Journal of Productivity Analysis

, Volume 21, Issue 2, pp 113–132

Data Envelopment Analysis with Reverse Inputs and Outputs

  • Herbert F. Lewis
  • Thomas R. Sexton


Data envelopment analysis (DEA) assumes that inputs and outputs are measured on scales in which larger numerical values correspond to greater consumption of inputs and greater production of outputs. We present a class of DEA problems in which one or more of the inputs or outputs are naturally measured on scales in which higher numerical values represent lower input consumption or lower output production. We refer to such quantities as reverse inputs and reverse outputs. We propose to incorporate reverse inputs and outputs into a DEA model by returning to the basic principles that lead to the DEA model formulation. We compare our method to reverse scoring, the most commonly used approach, and demonstrate the relative advantages of our proposed technique. We use this concept to analyze all 30 Major League Baseball (MLB) organizations during the 1999 regular season to determine their on-field and front office relative efficiencies. Our on-field DEA model employs one output and two symmetrically defined inputs, one to measure offense and one to measure defense. The defensive measure is such that larger values correspond to worse defensive performance, rather than better, and hence is a reverse input. The front office model uses one input. Its outputs, one of which is a reverse output, are the inputs to the on-field model. We discuss the organizational implications of our results.

DEA reverse inputs reverse outputs Major League Baseball 


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  1. Anderson, T. “DEA WWW Bibliography.” Scholar
  2. Anderson, T. R. and G. P. Sharp. (1997). “A New Measure of Baseball Batters Using DEA.” Annals of Operations Research 73, 141–155.Google Scholar
  3. Baseball Archive Database. (1999). Version 3.0. Scholar
  4. Bessent, A., W. Bessent, J. Kennington and B. Reagan. (1982). “An Application of Mathematical Programming to Assess Productivity in the Houston Independent School District.” Management Science 28(12), 1355–1367.Google Scholar
  5. Byrnes, P., R. Fare and S. Grosskopf. (1984). “Measuring Productive Efficiency: An Application to Illinois Strip Mines.” Management Science 30(6), 671–681.Google Scholar
  6. Charnes, A. and W. W. Cooper. (1978). “Managerial Economics: Past, Present and Future.” Journal of Enterprise Management 1(1), 5–23.Google Scholar
  7. Charnes, A., W. W. Cooper and E. Rhodes. (1978). “Measuring the Efficiency of Decision Making Units.” European Journal of Operational Research 2(6), 429–444.Google Scholar
  8. Charnes, A., W. W. Cooper and E. Rhodes. (1979). “Measuring the Efficiency of Decision Making Units: Short Communication.” European Journal of Operational Research 3(4), 339.Google Scholar
  9. Chames, A., W. W. Cooper and E. Rhodes. (1981). “Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through.” Management Science 27(6), 668–697.Google Scholar
  10. Cooper, W. W., L. M. Seiford and K. Tone. (1999). “Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software.” Boston: Kluwer Academic Publishers.Google Scholar
  11. Emrouznejad, A. “DEA Bibliography.” Scholar
  12. Fare, R. and D. Primont. (1984). “Efficiency Measures for Multiplant Firms.” Operations Research Letters 3(5), 257–260.Google Scholar
  13. Farrell, M. J. (1957). “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society Series A, III, 253–290.Google Scholar
  14. Forsund, F. R., C. A. Knox-Lovell and P. Schmidt. (1980). “A Survey of Frontier Production Functions and of their Relationship to Efficiency Measurement.” Journal of Econometrics 13, 5–25.Google Scholar
  15. Fried, H. O., S. S. Schmidt and S. Yaisawarng. (1999). “Incorporating the Operating Environment into a Nonparametric Measure of Technical Efficiency.” Journal of Productivity Analysis 12, 249–267.Google Scholar
  16. Hollingsworth, B., P. Dawson and N. Maniadakis. (1999). “Measurement of Health Care: A Review of Non-Parametric Methods and Applications.” Health Care Management Science 2(3), 161–172.Google Scholar
  17. Howard, L. H. and J. L. Miller. (1993). “Fair Pay for Fair Play: Estimating Pay Equity in Professional Baseball with Data Envelopment Analysis.” Academy of Management Journal 36(4), 882–894.Google Scholar
  18. Lewin, A. Y., R. C. Morey and T. J. Cook. (1982). “Evaluating the Administrative Efficiency of Courts.” Omega 10(4), 401–426.Google Scholar
  19. Lewis, H. F. and T. R. Sexton. “Network DEA: Efficiency Analysis of Organizations with Complex Internal Structure.” Computers and Operations Research forthcoming.Google Scholar
  20. Mazur, M. J. (1994). “Evaluating the Relative Efficiency of Baseball Players.” In A. Charnes, W. W. Cooper, A. Lewin and L. M. Seiford (eds.), Data Envelopment Analysis: Theory, Methodology, and Applications. Kluwer Academic Publishers, 369–391.Google Scholar
  21. Nunamaker, T. R. (1983). “Measuring Routine Nursing Service Efficiency: A Comparison of Cost per Patient Day and Data Envelopment Analysis Models.” Health Services Research 18(2), 183–205.Google Scholar
  22. Rhodes, E. L. (1982). A Study of U.S. National Park Service Performance Variations: An Application of Data Envelopment Analysis. Working Paper Series No. 531. Buffalo: School of Management, State University of New York.Google Scholar
  23. Sexton, T. R., A. M. Leiken, A. H. Nolan, S. Liss, A. J. Hogan and R. H. Silkman. (1989). “Evaluating Managerial Efficiency of Veterans Administration Medical Centers using Data Envelopment Analysis.” Medical Care 27(12), 1175–1188.Google Scholar
  24. Sexton, T. R. and H. F. Lewis. (2003). “Two-Stage DEA: An Application to Major League Baseball.” Journal of Productivity Analysis 19(2/3), 227–249.Google Scholar
  25. Sexton, T. R. (1986). “The Methodology of Data Envelopment Analysis.” In R. H. Silkman (ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis. New Directions for Program Evaluation, No. 32, San Francisco: Jossey-Bass, 7–29.Google Scholar
  26. Sexton, T. R., R. H. Silkman and A. Hogan. (1986). “Data Envelopment Analysis: Critique and Extensions.” In R. H. Silkman (ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis. New Directions for Program Evaluation, No. 32, San Francisco: Jossey-Bass, 73–105.Google Scholar
  27. Sexton, T. R., R. Taggart and S. Sleeper. (1994). “Improving Pupil Transportation in North Carolina.” Interfaces January–February, 24(1), 87–103.Google Scholar
  28. Sexton, T. R., R. N. Norton and R. H. Silkman. (2002). “Firm-Specific Productive Efficiency Offsets in the Development of a Price Cap Formula.” The Electricity Journal 15(10), December.Google Scholar
  29. Sherman, H. D. (1984). “Hospital Efficiency Measurement and Evaluation: Empirical Test of a New Technique.” Medical Care 22(10), 922–938.Google Scholar
  30. USA Today. (2000). Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Herbert F. Lewis
    • 1
  • Thomas R. Sexton
    • 1
  1. 1.Harriman School for Management and PolicyState University of New York at Stony BrookFrance

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