Journal of Optimization Theory and Applications

, Volume 164, Issue 2, pp 679–701 | Cite as

A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry

  • Adel Hatami-Marbini
  • Madjid Tavana
  • Kobra Gholami
  • Zahra Ghelej Beigi
Article

Abstract

Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. The conventional DEA methods require accurate measurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are often imprecise or vague. Fuzzy set theory is widely used to quantify imprecise and vague data in DEA models. In this paper, we propose a four-step bounded fuzzy DEA model, where the inputs and outputs are assumed to be fuzzy numbers. In the first step, we create a hypothetical fuzzy anti-ideal DMU and calculate its best fuzzy relative efficiency. In the second step, we propose a pair of fuzzy DEA models to obtain the upper- and the lower-bounds of the fuzzy efficiency, where the lower-bound is at least equal to the fuzzy efficiency of the anti-ideal DMU, and the upper-bound is at most equal to one. In step three, we use multi-objective programming to solve the proposed fuzzy programs. In the fourth step, we propose a new method for ranking the bounded fuzzy efficiency scores. We also present a case study to demonstrate the applicability of the proposed model and the efficacy of the procedures and algorithms in measuring the safety performance of eight semiconductor facilities.

Keywords

Data envelopment analysis Fuzzy data Interval efficiency Safety Semiconductor industry 

Mathematical Subject Classification (2010)

