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Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

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Abstract

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.

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Notes

  1. See Sobczyk (1956) for a definition of gauge functions and their uses with convex regions.

  2. The concept of a “directed distance” is discussed in terms of the distance from a point to a hyperplane on page 164 in Charnes and Cooper (1961).

  3. Our attention has recently been called to Sueyoshi and Sekitani (2007) that uses cone programming based approach to solve (9) in a straightforward manner. Hence practically implementable alternative are now available. See Cooper et al. (2007) for the advantages of using ERM rather than RM to deal with the aggregation problem in DEA.

  4. Russell (1985) refers to this property as “commensurability” but we think that “affine invariant” is more descriptive.

References

  • Ahn T, Charnes A, Cooper WW (1988) Efficiency characterizations in different DEA models. Soc-Econ Plan Sci 22:253–257

    Article  Google Scholar 

  • Ali I, Seiford LM (1990a) Computational accuracy and infinitesimals in Data Envelopment Analysis. INFORMS 31:290–297

    Google Scholar 

  • Ali I, Seiford LM (1990b) Translational invariance in data envelopment analysis. Oper Res Lett 9:403–405

    Article  Google Scholar 

  • Arnold V, Bardhan I, Cooper WW, Gallegos A (1997) Primal and dual optimality in computer codes using two-stage solution procedure in DEA. In: Aronson JA, Zionts S (eds) Operations research methods, models and applications. Quorum Books, New York

    Google Scholar 

  • Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale efficiencies in DEA. Manage Sci 30:1078–1092

    Google Scholar 

  • Banker RD, Cooper WW, Seiford LM, Zhu J (2004) Returns to scale in DEA, Chapter 2. In Cooper, Seiford, Zhu (eds) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, Mass

  • Banker RD, Natarajan R (2004) Statistical tests based on DEA efficiency scores. In: Cooper WW, Seiford LM, Zhu J (eds) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Bardhan I, Bowlin WF, Cooper WW, Sueyoshi T (1996) Models and measures for efficiency dominance in DEA, Part II: free disposal hull (FDH) and Russell measure (RM) approaches. J Oper Res Soc Jpn 39:333–345

    Google Scholar 

  • Bardhan I, Cooper WW, Kumbhakar SC (1998) A simulation study of joint uses of DEA and statistical regressions for production function estimation and efficiency evaluation. J Prod Anal 9:249–278

    Article  Google Scholar 

  • Blackorby C, Russell RR (1999) Aggregation of efficiency indexes. J Prod Anal 12:5–20

    Article  Google Scholar 

  • Bowlin WF (1984) A Data Envelopment Analysis approach to performance evaluation in not-for-profit entities with an illustrative application to the U.S. Air Force. Ph.D. Thesis University of Texas Graduate School of Business, Austin Texas. Also available from University Micro-Films, Inc. in Ann Arbor, Michigan

  • Brockett PL, Cooper WW, Golden L, Kumbhakar SC, Kwinn MJ, Layton B (2007) Estimating elasticities with frontier and other regression for use in evaluating alternative advertising strategies for use in U.S. Army recruitment. Soc-Econ Plan Sci (to appear)

  • Brockett PL, Cooper WW, Deng H, Golden L, Kwinn MJ, Thomas DA (2002) The efficiency of joint advertising vs. service-specific advertising. Military Oper Res 7:57–75

    Google Scholar 

  • Brockett PL, Cooper WW, Kumbhakar SC, Kwinn MJ, Jr, McCarthy D (2004) Alternative statistical regression studies of the effects of joint and service specific advertising in military recruitment. J Oper Res Soc 55:1039–1048

    Article  Google Scholar 

  • Bulla S, Cooper WW, Park KS, Wilson D (2000) Evaluating efficiencies of turbofan jet engines: a data envelopment analysis approach. J Prop Power 16:431–439

    Article  Google Scholar 

  • Charnes A, Clarke RL, Cooper WW (1989) An approach to testing for organizational slack with R.D. Banker’s game theoretic formulation of DEA. Res Governm Non-Profit Account 5:211–230

    Google Scholar 

  • Charnes A, Cooper WW (1961) Management models and industrial applications of linear programming, vol 2, with A. Charnes. John Wiley and Sons, Inc., New York

  • Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Naval Res Logist Quart 9:181–186

    Article  Google Scholar 

  • Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J Econ 30:91–l07

    Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. J Oper Res 2:429–444

    Article  Google Scholar 

  • Charnes A, Cooper WW, Seiford LM, Stutz J (1983) Invariant multiplicative efficiency and piecewise Cobb-Douglas envelopments. Oper Res Lett 2:101–103

    Article  Google Scholar 

  • Charnes A, Cooper WW, Sueyoshi T (1985) Least squares/ridge regression and goal programming/constrained regression altenatives. Eur J Oper Res 27:144–157

    Google Scholar 

  • Coelli TJ (1998) A multi-stage methodology for the solution of orientated DEA models. Oper Res Lett 23:143–149

    Article  Google Scholar 

  • Cook WD, Kress M, Seiford LM (1993) On the use of ordinal Data Envelopment Analysis. J Oper Res Soc 44:133–140

