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A modified DEA cross efficiency method with negative data and its application in supplier selection

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Abstract

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

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References

  • Amini A, Alinezhad A (2016) A Combined evaluation method to rank alternatives based on VIKOR and DEA with BELIEF structure under uncertainty. Iran J Optim 8(2):111–122

    Google Scholar 

  • Andersen P, Petersen NC (1993) A procedure for ranking efficient units in data envelopment analysis. Manag Sci 39(10):1261–1294

    MATH  Google Scholar 

  • Anderson TR, Hollingsworth KB, Inman LB (2002) The fixed weighting nature of a cross-evaluation model. J Prod Anal 18(1):249–255

    Google Scholar 

  • Asmild M, Pastor JT (2010) Slack free MEA and RDM with comprehensive efficiency measures. Omega 38(6):475–483

    Google Scholar 

  • Azizi H, Amir Teymori A, Farzipour Samen R (2018) Supplier selection based on optimistic and pessimistic perspectives. J Dev Evolut Manag 31:11–20

    Google Scholar 

  • Badorf F, Wagner SM, Hoberg K, Papier F (2019) How supplier economies of scale drive supplier selection decisions. J Supply Chain Manag 55(3):45–67

    Google Scholar 

  • Bai CH, Kusi-Sarpong S, Badri-Ahmadi H, Sarkis J (2019) Social sustainable supplier evaluation and selection: a group decision-support approach. Int J Prod Res. https://doi.org/10.1080/00207543.2019.1574042

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Bardhan I, Bowlin WF, Cooper WW, Sueyoshi T (1996) Models for efficiency dominance in data envelopment analysis: part i: additive models and MED measures. J Oper Res Soc Jpn 39:322–332

    MATH  Google Scholar 

  • Beil DR (2010) Supplier selection. In: Cochran JJ (ed.), Wiley encyclopedia of operations research and management science

  • Bilisik ME, Caglar N, Bilisik ON (2012) A comparative performance analysis model and supplier positioning in performance maps for supplier selection and evaluation. Procedia Soc Behav Sci 58:1434–1442

    Google Scholar 

  • Chai J, Ngai EWT (2019) Decision-making techniques in supplier selection: recent accomplishments and what lies ahead. Exp Syst Appl. https://doi.org/10.1016/j.eswa.2019.112903

    Article  Google Scholar 

  • Chai J, Liu JNK, Ngai EWT (2013) Application of decision-making techniques in supplier selection: a systematic review of the literature. Expert Syst Appl 40(10):3872–3885

    Google Scholar 

  • Chang CL (2009) A modified vikor method for multiple criteria analysis. Environ Monit Assess 168(1):339–344

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Chen SJ, Hwang CL (1992) Fuzzy multiple attribute decision making. Springer

    MATH  Google Scholar 

  • Chen LY, Wang TC (2009) Optimizing partners’ choice in IS/IT outsourcing projects: the strategic decision of fuzzy VIKOR. Int J Prod Econ 120(1):233–242

    Google Scholar 

  • Cheng G, Zervopoulos P, Qian Z (2013) A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis. Eur J Oper Res 225(1):100–105

    Google Scholar 

  • Davtalab-Olyaie M (2018) A secondary goal in DEA cross efficiency evaluation: a “one home run is much better than two doubles” criterion. J Oper Res Soc 70(5):807–816

    Google Scholar 

  • Dempsy WA (1978) Vendor selection and the buying process. Ind Mark Manag 7(4):257–267

    Google Scholar 

  • Dickson G (1966) An analysis of vendor selection systems and decisions. J Purch 2(1):5–17

    Google Scholar 

  • Dobos I, Vörösmarty G (2018) Inventory-related costs in green supplier selection problems with data envelopment analysis (DEA). Int J Prod Econ. https://doi.org/10.1016/j.ijpe.2018.03.022

    Article  MATH  Google Scholar 

  • Dodkanloo Milan M, Jafarzadeh-Ghoushchi S (2017) Providing a hybrid model to evaluate and select suppliers based on the criterion loss and the preferential structure of the decision-maker. J Oper Res Appl 14(4):45–65

    Google Scholar 

  • Doyle J, Green R (1994) Efficiency and cross efficiency in DEA: derivations, meanings and the uses. J Oper Res Soc 45(5):567–578

