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Computational and Applied Mathematics

, Volume 36, Issue 1, pp 45–61 | Cite as

A linear relational DEA model to evaluate two-stage processes with shared inputs

  • Mehdi Toloo
  • Ali Emrouznejad
  • Plácido Moreno
Article

Abstract

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach.

Keywords

Data envelopment analysis (DEA) Shared inputs Two-stage processes  IT investment Research income 

Mathematics Subject Classification

90C05 90C30 90C90 

Notes

Acknowledgments

The research was supported by the Czech Science Foundation (GACR project 14-31593S) and through European Social Fund within the project CZ.1.07/2.3.00/20.0296.

References

  1. Agrell PJ, Hatami-Marbini A (2013) Frontier-based performance analysis models for supply chain management: state of the art and research directions. Comput Ind Eng 66(3):567–583Google Scholar
  2. Akther S, Fukuyama H, Weber WL (2013) Estimating two-stage network Slacks-based inefficiency: an application to Bangladesh banking. Omega 41(1):88–96CrossRefGoogle Scholar
  3. Amirteimoori A, Kordrostami S (2005) Multi-component efficiency measurement with imprecise data. Appl Math Comput 162:1265–1277MathSciNetzbMATHGoogle Scholar
  4. Amirteimoori A, Emrouznejad A, Khoshandam L (2013) Classifying flexible measures in data envelopment analysis: a slacks-based measure. Measurement 46(10):4100–4107CrossRefGoogle Scholar
  5. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiency in data envelopment analysis. Manag Sci 30:1078–1092CrossRefzbMATHGoogle Scholar
  6. Banker RD, Kauffman RJ, Morey RC (1990) Measuring gains in operational efficiency from information technology: a study of the positran deployment at Hardee’s Inc. J Manag Inf Syst 7(2):29–54CrossRefGoogle Scholar
  7. Barros CP, Managi S, Matousek R (2012) The technical efficiency of the Japanese banks: non-radial directional performance measurement with undesirable output. Omega 40(1):1–8CrossRefGoogle Scholar
  8. Beasley JE (1990) Comparing university departments. Omega 18(2):171–183CrossRefGoogle Scholar
  9. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444MathSciNetCrossRefzbMATHGoogle Scholar
  10. Chen Y, Zhu J (2004) Measuring information technology’s indirect impact on firm performance. Inf Technol Manag J 5(1–2):9–22CrossRefGoogle Scholar
  11. Chen Y, Liangb L, Yangb F, Zhu J (2006) Evaluation of information technology investment: a data envelopment analysis approach. Comput Oper Res 33:1368–1379CrossRefGoogle Scholar
  12. Chen Y, Du J, David H, Zhu SJ (2010) DEA model with shared resources and efficiency decomposition. Eur J Oper Res 207(1):339–349MathSciNetCrossRefzbMATHGoogle Scholar
  13. Cook WD, Hababou M, Tuenter HJH (2000) Multicomponent efficiency measurement and shared inputs in data envelopment analysis: an application to sales and service performance in bank branches. J Product Anal 14:209–224CrossRefGoogle Scholar
  14. Cook WD, Zhu J (2007) Classifying inputs and outputs in DEA. Eur J Oper Res 180:692–699CrossRefzbMATHGoogle Scholar
  15. Cook WD, Liang L, Zhu J (2010) Measuring performance of two-stage network structures by DEA: a review and future perspective. Omega 38:423–430CrossRefGoogle Scholar
  16. de Mello Soares JCCB, Gomes EG, Angulo Meza L, Soares de Mello MHC, Soares de Mello AJR (2006) Engineering post-graduate programmes: a quality and productivity analysis. Stud Edu Eval 32:136–152Google Scholar
  17. Ebrahimnejad A, Tavana M, Lotfi FH, Shahverdi R, Yousefpour M (2014) A three-stage data envelopment analysis model with application to banking industry. Measurement 49:308–319CrossRefGoogle Scholar
  18. Emrouznejad A, Anouze AL (2010) DEA/C&R: DEA with classification and regression tree: a case of banking efficiency. Expert Syst 27(4):231–246CrossRefGoogle Scholar
  19. Emrouznejad A, Anouze AL (2009) A note on the modeling the efficiency of top Arab banks. Expert Syst Appl 36 (3, part 1):5741–5744Google Scholar