    Article  Google Scholar 

  • Cooper WW (2005) Origins, uses of and relations between goal programming and Data Envelopment Analysis. J Multi-Criteria Decision Anal 13:3–11

    Article  Google Scholar 

  • Cooper WW, Huang Z, Li S (1996) Satisficing DEA models under chance constraints. In Annals of operations research, vol. 66, 1996, pp. 279–295. Special issue on Extensions and New Developments in DEA edited by W.W. Cooper, R.G. Thompson and R.M. Thrall

  • Cooper WW, Huang ZM, Li S, Parker B, Pastor JT (2007) Efficiency aggregation with enhanced Russell measures in DEA. Socio-Economic Planning Sciences (to appear)

  • Cooper WW, Huang Z, Li S, Zhu J (2006) Critique of Dmitruk and Koshevoy and of Bol Plus Expanded Opportunities for Efficiency and Effectiveness Evaluations with DEA. Working paper% W.W. Cooper, The Red McCombs School of Business, The University of Texas at Austin, Texas 78712

  • Cooper WW, Park KS, Pastor JT (2000) Marginal rates and elasticities of substitution in DEA. J Prod Anal 13:105–123

    Article  Google Scholar 

  • Cooper WW, Park KS, Pastor JT (1999a) RAM: a range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA. J Prod Anal 11:5–42

    Article  Google Scholar 

  • Cooper WW, Park KS, Pastor JT (2001) The range adjusted measure (RAM) in DEA: A response to the comments by Steinmann and Zweifl. J Prod Anal 15:145–152

    Article  Google Scholar 

  • Cooper WW, Park KS, Yu G (1999b) IDEA and AR-IDEA: Models for dealing with imprecise data in DEA. Manage Sci 45:597–607

    Google Scholar 

  • Cooper WW, Park KS, Yu G (2001) An illustrative application of IDEA (Imprecise Data Envelopment Analysis) to a Korean mobile telecommunication company. Oper Res 49:807–820

    Article  Google Scholar 

  • Cooper WW, Seiford LM, Tone K (2000) Data envelopment analysis: a comprehensive text with models, applications, references and DEA Solver Software. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Cooper WW, Seiford LM, Tone K (2006) Introduction to data envelopment analysis and its uses. Springer Science and Business Media. Inc., New York

    Google Scholar 

  • Cooper WW, Seiford LM, Zhu J (2004) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Dantzig G (1963) Linear programming and extensions. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Debreu G (1951) The Coefficient of resource utilization. Econometrica 9:273–292

    Article  Google Scholar 

  • Despotis DK (2005) Measuring human development via Data Envelopment Analysis, the Case of Asia and the Pacific. Omega 33:285–390

    Article  Google Scholar 

  • Dmitruk AV, Koshevaz GA (1991) On the existence of a technical efficiency criteria. J Econ Theory 55:121–144

    Article  Google Scholar 

  • Emrouznejad A, Parker B, Tavares G (2007) A bibliography of Data Envelopment Analysis (1978–2001). Soc-Econ Plan Sci (to appear)

  • Färe R, Grosskopf S (1996) Intertemporal production functions with dynamic DEA. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK (1994) Production frontiers. Press Syndicate of the University of Cambridge, Cambridge

    Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Färe R, Lovell CAK (1978) Measuring the technical efficiency of production. J Econ Theory 19:156–162

    Article  Google Scholar 

  • Farrell MJ (1957) The measurement of production efficiency. J Roy Stat Soc 120:253–290

    Article  Google Scholar 

  • Gattoufi S, Oral M, Reisman A (2004) Data Envelopment Analysis literature, A bibliography update (1951–2001). Soc-Econ Plan Sci 38:159–229

    Article  Google Scholar 

  • Gigerenzer G (2004) Striking a blow for sanity in theories of rationality. In: Augier M, March JG (eds) Models of a man, essays in memory of Herbert A. Simon. The MIT Press, Cambridge Mass

  • Golany B, Thore S (1997) The economic and social performance of nations: efficiency and returns to scale. Soc-Econ Plan Sci 31:191–204

    Article  Google Scholar 

  • Grosskopf S, Hayes KJ, Taylor LL, Weber WL (1999) Anticipating the consequences of school reform: a new use of DEA. Manage Sci 45:605–620

    Google Scholar 

  • Koopmans T (1951) Activity analysis of production and allocation. John Wiley & Sons, New York

    Google Scholar 

  • Lancaster KJ (1966) A new approach to consumer theory. J Political Econ 74:132–157

    Article  Google Scholar 

  • Lee J-D, Seogwon H, Kim T-Y (2005) The measurement of consumer efficiency considering the discrete choice of consumers. J Prod Anal 23:65–84

    Google Scholar 

  • Lovell CAK, Pastor JT (1995) Units invariant and translation invariant DEA models. Oper Res Lett 18:147–151