90B50 68M20 90C70 

References

  1. 1.
    Charnes, A., Cooper, W.W., Rhodes, E.L.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2(6), 429–444 (1978)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Banker, R.D., Charnes, A., Cooper, W.W.: Some methods for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30(9), 1078–1092 (1984)CrossRefMATHGoogle Scholar
  3. 3.
    Cooper, W.W., Seiford, L.M., Tone, K.: Introduction to Data Envelopment Analysis and Its Uses with DEA Solver Software and References. Springer, New York (2006)Google Scholar
  4. 4.
    Emrouznejad, A., Parker, B.R., Tavares, G.: Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Soc. Econ. Plan. Sci. 42(3), 151–157 (2008)CrossRefGoogle Scholar
  5. 5.
    Cook, W.D., Seiford, L.M.: Data envelopment analysis (DEA)—thirty years on. Eur. J. Oper. Res. 192, 1–17 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Sengupta, J.K.: A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24(8–9), 259–266 (1992)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Kao, C., Liu, S.T.: A mathematical programming approach to fuzzy efficiency ranking. Int. J. Prod. Econ. 86(2), 145–154 (2003)CrossRefGoogle Scholar
  9. 9.
    Hatami-Marbini, A., Saati, S., Tavana, M.: An ideal-seeking fuzzy data envelopment analysis framework. Appl. Soft Comput. 10(4), 1062–1070 (2010)CrossRefGoogle Scholar
  10. 10.
    Guo, P., Tanaka, H.: Fuzzy DEA: a perceptual evaluation method. Fuzzy Set Syst. 119(1), 149–160 (2001)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Lertworasirikul, S., Fang, S.C., Joines, J.A., Nuttle, H.L.W.: Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Set Syst. 139(2), 379–394 (2003)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Hatami-Marbini, A., Emrouznejad, A., Tavana, M.: A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur. J. Oper. Res. 214, 457–472 (2011)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Bellman, R.E., Azadeh, L.: Decision making in a fuzzy environment. Manag. Sci. 17, 141–164 (1970)CrossRefGoogle Scholar
  14. 14.
    Despotis, D.K., Smirlis, Y.G.: Data envelopment analysis with imprecise data. Eur. J. Oper. Res. 140, 24–36 (2002)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Wang, Y.M., Greatbanks, R., Yang, J.: Interval efficiency assessment using data envelopment analysis. Fuzzy Set Syst. 153, 347–370 (2005)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wang, Y.M., Luo, Y.: DEA efficiency assessment using ideal and anti-ideal decision making units. Appl. Math. Comput. 173, 902–915 (2006)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Wu, D.: A note on DEA efficiency assessment using ideal point: an improvement of Wang and Luo’s model. Appl. Math. Comput. 183, 819–830 (2006)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Chen, J.X.: A comment on DEA efficiency assessment using ideal and anti-ideal decision making units. Appl. Math. Comput. 219, 583–591 (2012)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Wang, Y.M., Yang, J.B.: Measuring the performances of decision-making units using interval efficiencies. J. Comput. Appl. Math. 198, 253–267 (2007)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Wang, N.S., Yi, R.H., Wang, W.: Evaluating the performances of decision-making units based on interval efficiencies. J. Comput. Appl. Math. 216, 328–343 (2008)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Azizi, H., Wang, Y.M.: Improved DEA models for measuring interval efficiencies of decision-making units. Measurement 46, 1325–1332 (2013)CrossRefGoogle Scholar
  22. 22.
    Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Rezaie, V., Khanmohammadi, M.: Ranking DMUs by ideal points with interval data in DEA. Appl. Math. Model. 35, 218–229 (2011)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Sun, J., Wu, J., Guo, D.: Performance ranking of units considering ideal and anti-ideal DMU with common weights. Appl. Math. Model. 37(9), 6301–6310 (2013)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Azadeh, A., Mohammad Fam, I., Nazifkar, N.: The evaluation and improvement of safety behaviors among contractors of a large steel manufacturing company by fuzzy data envelopment analysis. J. Chin. Inst. Eng. 33(6), 823–832 (2010)CrossRefGoogle Scholar
  25. 25.
    Mohd Said, S., Sanwari, S.R., Said, F.: Technical and scale efficiency in Malaysian manufacturing industries in the presence of industrial accidents. World Appl. Sci. J. 24(7), 862–871 (2013)Google Scholar
  26. 26.
    El-Mashaleh, M.S., Rababeh, S.M., Hyari, K.H.: Utilizing data envelopment analysis to benchmark safety performance of construction contractors. Int. J. Proj. Mang. 28(1), 61–67 (2010)CrossRefGoogle Scholar
  27. 27.
    Rajaprasad, S.V.S., Prasada Rao, Y.V.S.S.V., Venkata Chalapathi, P.: Evaluation of safety performance in Indian construction segments using data envelope analysis. Asia Pac. J. Bus Manag. 4(1), 1–13 (2013)Google Scholar
  28. 28.
    Shen, Y., Hermans, E., Brijs, T., Wets, G., Vanhoof, K.: Road safety risk evaluation and target setting using data envelopment analysis and its extensions. Accid. Anal. Prev. 48, 430–441 (2012)CrossRefGoogle Scholar
  29. 29.
    Kelle, P., Schneider, H., Raschke, C., Shiraziff, H.: Highway improvement project selection by the joint consideration of cost-benefit and risk criteria. J. Oper. Res. Soc. 64, 313–325 (2013)CrossRefGoogle Scholar
  30. 30.
    Noroozzadeh, A., Sadjadi, S.: A new approach to evaluate railways efficiency considering safety measures. Decis. Sci. Lett. 2(2), 71–80 (2013)CrossRefGoogle Scholar
  31. 31.
    Mark, B.A., Jones, C.B., Lindley, L., Ozcan, Y.A.: An examination of technical efficiency, quality, and patient safety in acute care nursing units. Policy Polit. Nurs. Pract. 10(3), 180–186 (2009)CrossRefGoogle Scholar
  32. 32.
    Entani, T., Maeda, Y., Tanaka, H.: Dual models of interval DEA and its extension to interval data. Eur. J. Oper. Res. 136(1), 32–45 (2002)CrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Nav. Res Logist. Q. 9, 181–186 (1962)CrossRefMATHMathSciNetGoogle Scholar
  34. 34.
    Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York (1991)MATHGoogle Scholar
  35. 35.
    Zimmermann, H.J.: Fuzzy Sets Theory and Its Applications. Kluwer Academic Publishers, Boston (1996)CrossRefGoogle Scholar
  36. 36.
    Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9, 613–626 (1978)CrossRefMATHMathSciNetGoogle Scholar
  37. 37.
    Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, New York (1995)MATHGoogle Scholar
  38. 38.
    Ramík, J., Rímánk, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Set Syst. 16, 123–138 (1985)CrossRefMATHGoogle Scholar
  39. 39.
    Dubois, D., Prade, H.: Systems of linear fuzzy constraints. Fuzzy Set Syst. 3, 37–48 (1980)CrossRefMATHMathSciNetGoogle Scholar
  40. 40.
    Wang, Y.M., Luo, Y., Liang, L.: Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Syst. Appl. 36(3), 5205–5211 (2009)CrossRefGoogle Scholar
  41. 41.
    Hwang, C.L., Masud, A.S.M.: Multiple Objective Decision Making-Methods and Applications: A State-of-the-Art Survey. Springer, Berlin (1979)CrossRefMATHGoogle Scholar
  42. 42.
    Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Application. Wiley, New York (1986)MATHGoogle Scholar
  43. 43.
    Freed, N., Glover, F.: Simple but powerful goal programming model for discriminant problems. Eur. J. Oper. Res. 7, 44–60 (1981)CrossRefMATHGoogle Scholar
  44. 44.
    Freed, N., Glover, F.: Resolving certain difficulties and improving the classification power of the LP discriminant analysis procedure. Decis. Sci. 17, 589–595 (1986)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Adel Hatami-Marbini
    • 1
  • Madjid Tavana
    • 2
    • 3
  • Kobra Gholami
    • 4
  • Zahra Ghelej Beigi
    • 5
  1. 1.Louvain School of Management, Center of Operations Research and Econometrics (CORE)Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision SciencesLa Salle UniversityPhiladelphiaUSA
  3. 3.Business Information Systems Department, Faculty of Business Administration and EconomicsUniversity of PaderbornPaderbornGermany
  4. 4.Department of ScienceIslamic Azad UniversityBushehrIran
  5. 5.Department of MathematicsIslamic Azad UniversityIsfahanIran

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