IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v57y2011i1p200-214.html
   My bibliography  Save this article

Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

Author

Listed:
  • Ahti Salo

    (Systems Analysis Laboratory, Aalto University School of Science, 00076 Aalto, Finland)

  • Antti Punkka

    (Systems Analysis Laboratory, Aalto University School of Science, 00076 Aalto, Finland)

Abstract

We develop comparative results for ratio-based efficiency analysis (REA) based on the decision-making units' (DMUs') relative efficiencies over sets of feasible weights that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals, which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs; (ii) dominance relations, which show what other DMUs a given DMU dominates in pairwise efficiency comparisons; and (iii) efficiency bounds, which show how much more efficient a given DMU can be relative to some other DMU or a subset of other DMUs. Unlike conventional efficiency scores, these results are insensitive to outlier DMUs. They also show how the DMUs' efficiency ratios relate to each other for all feasible weights, rather than for those weights only for which the data envelopment analysis (DEA) efficiency score of some DMU is maximized. We illustrate the usefulness of these results by revisiting reported DEA studies and by describing a recent case study on the efficiency comparison of university departments. This paper was accepted by Teck-Hua Ho, decision analysis.

Suggested Citation

  • Ahti Salo & Antti Punkka, 2011. "Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis," Management Science, INFORMS, vol. 57(1), pages 200-214, January.
    • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:200-214
    DOI: 10.1287/mnsc.1100.1265
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1100.1265
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1100.1265?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Köksalan, Murat & Büyükbasaran, Tayyar & Özpeynirci, Özgür & Wallenius, Jyrki, 2010. "A flexible approach to ranking with an application to MBA Programs," European Journal of Operational Research, Elsevier, vol. 201(2), pages 470-476, March.
    2. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    3. Tarja Joro & Pekka Korhonen & Jyrki Wallenius, 1998. "Structural Comparison of Data Envelopment Analysis and Multiple Objective Linear Programming," Management Science, INFORMS, vol. 44(7), pages 962-970, July.
    4. Pekka Korhonen & Margareta Soismaa & Aapo Siljamäki, 2002. "On the Use of Value Efficiency Analysis and Some Further Developments," Journal of Productivity Analysis, Springer, vol. 17(1), pages 49-64, January.
    5. Merja Halme & Tarja Joro & Pekka Korhonen & Seppo Salo & Jyrki Wallenius, 1999. "A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis," Management Science, INFORMS, vol. 45(1), pages 103-115, January.
    6. Salo, Ahti A., 1995. "Interactive decision aiding for group decision support," European Journal of Operational Research, Elsevier, vol. 84(1), pages 134-149, July.
    7. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    8. Halme, Merja & Korhonen, Pekka, 2000. "Restricting weights in value efficiency analysis," European Journal of Operational Research, Elsevier, vol. 126(1), pages 175-188, October.
    9. D Bouyssou, 1999. "Using DEA as a tool for MCDM: some remarks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(9), pages 974-978, September.
    10. 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.
    11. 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.
    12. Russell G. Thompson & F. D. Singleton & Robert M. Thrall & Barton A. Smith, 1986. "Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas," Interfaces, INFORMS, vol. 16(6), pages 35-49, December.
    13. Korhonen, Pekka & Tainio, Risto & Wallenius, Jyrki, 2001. "Value efficiency analysis of academic research," European Journal of Operational Research, Elsevier, vol. 130(1), pages 121-132, April.
    14. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    15. Wade D. Cook & Joe Zhu, 2008. "CAR-DEA: Context-Dependent Assurance Regions in DEA," Operations Research, INFORMS, vol. 56(1), pages 69-78, February.
    16. Avkiran, Necmi K. & Parker, Barnett R., 2010. "Pushing the DEA research envelope," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 1-7, March.
