Skip to main content
SpringerLink
Log in

Rang-adjusted measure: modelling and computational aspects from internal and external perspectives for network DEA

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

The range-adjusted measure (RAM) as one of the non-radial data envelopment analysis (DEA) models has been broadly used in the assessment of decision-making units (DMUs). In many situations, the DMUs have a multi-component (network) structure, where the output of each component can be used as the input of another component, which is referred to as intermediate output. Various methods with different forms of production possibility sets (PPSs) have been suggested to formulate the intermediate output in efficiency calculations that link network components and each of these methods leads to different efficiency scores. These different forms of PPSs include independent, relational, and cooperative, which can appraise the efficiency of a DMU from internal and external perspectives. This paper aims to clarify the relationship among different forms of PPSs for the network RAM-DEA model from internal and external perspectives by emphasizing the development of a network RAM-DEA model. This study shows that from internal evaluation, a DMU with a network structure may operate efficiently while it is inefficient from external evaluation. This study proves that to evaluate a DMU with a network structure, the cooperative form of PPS is more suitable from both internal and external perspectives. The independent form of PPS does not exactly define the relationships among the components, so it is not recommended for computing the efficiency of a network. Models associated with the relational form of PPS may cause excess supply (waste) in the network, which is not appropriate for internal evaluation. Finally, a real example illustrates the applicability of the presented model.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. The concept of weak disposability was first defined by Färe et al. (1989). This concept means that undesirable outputs can be reduced by the same reduction factor so that the relative proportions between the resulting outputs are kept constant. With this concept, the RAM-DEA model in this study can easily increase desirable outputs and simultaneously reduce undesirable outputs. The classification of technologies based on the hypothesis of weak disposability of outputs is reviewed in detail by Pham and Zelenyuk (2019).

References

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

    Google Scholar 

  • Avkiran NK, McCrystal A (2012) Sensitivity analysis of network DEA: NSBM versus NRAM. Appl Math Comput 218(22):11226–11239

    Google Scholar 

  • Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30(9):1078–1092

    Google Scholar 

  • Bardhan I, Bowlin W, Cooper WW, Sueyoshi T (1996) Models for measuring amounts of efficiency dominance in DEA: part i additive models and MED measures. J Operat Res Soc Japan 39:322–332

    Google Scholar 

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

    Google Scholar 

  • Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J Econ 30(1–2):91–107

    Google Scholar 

  • Chen K, Zhu J (2020) Additive slacks-based measure: computational strategy and extension to network DEA. Omega 91:102022

    Google Scholar 

  • Chen C, Zhu J, Yu JY, Noori H (2012) A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis. Eur J Oper Res 221(2):348–359

    Google Scholar 

  • Chen Y, Li Y, Liang L, Salo A, Wu H (2016) Frontier projection and efficiency decomposition in two-stage processes with slacks-based measures. Eur J Oper Res 250(2):543–554

    Google Scholar 

  • Conover WJ (1999) Practical nonparametric statistics, 3rd edn. Wiley, New York, p 578

    Google Scholar 

  • Cook WD, Hababou M (2001) Sales performance measurement in bank branches. Omega 29(4):299–307

    Google Scholar 

  • Cook WD, Zhu J, Bi G, Yang F (2010) Network DEA: additive efficiency decomposition. Eur J Oper Res 207(2):1122–1129

    Google Scholar 

  • Cooper WW, Park KS, Pastor JT (1999) RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J Prod Anal 11(1):5–42

    Google Scholar 

  • Cooper WW, Park KS, Pastor JT (2001) The range adjusted measure (RAM) in DEA: a response to the comment by steinmann and Zweifel. J Prod Anal 145:152

    Google Scholar 

  • Cui Q, Li Y (2018) Airline environmental efficiency measures considering materials balance Principles: an application of a network range-adjusted measure with weak-G disposability. J Environ Planning Manage 61(13):2298–2318

    Google Scholar 

  • FakhrMousavi SM, Amirteimoori A, Kordrostami S, Vaez-Ghasemi M (2022) Estimation of efficiency of two-stage processes using a fully fuzzy range-adjusted measure approach and strong complementary slackness conditions. Modern Res Decis Making 7(2):29–51

    Google Scholar 

  • Faramarzi GR, Khodakarami M, Shabani A, Saen RF, Azad F (2015) New network data envelopment analysis approaches: an application in measuring sustainable operation of combined cycle power plants. J Clean Prod 108:232–246

    Google Scholar 

  • Färe R, Grosskopf S (1997) Intertemporal production frontiers: with dynamic DEA. J Operat Res Soc 48(6):656–656

