Skip to main content
SpringerLink
Log in

Ranking of Efficient DMUs Using Super-Efficiency Inverse DEA Model

  • Conference paper
  • First Online:
Soft Computing for Problem Solving

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 547))

  • 344 Accesses

Abstract

The overall potential for improving the relative efficiency of decision-making units (DMUs) is revealed by applying the data envelopment analysis (DEA) model. This study proposes a ranking system for ordering efficient DMUs with a super-efficiency inverse DEA (IDEA) model under a constant return to scale (CRS) assumption. IDEA is applied to evaluate the expected output or input variation level while keeping the efficiency value unchanged. For a numerical illustration of the proposed model in real-life problems, firstly, this study calculated the efficiency score of all 52 bus depots of Rajasthan State Road Transport Corporation (RSRTC) for the year 2018–19, applying the DEA model under the CRS assumption. The results revealed that 7 bus depots are efficient. Secondly, these 7 efficient depots have been ranked using the proposed super-efficiency IDEA model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Amin GR, Emrouznejad A, Gattoufi S (2017) Minor and major consolidations in inverse DEA: definition and determination. Comput Ind Eng 103:193–200

    Article  Google Scholar 

  2. https://www.financialexpress, August2020. Accessed on 2 Apr 2021

  3. Cafiso S, Di Graziano A, Pappalardo G (2013) Road safety issues for bus transport management. Accid Anal Prev 60:324–333

    Article  Google Scholar 

  4. De Oña J, De Oña R, Eboli L, Mazzulla G (2013) Perceived service quality in bus transit service: a structural equation approach. Transp Policy 29:219–226

    Article  Google Scholar 

  5. https://bit.ly/2WKHOSf. Accessed on 12 May 2020

  6. https://transport.rajasthan.gov.in/content/transportportal/en/RSRTC/public-relation/AnnualReport.html. Accessed on 23 Sept 2020

  7. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444

    Article  MathSciNet  MATH  Google Scholar 

  8. Cavaignac L, Petiot R (2017) A quarter century of data envelopment analysis applied to the transport sector: a bibliometric analysis. Socioecon Plann Sci 57:84–96

    Article  Google Scholar 

  9. Wei Q, Zhang J, Zhang X (2000) An inverse DEA model for inputs/outputs estimate. Eur J Oper Res 121(1):151–163

    Article  MathSciNet  MATH  Google Scholar 

  10. Yan H, Wei Q, Hao G (2002) DEA models for resource reallocation and production input/output estimation 136(1):19–31

    Google Scholar 

  11. Hadi-Vencheh A, Foroughi AA (2006) A generalized DEA model for inputs/outputs estimation. Math Comput Modell 43(5-6):447–457

    Google Scholar 

  12. Jahanshahloo GR, Hosseinzadeh Lotfi F, Rostamy-Malkhalifeh M, Ghobadi S (2014) Using enhanced Russell model to solve inverse data envelopment analysis problems. Sci World J

    Google Scholar 

  13. Jahanshahloo GR, Soleimani-Damaneh M, Ghobadi S (2015) Inverse DEA under inter-temporal dependence using multiple-objective programming. Eur J Oper Res 240(2):447–456

    Google Scholar 

  14. Hadi-Vencheh A, Hatami-Marbini A, Ghelej Beigi Z, Gholami K (2015) An inverse optimization model for imprecise data envelopment analysis Optimization 64(11):2441–2454

    Google Scholar 

  15. Amin GR, Al-Muharrami S, Toloo M (2019) A combined goal programming and inverse DEA method for target setting in mergers. Expert Syst Appl 115:412–417

    Google Scholar 

  16. Le MH, Afsharian M, Ahn H (2021) Inverse frontier-based benchmarking for investigating the efficiency and achieving the targets in the vietnamese education system. Omega 103:102427

    Article  Google Scholar 

  17. Soleimani-Chamkhorami K, Hosseinzadeh Lotfi F, Jahanshahloo G, Rostamy-Malkhalifeh M (2020) A ranking system based on inverse data envelopment analysis. IMA J Manag Math 31(3):367–385

    Google Scholar 

  18. Sexton TR, Silkman RH, Hogan AJ (1986) Data envelopment analysis: critique and extensions. New Direct Prog Eval 1986(32):73–105