    17. Loren Tauer & Harold Fried & William Fry, 2007. "Measuring Efficiencies of Academic Departments within a College," Education Economics, Taylor & Francis Journals, vol. 15(4), pages 473-489.
    18. 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.
    19. Eilat, Harel & Golany, Boaz & Shtub, Avraham, 2008. "R&D project evaluation: An integrated DEA and balanced scorecard approach," Omega, Elsevier, vol. 36(5), pages 895-912, October.
    20. Johnes, Jill, 2006. "Data envelopment analysis and its application to the measurement of efficiency in higher education," Economics of Education Review, Elsevier, vol. 25(3), pages 273-288, June.
    21. C S Sarrico & R G Dyson, 2000. "Using DEA for planning in UK universities—an institutional perspective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(7), pages 789-800, July.
    22. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    23. Podinovski, Victor V., 2001. "DEA models for the explicit maximisation of relative efficiency," European Journal of Operational Research, Elsevier, vol. 131(3), pages 572-586, June.
    24. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    25. 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, Elsevier, vol. 132(2), pages 245-259, July.
    26. Ahn, Taesik & Charnes, Abraham & Cooper, William W., 1988. "Some statistical and DEA evaluations of relative efficiencies of public and private institutions of higher learning," Socio-Economic Planning Sciences, Elsevier, vol. 22(6), pages 259-269.
    27. Talluri, Srinivas & Paul Yoon, K., 2000. "A cone-ratio DEA approach for AMT justification," International Journal of Production Economics, Elsevier, vol. 66(2), pages 119-129, June.
    28. V V Podinovski, 2005. "The explicit role of weight bounds in models of data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1408-1418, December.
    29. Ahti A. Salo & Raimo P. Hämäläinen, 1992. "Preference Assessment by Imprecise Ratio Statements," Operations Research, INFORMS, vol. 40(6), pages 1053-1061, December.
    30. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 151-157, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schang, Laura & Hynninen, Yrjänä & Morton, Alec & Salo, Ahti, 2016. "Developing robust composite measures of healthcare quality – Ranking intervals and dominance relations for Scottish Health Boards," Social Science & Medicine, Elsevier, vol. 162(C), pages 59-67.
    2. Kangaspunta, Jussi & Liesiö, Juuso & Salo, Ahti, 2012. "Cost-efficiency analysis of weapon system portfolios," European Journal of Operational Research, Elsevier, vol. 223(1), pages 264-275.
    3. Xiyang Lei & Yongjun Li & Alec Morton, 2022. "Dominance and ranking interval in DEA parallel production systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 649-675, June.
    4. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    5. Harju, Mikko & Liesiö, Juuso & Virtanen, Kai, 2019. "Spatial multi-attribute decision analysis: Axiomatic foundations and incomplete preference information," European Journal of Operational Research, Elsevier, vol. 275(1), pages 167-181.
    6. 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.
    7. Roza Azizi & Reza Kazemi Matin, 2016. "Ranking Two-Stage Production Units in Data Envelopment Analysis," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-19, February.
    8. Akram Dehnokhalaji & Behjat Hallaji & Narges Soltani & Jafar Sadeghi, 2017. "Convex cone-based ranking of decision-making units in DEA," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 861-880, July.
    9. Liesiö, Juuso & Andelmin, Juho & Salo, Ahti, 2020. "Efficient allocation of resources to a portfolio of decision making units," European Journal of Operational Research, Elsevier, vol. 286(2), pages 619-636.
    10. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2013. "Weight Restrictions and Free Production in Data Envelopment Analysis," Operations Research, INFORMS, vol. 61(2), pages 426-437, April.
    11. Kairui Zuo & Jiancheng Guan, 2017. "Measuring the R&D efficiency of regions by a parallel DEA game model," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 175-194, July.