    Google Scholar 

  • Färe R, Grosskopf S (2000) Network DEA. Socioecon Plann Sci 34:35–49

    Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK, Pasurka C (1989) Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. Rev Econ Stat 71:90–98

    Google Scholar 

  • Färe R, Grosskopf S, Pasurka CA Jr (2007) Environmental production functions and environmental directional distance functions. Energy 32(7):1055–1066

    Google Scholar 

  • Heydari C, Omrani H, Taghizadeh R (2020) A fully fuzzy network DEA-Range adjusted measure model for evaluating airlines efficiency: a case of Iran. J Air Transp Manag 89:101923

    Google Scholar 

  • Huang HC, Hu CF (2021) Performance measurement for the recycling production system using cooperative game network data envelopment analysis. Sustainability 13(19):11060

    Google Scholar 

  • Hwang SN, Tong-Liang K (2006) Measuring managerial efficiency in non-life insurance companies: an application of two-stage data envelopment analysis. Int J Manag 23(3):699

    Google Scholar 

  • Kalantary M, Farzipoor Saen R, Toloie Eshlaghy A (2018) Sustainability assessment of supply chains by inverse network dynamic data envelopment analysis. Sci Iranica 25(6):3723–3743

    Google Scholar 

  • Kao C (2014) Efficiency decomposition in network data envelopment analysis with slacks-based measures. Omega 45:1–6

    Google Scholar 

  • Kao C (2016) Efficiency decomposition and aggregation in network data envelopment analysis. Eur J Oper Res 255(3):778–786

    Google Scholar 

  • Kao C (2018) A classification of slacks-based efficiency measures in network data envelopment analysis with an analysis of the properties possessed. Eur J Oper Res 270(3):1109–1121

    Google Scholar 

  • Kao C, Hwang SN (2008) Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. Eur J Oper Res 185(1):418–429

    Google Scholar 

  • Kao C, Hwang SN (2010) Efficiency measurement for network systems: IT impact on firm performance. Decis Support Syst 48(3):437–446

    Google Scholar 

  • Khalili-Damghani K, Tavana M (2013) A new fuzzy network data envelopment analysis model for measuring the performance of agility in supply chains. Int J Adv Manuf Technol 69(1):291–318

    Google Scholar 

  • Li Y, Cui Q (2017) Carbon neutral growth from 2020 strategy and airline environmental inefficiency: a network range adjusted environmental data envelopment analysis. Appl Energy 199:13–24

    Google Scholar 

  • Li Y, Cui Q (2018) Airline efficiency with optimal employee allocation: an input-shared network range adjusted measure. J Air Transp Manag 73:150–162

    Google Scholar 

  • Mahmoudabadi MZ, Azar A, Emrouznejad A (2018) A novel multilevel network slacks-based measure with an application in electric utility companies. Energy 158:1120–1129

    Google Scholar 

  • Omrani H, Soltanzadeh E (2016) Dynamic DEA models with network structure: An application for Iranian airlines. J Air Transp Manag 57:52–61

    Google Scholar 

  • Petridis K, Ünsal MG, Dey PK, Örkcü HH (2019) A novel network data envelopment analysis model for performance measurement of Turkish electric distribution companies. Energy 174:985–998

    Google Scholar 

  • Pham MD, Zelenyuk V (2019) Weak disposability in nonparametric production analysis: a new taxonomy of reference technology sets. Eur J Oper Res 274(1):186–198

    Google Scholar 

  • Sarkhosh-Sara A, Tavassoli M, Heshmati A (2020) Assessing the sustainability of high-, middle-, and low-income countries: A network DEA model in the presence of both zero data and undesirable outputs. Sustainable Production and Consumption 21:252–268

    Google Scholar 

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

    Google Scholar 

  • Shermeh HE, Najafi SE, Alavidoost MH (2016) A novel fuzzy network SBM model for data envelopment analysis: a case study in Iran regional power companies. Energy 112:686–697

    Google Scholar 

  • Statistics and Information of Ministry Energy (2017), http://isn.moe.gov.ir//.