  20. Emrouznejad A, Parker BR, Tavares G (2008) Evaluation of research in efficiency and productivity: a thirty years survey of the scholarly literature in DEA. Soc Econ Plan 42(3):151–157Google Scholar
  21. Fare R, Grosskopf S (2000) Network DEA. Soc Econ Plan Sci 34(1):35–49CrossRefzbMATHGoogle Scholar
  22. Jahanshahloo GR, Amirteimoori AR, Kordrostami S (2004) Measuring the multi-component efficiency with shared inputs and outputs in data envelopment analysis. Appl Math Comput 155:283–293MathSciNetzbMATHGoogle Scholar
  23. Kao C, Hwang S-N (2008) Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. Eur J Oper Res 185:418–429CrossRefzbMATHGoogle Scholar
  24. Kao C (2009) Efficiency decomposition in network data envelopment analysis: a relational model. Eur J Oper Res 192:949–962CrossRefzbMATHGoogle Scholar
  25. Kao C, Hwang S-N (2010) Efficiency measurement for network systems: IT impact on firm performance. Decis Support Syst 48(3):437–446CrossRefGoogle Scholar
  26. Kao C (2014) Network data envelopment analysis: a review. Eur J Oper Res 239:1–16MathSciNetCrossRefzbMATHGoogle Scholar
  27. Kwimbere FJ (1987) Measuring efficiency in not-for-profit organisations: an attempt to evaluate efficiency in selected UK university departments using data envelopment analysis (DEAl. MSC thesis). School of Management, University of Bath, Claverton Down. Bath BA2 7AY, UKGoogle Scholar
  28. Paradi JC, Rouatt S, Zhu H (2011) Two-stage evaluation of bank branch efficiency using data envelopment analysis. Omega 39(1):99–109CrossRefGoogle Scholar
  29. Paradi JC, Zhu H (2013) A survey on bank branch efficiency and performance research with data envelopment analysis. Omega 1(1):61–79CrossRefGoogle Scholar
  30. Premachandra IM, Chen Y, Watson J (2011) DEA as a tool for predicting corporate failure and success: a case of bankruptcy assessment. Omega 39(6):620–626CrossRefGoogle Scholar
  31. Tavassoli M, Faramarzi GR, Farzipoor Saen R (2014) Efficiency and effectiveness in airline performance using a SBM-NDEA model in the presence of shared input. J Air Trans Manag 34:146–153CrossRefGoogle Scholar
  32. Toloo M (2009) On classifying inputs and outputs in DEA: a revised model. Eur J Oper Res 198:358–360MathSciNetCrossRefzbMATHGoogle Scholar
  33. Toloo M, Sohrabi B, Nalchigar S (2009) A new method for ranking discovered rules from data mining by DEA. Expert Syst Appl 36(4):8503–8508CrossRefGoogle Scholar
  34. Toloo M (2012) Alternative solutions for classifying inputs and outputs in data envelopment analysis. Comput Math Appl 63:1104–1110MathSciNetCrossRefzbMATHGoogle Scholar
  35. Toloo M (2013) The most efficient unit without explicit inputs: an extended MILP-DEA model. Measurement 46(9):3628–3634CrossRefGoogle Scholar
  36. Toloo M (2014a) Notes on classifying inputs and outputs in data envelopment analysis: a comment. Eur J Oper Res 235(3):810–812Google Scholar
  37. Toloo M (2014b) An epsilon-free approach for finding the most efficient unit in DEA. Appl Math Model 38:3182–3192Google Scholar
  38. Tomkins C, Green R (1988) An experiment in the use of data envelopment analysis for evaluating the efficiency of UK university departments of accounting. Fin Account Mgmt 4(2):147–164CrossRefGoogle Scholar
  39. Wang CH, Gopal R, Zionts S (1997) Use of data envelopment analysis in assessing information technology impact on firm performance. Ann Oper Res 73:191–213CrossRefzbMATHGoogle Scholar
  40. Yu M, Fan C (2009) Measuring the performance of multimode bus transit: a mixed structure network DEA model. Trans Res Part E 45:501–515CrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  1. 1.Department of Business AdministrationTechnical University of OstravaOstravaCzech Republic
  2. 2.Aston Business SchoolAston UniversityBirminghamUK
  3. 3.Department of Industrial ManagementUniversity of SevilleSevilleSpain

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