DEA에서 교차효율성의 공격적 정형화

An Aggressive Formulation of Cross-efficiency in DEA

  • 임성묵 (고려대학교 경상대학 경영학부)
  • 발행 : 2008.12.31

초록

We propose a new aggressive formulation of cross-efficiency in Data Envelopment Analysis(DEA). In the traditional aggressive formulation, the efficiency score of a test DMU is maximized as the first goal while an average of efficiency scores of peer DMUs is minimized as the second goal. The proposed model replaces the second goal with the minimization of the best efficiency score of peer DMUs. We showed the model is a quasi-convex optimization problem, and for a solution method we developed a bisection method whose computational complexity is polynomial-time. We tested the model on 200 randomly generated DEA problems, and compared it with the traditional model in terms of various criteria. The experimental results confirmed the effectiveness and usefulness of the proposed model.

키워드

참고문헌

  1. Andersen, P. and N.C. Petersen, "A procedure for ranking efficient units in data envelopment analysis," Management Science, Vol.39, No.10(1993), pp.1261-1264 https://doi.org/10.1287/mnsc.39.10.1261
  2. Banker, R., A. Charnes, and W.W. Cooper, "Some models for estimating technical and scale inefficiencies in data envelopment analysis," Management Science, Vol.30, No. 9(1984), pp.1078-1092 https://doi.org/10.1287/mnsc.30.9.1078
  3. Boussofiane, A., R.G. Dyson, and E. Thanassoulis, "Applied data envelopment analysis," European Journal of Operational Research, Vol.52, No.1(1991), pp.1-15 https://doi.org/10.1016/0377-2217(91)90331-O
  4. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004
  5. Brockett, P. and B. Golany, "Using rank statistics for determining programmatic efficiency differences in data envelopment analysis," Management Science, Vol.42, No. 3(1996), pp.466-472 https://doi.org/10.1287/mnsc.42.3.466
  6. Chang, H.H., "Determinants of hospital efficiency:the case of central government-owned hospitals in Taiwan," The International Journal of Management Science, Vol.26, No.2(1998), pp.307-317
  7. Charnes, A. and W. Cooper, "Data Envelopment Analysis," in H.E. Bradley (Ed.) Operational Research '90, pp.641-646. Pergamon Press, Oxford, 1991
  8. Charnes, A., W.W. Cooper, and E. Rhodes, "Measuring the efficiency of decision making units," European Journal of Operational Research, Vol.2, No.6(1978), pp.429-444 https://doi.org/10.1016/0377-2217(78)90138-8
  9. Cooper, W.W., L.M. Seiford, and K. Tone, Data envelopment analysis:a comprehensive text with models, applications, references and DEA-solver software, Kluwer academic publishers, Boston, 2000
  10. Donthu, N., E.K. Hershberger, and T. Osmonbekov, "Benchmarking marketing productiviey using data envelopment analysis," Journal of Business Research, Vol.58, No. 11(2005), pp.1474-1482 https://doi.org/10.1016/j.jbusres.2004.05.007
  11. Doyle, J.R. and R.H. Green, "Cross-evaluation in DEA:Improving discrimination among DMUs," INFOR, Vol.33, No.3(1995), pp. 205-222
  12. Doyle, J. and R. Green, "Efficiency and Cross-efficiency in DEA:Derivations, Meanings and Uses," Journal of Operational Research Society, Vol.45, No.5(1994), pp.567-578 https://doi.org/10.2307/2584392
  13. Grosskopf, S. and C. Moutray, "Evaluating performance in Chicago public high schools in the wake of decentralization," Economics of Education Review, Vol.20, No.1(2001), pp.1-14 https://doi.org/10.1016/S0272-7757(99)00065-5
  14. Luo, X., "Evaluating the profitability and marketability efficiency of large banks-an application of data envelopment analysis," Journal of Business Research, Vol.56, No. 8(2003), pp.627-635 https://doi.org/10.1016/S0148-2963(01)00293-4
  15. Mcmullen, P.R. and G.V. Frazier, "Using simulation and data envelopment analysis to compare assembly line balancing solutions," Journal of Productivity Analysis, Vol.11, No.2(1998), pp.149-168 https://doi.org/10.1023/A:1007732016717
  16. Sexton, T.R., R.H. Silkman, and A.J. Hogan, "Data Envelopment Analysis:critique and extensions," In Measuring Efficiency:An Assessment of Data Envelopment Analysis. (Silkman, R.H., Ed.) pp.73-104. Jossey-Bass, San Francisco, 1986
  17. Shafer, S.M. and T.A. Byrd, "A framework for measuring the efficiency of organizational investments in information technology using data envelopment analysis," The International Journal of Management Science, Vol.28(2000), pp.125-141
  18. Sueyoshi, T., K. Ohnishi, and Y. Kinase, "A benchmark approach for baseball evaluation," European Journal of Operational Research, Vol.115, No.3(1999), pp.429-448 https://doi.org/10.1016/S0377-2217(98)00126-X
  19. Talluri, S., "A benchmarking method for business-process reengineering and improvement," The International Journal of Flexible Manufacturing Systems, Vol.12, No.4(2000), pp.291-304 https://doi.org/10.1023/A:1008174116461
  20. Talluri, S., "Data envelopment analysis:models and extensions," Decision Line, Vol. 31(2000), pp.8-11
  21. Talluri, S. and J. Sarkis, "Extensions in efficiency measurement of alternate machine component grouping solutions via data envelopment analysis," IEEE Transactions on Engineering Management, Vol.44, No.3 (1997), pp.299-304 https://doi.org/10.1109/17.618171
  22. The MathWorks, Inc., MATLAB(software package), http://www.mathworks.com, 2004. 100-109