  • Sueyoshi T, Goto M (2012) Efficiency-based rank assessment for electric power industry: a combined use of data envelopment analysis (DEA) and DEA-discriminant analysis (DA). Energy Economics 34(3):634–644

    Google Scholar 

  • Sueyoshi T, Sekitani K (2009) An occurrence of multiple projections in DEA-based measurement of technical efficiency: theoretical comparison among DEA models from desirable properties. Eur J Oper Res 196(2):764–794

    Google Scholar 

  • Sueyoshi T, Goto M, Ueno T (2010) Performance analysis of US coal-fired power plants by measuring three DEA efficiencies. Energy Policy 38:1675–1688

    Google Scholar 

  • Tavassoli M, Saen RF (2022) A new fuzzy network data envelopment analysis model for measuring efficiency and effectiveness: assessing the sustainability of railways. Appl Intell 52(12):13634–13658

    Google Scholar 

  • Tavassoli M, Faramarzi GR, Saen RF (2014) Efficiency and effectiveness in airline performance using a SBM-NDEA model in the presence of shared input. J Air Transp Manag 34:146–153

    Google Scholar 

  • Tavassoli M, Fathi A, Saen RF (2021) Assessing the sustainable supply chains of tomato paste by fuzzy double frontier network DEA model. Ann Operat Res 12:1–33

    Google Scholar 

  • Tavassoli M, Ketabi S, Ghandehari M (2022) A novel fuzzy network DEA model to evaluate efficiency of Iran’s electricity distribution network with sustainability considerations. Sustain Energy Technol Assess 52:102269

    Google Scholar 

  • Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130(3):498–509

    Google Scholar 

  • Tone K, Tsutsui M (2009) Network DEA: a slacks-based measure approach. Eur J Oper Res 197(1):243–252

    Google Scholar 

  • Tone K, Tsutsui M (2010) Dynamic DEA: a slacks-based measure approach. Omega 38(3–4):145–156

    Google Scholar 

  • Wang M, Chen Y, Zhou Z (2021) Assessing environmental efficiency of China’s industry system using two-stage range-adjusted measure model. Manag Environ Qual Int J 32(6):1401–1421

    Google Scholar 

  • Wu J, Xu G, Zhu Q, Zhang C (2021) Two-stage DEA models with fairness concern: modelling and computational aspects. Omega 105:102521

    Google Scholar 

  • Yu MM, Lin ET (2008) Efficiency and effectiveness in railway performance using a multi-activity network DEA model. Omega 36(6):1005–1017

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management, Faculty of Administrative Science and Economics, Lorestan University, Khorramabad, Iran

    Mohammad Tavassoli

  2. Department of Management, Faculty of Administrative Sciences and Economics, University of Isfahan, Isfahan, Iran

    Mahsa Ghandehari

  3. Department of Accounting, Faculty of Administrative Science and Economics, Lorestan University, Khorramabad, Iran

    Masoud Taherinia

Authors
  1. Mohammad Tavassoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahsa Ghandehari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masoud Taherinia
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MT is an Assistant Professor at the Department of Industrial Management, Lorestan University, in Iran. MT has published over 25 refereed papers in peer-reviewed journals. His H-index in Google Scholar is 15. He has 10 years of industrial and consultation experience. He has published several refereed papers in many prestigious journals such as Operations Management Research, Sustainable production and consumption, Annals of Operations Research, Journal of Air Transport Management, international Journal of Electrical Power & Energy Systems. MG is an Associate Professor at the Department of Industrial Management, University of Esfahan, in Iran. In 2006, he obtained his PhD in Industrial Management from Sharif University, in Iran. He has published several papers in many prestigious journals such as Computers & Industrial Engineering, Sustainable Energy Technologies and Assessments, Journal of Industrial and Systems Engineering, International Journal of Mathematics in Operational Research. MT is a member of faculty in area of finance and accounting. He received his BS and MA in Accounting from Allameh Tabatabai University, Tehran, in Iran. He obtained his PhD in Accounting from Pune University, in India. He has published several refereed papers in many journals such as The Journal of Asian Finance, Economics and Business (JAFEB), International Journal of Economics and Financial Issues, Advances in Mathematical Finance and Applications, Australasian Accounting, Business and Finance Journal, International Journal of Finance & Managerial Accounting, Journal of Management Accounting and Auditing Knowledge, Journal of Accounting and Social Interests, International Journal of Nonlinear Analysis and Applications, Empirical Research in Accounting and Journal of Hunan University Natural Sciences.

Corresponding author

Correspondence to Mohammad Tavassoli.

Ethics declarations

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix 1

Appendix 1

See Tables 6 and 7.

Table 6 The results of Wilcoxon rank-sum test for the ESCs
Full size table
Table 7 The results of Wilcoxon rank-sum test for the ESCs components
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tavassoli, M., Ghandehari, M. & Taherinia, M. Rang-adjusted measure: modelling and computational aspects from internal and external perspectives for network DEA. Oper Res Int J 23, 62 (2023). https://doi.org/10.1007/s12351-023-00802-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12351-023-00802-9

Keywords

Search

Navigation