    Article  Google Scholar 

  • Mattingly JD (1996) Elements of gas turbine propulsion. McGraw-Hill, New York

    Google Scholar 

  • Pareto V (1909) Manuel d’Economie Politique. Giars & Briere, Paris

    Google Scholar 

  • Park KS (2004) Simplification of the transformations and redundancy of assurance regions in IDEA (Imprecise DEA). J Oper Res Soc 55:1333–1336

    Article  Google Scholar 

  • Pastor JT, Ruiz JL, Sirvent I (1999) An enhanced DEA Russell graph efficiency measure. J Oper Res Soc 115:596–607

    Google Scholar 

  • Portela MCAS, Borges PC, Thanassoulis E (2003) Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. J Prod Anal 19(2–3):251–269

    Article  Google Scholar 

  • Portela MCAS, Thanassoulis E, Simpson G (2004) Negative data in DEA: a directional distance approach applied to bank branches. J Oper Res Soc 55:1111–1121

    Article  Google Scholar 

  • Prieto AM, Zofio JL (2001) Evaluating effectiveness in public provision of infrastructure and equipment: the case of Spanish municipalities. J Prod Anal 15:41–58

    Article  Google Scholar 

  • Ramanathan R (2007) An application of Data Envelopment Analysis for Evaluating comparative performances of countries of the Middle East and North Africa. Soc-Econ Plan Sci (to appear)

  • Robinson J (1933) The economics of imperfect competition. Cambridge University Press, Cambridge

    Google Scholar 

  • Russell RR (1985) Measure of technical efficiency. J Econ Theory 35:109–126

    Article  Google Scholar 

  • Saaty TL, Braun J (1964) Nonlinear mathematics. Dover Publications, New York

    Google Scholar 

  • Schaible S (1996) Fractional programming. In: Gass SI, Harris CM (eds) Encyclopedia of operations research and management science. Kluwer Academic Publishers, Boston, pp 234–237

    Google Scholar 

  • Sengupta JK (1995) Dynamics of data envelopment analysis: theory of system efficiency. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Simar L, Wilson PW (2004) Performance of the bootstrap for DEA estimates and iterating the principle. In: Cooper WW, Seiford LM, Joe Zhu (eds) Handbook on DEA. Kluwer Academic Publishers, Norwell, Mass

    Google Scholar 

  • Simon HA (1957) Models of man: social and rational. John Wiley & Sons, New York

    Google Scholar 

  • Sobczyk A (1956) Symmetrical types of convex regions. Mathemat Magaz 29:175–192

    Article  Google Scholar 

  • Steinmann L, Zweifel P (2001) The range adjusted measure (RAM) in DEA: comment. J Prod Anal 15:142–145

    Article  Google Scholar 

  • Sueyoshi T, Honma T (2003) DEA network computing in multi-stage parallel processes. Int Trans Oper Res 10:1–27

    Article  Google Scholar 

  • Sueyoshi T, Sekitani K (2007) Computational strategy for Russell measure in DEA: second order cone programming. Eur J Oper Res 180:459–471

    Article  Google Scholar 

  • Takamura Y, Tone K (2003) A comparative site evaluation study for relocating Japanese government agencies out of Tokyo. Soc-Econ Plan Sci 37:85–102

    Article  Google Scholar 

  • Thompson RG, Langmeier LM, Lee CT, Lee E, Thrall RM (1990) The role of multiplier bounds in efficiency analysis with applications to Kansas farming. J Econ 46:93–108

    Google Scholar 

  • Thompson RG, Singleton FDJ, Thrall RM, Smith BA (1986) Comparative site evaluations for locating a high-energy physics lab in Texas. Interfaces 16:35–49

    Google Scholar 

  • Tone K (2001) A slacks based measure of efficiency in Data Envelopment Analysis. Eur J Oper Res 130:498–509

    Article  Google Scholar 

  • Thrall RM (1996) Duality, classification and slacks in DEA. Ann Oper Res 66:109–128

    Article  Google Scholar 

  • Tulkens H (1993) On FDH efficiency analysis: some methodological issues and applications in retail banking, courts and urban transit. J Prod Anal 1/2:83–210

    Article  Google Scholar 

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Acknowledgment

Professor Cooper would like to express his appreciation to the IC2 Institute of the University of Texas for support of his research.

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Authors and Affiliations

  1. The Red McCombs School of Business, The University of Texas at Austin, University Station One, Austin, B6500, TX, USA

    W. W. Cooper

  2. College of Engineering, Industrial and Operations Engineering, The University of Michigan, 1677 A IOE Building, Ann Arbor, 48109-2117, MI, USA

    L. M. Seiford

  3. National Graduate Institute for Policy Studies, 7-22-1 Roppongi, Minato-ku, Tokyo, 106-8677, Japan

    K. Tone

  4. Department of Management, Worcester Polytechnic Institute, Worcester, 01609, MA, USA

    J. Zhu

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  1. W. W. Cooper
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Correspondence to W. W. Cooper.

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Cooper, W.W., Seiford, L.M., Tone, K. et al. Some models and measures for evaluating performances with DEA: past accomplishments and future prospects. J Prod Anal 28, 151–163 (2007). https://doi.org/10.1007/s11123-007-0056-4

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