    12. Chen, Ya & Li, Yongjun & Liang, Liang & Salo, Ahti & Wu, Huaqing, 2016. "Frontier projection and efficiency decomposition in two-stage processes with slacks-based measures," European Journal of Operational Research, Elsevier, vol. 250(2), pages 543-554.
    13. Lim, Sungmook & Oh, Kwang Wuk & Zhu, Joe, 2014. "Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market," European Journal of Operational Research, Elsevier, vol. 236(1), pages 361-368.
    14. Ahti Salo, 2012. "A Seminar for Solving Client Problems in Project Teams," INFORMS Transactions on Education, INFORMS, vol. 13(1), pages 17-27, September.
    15. Li, Yongjun & Xie, Jianhui & Wang, Meiqiang & Liang, Liang, 2016. "Super efficiency evaluation using a common platform on a cooperative game," European Journal of Operational Research, Elsevier, vol. 255(3), pages 884-892.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giannis Karagiannis & Panagiotis Ravanos, 2023. "On Value Efficiency Analysis and Cone-Ratio Data Envelopment Analysis models," Discussion Paper Series 2023_03, Department of Economics, University of Macedonia, revised Mar 2023.
    2. Pereira, Miguel Alves & Camanho, Ana Santos & Figueira, José Rui & Marques, Rui Cunha, 2021. "Incorporating preference information in a range directional composite indicator: The case of Portuguese public hospitals," European Journal of Operational Research, Elsevier, vol. 294(2), pages 633-650.
    3. Tavana, Madjid & Ebrahimnejad, Ali & Santos-Arteaga, Francisco J. & Mansourzadeh, Seyed Mehdi & Matin, Reza Kazemi, 2018. "A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 70-89.
    4. Dyckhoff, Harald & Souren, Rainer, 2022. "Integrating multiple criteria decision analysis and production theory for performance evaluation: Framework and review," European Journal of Operational Research, Elsevier, vol. 297(3), pages 795-816.
    5. Sarrico, C. S. & Dyson, R. G., 2004. "Restricting virtual weights in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 159(1), pages 17-34, November.
    6. Victor V. Podinovski & Tatiana Bouzdine-Chameeva, 2013. "Weight Restrictions and Free Production in Data Envelopment Analysis," Operations Research, INFORMS, vol. 61(2), pages 426-437, April.
    7. Henriques, C.O. & Marcenaro-Gutierrez, O.D., 2021. "Efficiency of secondary schools in Portugal: A novel DEA hybrid approach," Socio-Economic Planning Sciences, Elsevier, vol. 74(C).
    8. Panagiotis Ravanos & Giannis Karagiannis, 2022. "On VEA, Production Trade-offs and Weight Restrictions," Discussion Paper Series 2022_04, Department of Economics, University of Macedonia, revised Jun 2022.
    9. HOSSEINZADEH LOTFI, Farhad & HATAMI-MARBINI, Adel & AGRELL, Per & GHOLAMI, Kobra, 2013. "Centralized resource reduction and target setting under DEA control," LIDAM Discussion Papers CORE 2013005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.
    11. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    12. T Joro & E-J Viitala, 2004. "Weight-restricted DEA in action: from expert opinions to mathematical models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 814-821, August.
    13. 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.
    14. 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.
    15. V V Podinovski, 2004. "Production trade-offs and weight restrictions in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1311-1322, December.
    16. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    17. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "A multiplier bound approach to assess relative efficiency in DEA without slacks," European Journal of Operational Research, Elsevier, vol. 203(1), pages 261-269, May.
    18. Yang, Jian-Bo & Wong, Brandon Y.H. & Xu, Dong-Ling & Stewart, Theodor J., 2009. "Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods," European Journal of Operational Research, Elsevier, vol. 195(1), pages 205-222, May.
    19. Kristof De Witte & Laura López-Torres, 2017. "Efficiency in education: a review of literature and a way forward," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 339-363, April.
    20. Tzeremes, Nickolaos & Halkos, George, 2010. "A DEA approach for measuring university departments’ efficiency," MPRA Paper 24029, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:57:y:2011:i:1:p:200-214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.