), pages 281-291.
    35. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
    36. Kao, Chiang, 2006. "Interval efficiency measures in data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1087-1099, October.
    37. Despotis, Dimitris K. & Smirlis, Yiannis G., 2002. "Data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 140(1), pages 24-36, July.
    38. M C Gouveia & L C Dias & C H Antunes, 2013. "Super-efficiency and stability intervals in additive DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(1), pages 86-96, January.
    39. Seiford, Lawrence M. & Zhu, Joe, 1998. "Stability regions for maintaining efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 108(1), pages 127-139, July.
    40. Shaher Z. Zahran & Jobair Bin Alam & Abdulrahem H. Al-Zahrani & Yiannis Smirlis & Stratos Papadimitriou & Vangelis Tsioumas, 2020. "Analysis of port efficiency using imprecise and incomplete data," Operational Research, Springer, vol. 20(1), pages 219-246, March.
    41. SHOKOUHI, Amir H. & HATAMI-MARBINI, Adel & TAVANA, Madjid & SAATI, Saber, 2010. "A robust optimization approach for imprecise data envelopment analysis," LIDAM Reprints CORE 2215, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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