    Article  Google Scholar 

  19. Wu J, Sun J, Liang L, Zha Y (2011) Determination of weights for ultimate cross efficiency using Shannon entropy. Expert Syst Appl 38(5):5162–5165

    Article  Google Scholar 

  20. Jahanshahloo GR, Lotfi FH, Jafari Y, Maddahi R (2011) Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. Appl Math Model 35(1):544–549

    Article  MathSciNet  MATH  Google Scholar 

  21. Andersen P, Petersen NC (1993) A procedure for ranking efficient units in data envelopment analysis. Manage Sci 39(10):1261–1264

    Article  MATH  Google Scholar 

  22. Mehrabian S, Alirezaee MR, Jahanshahloo GR (1999) A complete efficiency ranking of decision making units in data envelopment analysis. Comput Optim Appl 14(2):261–266

    Article  MathSciNet  MATH  Google Scholar 

  23. Tone K (2002) A slacks-based measure of super-efficiency in data envelopment analysis. Eur J Oper Res 143:32–41

    Article  MathSciNet  MATH  Google Scholar 

  24. Jahanshahloo GR, Lotfi FH, Shoja N, Tohidi G, Razavyan S (2004) Ranking using l1-norm in data envelopment analysis. Appl Math Comput 153(1):215–224

    MathSciNet  MATH  Google Scholar 

  25. Sueyoshi T, Ohnishi K, Kinase Y (1999) A benchmark approach for baseball evaluation. Eur J Oper Res 115(3):429–448

    Article  MATH  Google Scholar 

  26. Jahanshahloo GR, Junior HV, Lotfi FH, Akbarian D (2007) A new DEA ranking system based on changing the reference set. Eur J Oper Res 181(1):331–337

    Article  MATH  Google Scholar 

  27. Bian YW, Xu H (2013) DEA ranking method based upon virtual envelopment frontier and TOPSIS. Syst Eng Theo Pract 33(2):482–488

    Google Scholar 

  28. Li Y, Wang YZ, Cui Q (2015) Evaluating airline efficiency: an application of virtual frontier network SBM. Transp Res Part E: Logist Transp Rev 81:1–17

    Article  Google Scholar 

  29. Cui Q, Li Y (2014) The evaluation of transportation energy efficiency: an application of three-stage virtual frontier DEA. Transp Res Part D: Transp Environ 29:1–11

    Article  Google Scholar 

  30. Wanke P, Barros CP (2016) Efficiency in Latin American airlines: a two-stage approach combining virtual frontier dynamic DEA and simplex regression. J Air Transp Manag 54:93–103

    Article  Google Scholar 

  31. Barros CP, Wanke P, Dumbo S, Manso JP (2017) Efficiency in angolan hydro-electric power station: a two-stage virtual frontier dynamic DEA and simplex regression approach. Renew Sustain Energy Rev 78:588–596

    Article  Google Scholar 

  32. Aneja R, Sehrawat N (2020) Depot-wise efficiency of haryana roadways: a data envelopment analysis. Arthaniti: J Econom Theo Pract 0976747920954973

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, BITS Pilani, Pilani Campus, India

    Swati Goyal, Manpreet Singh Talwar, Shivi Agarwal & Trilok Mathur

Authors
  1. Swati Goyal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manpreet Singh Talwar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shivi Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Trilok Mathur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shivi Agarwal .

Editor information

Editors and Affiliations

  1. School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Manoj Thakur

  2. School of Computing and Electrical Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Samar Agnihotri

  3. School of Computing and Electrical Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Bharat Singh Rajpurohit

  4. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

  5. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  6. School of Mathematics, Computer Science and Engineering, Liverpool Hope University, Liverpool, UK

    Atulya K. Nagar

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Goyal, S., Talwar, M.S., Agarwal, S., Mathur, T. (2023). Ranking of Efficient DMUs Using Super-Efficiency Inverse DEA Model. In: Thakur, M., Agnihotri, S., Rajpurohit, B.S., Pant, M., Deep, K., Nagar, A.K. (eds) Soft Computing for Problem Solving. Lecture Notes in Networks and Systems, vol 547. Springer, Singapore. https://doi.org/10.1007/978-981-19-6525-8_47

Download citation

Publish with us

Policies and ethics

Search

Navigation