    MATH  Google Scholar 

  • Doyle JR, Green RH (1995) Cross-evaluation in DEA: improving discrimination among DMUs. Infor 33:205–222

    MATH  Google Scholar 

  • Ellram LM (1995) Total cost of ownership: an analysis approach for purchasing. Int J Phys Distrib Logist Manag 25(8):4–23

    Google Scholar 

  • Emrouznejad A, Anouze AL, Thanassoulis E (2010a) A semi-oriented radial measure for measuring the efficiency of decision-making units with negative data, using DEA. Eur J Oper Res 200(1):297–304

    MATH  Google Scholar 

  • Emrouznejad A, Amin GR, Thanassoulis E, Anouze AL (2010b) On the boundedness of the SORM DEA models with negative data. Eur J Oper Res 206(1):265–268

    MathSciNet  MATH  Google Scholar 

  • Fazeli Farsani M, Ziglari F, Asad Sh (2015) Scrutinizing the performance of commodity suppliers and contractors, supply chain gas company province Charmahal and Bakhtiari by methodology dea. J Strateg Manag Res 21(58):101–116

    Google Scholar 

  • Fei L, Deng Y, Hu Y (2018) DS-VIKOR: a new multi-criteria decision-making method for supplier selection. Int J Fuzzy Syst 21(1):157–175

    MathSciNet  Google Scholar 

  • Friedman L, Sinuany-Stern Z (1997) Scaling units via the canonical correlation analysis and the data envelopment analysis. Eur J Oper Res 100(3):629–637

    MATH  Google Scholar 

  • Fu HP (2014) Integrating VIKOR with DEA for efficiency performance measurement. In: International conference on e-Education, e-business and information management (ICEEIM 2014)

  • García-Lapresta JL, Martínez-Panero M (2009) Linguistic-based voting through centered OWA operators. Fuzzy Optim Decis Making 8:381–393

    MathSciNet  MATH  Google Scholar 

  • García-Lapresta JL, Pérez-Román D (2017) A consensus reaching process in the context of non- uniform ordered qualitative scales. Fuzzy Optim Decis Making 16:449–461

    MathSciNet  MATH  Google Scholar 

  • Golany B (1988) An interactive MOLP procedure for the extension of data envelopment analysis to effectiveness analysis. J Oper Res Soc 39(8):725–734

    MATH  Google Scholar 

  • Gupta P, Govindan K, Mehlawat MK, Kumar S (2016) Aweighted possibilistic programming approach for sustainable vendor selection and order allocation in a fuzzy environment. Int J Adv Manuf Technol 86(58):1785–1804

    Google Scholar 

  • Hashimoto A (1997) A ranked voting system using a DEA/AR exclusion model: a note. Eur J Oper Res 97:600–604

    MATH  Google Scholar 

  • Hatami-Marbini A, Agrell PJ, Tavana M, Khoshnevis P (2017) A flexible cross efficiency fuzzy data envelopment analysis model for sustainable sourcing. J Clean Prod 142:2761–2779

    Google Scholar 

  • Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing withwords. IEEE Trans Fuzzy Syst 8:746–752

    Google Scholar 

  • Ho W, Xu X, Dey PK (2010) Multi-criteria decision making approaches for supplier evaluation and selection: a literature review. Eur J Oper Res 202(1):16–24

    MATH  Google Scholar 

  • Izadikhah M, Farzipoor SR, Ahmadi K (2017) How to assess the sustainability of suppliers in volume discount context? A new data envelopment analysis approach. Transp Res Part D Transp Environ 51:102–121

    MATH  Google Scholar 

  • Jauhar SK, Pant M (2017) Integrating DEA with DE and MODE for sustainable supplier selection. J Comput Sci 21:299–306

    Google Scholar 

  • Jauhar SK, Pant M, Abraham A (2014). A novel approach for sustainable supplier selection using differential evolution: a case on pulp and paper industry. In: Intelligent data analysis and its applications, Volume II, (pp. 105–117). Springer, Cham

  • Jeya Girubha R, Vinodh S (2012) Application of fuzzy VIKOR and environmental impact analysis for material selection of an automotive component. Mater Des 37:478–486

    MATH  Google Scholar 

  • Kahraman C, Onar SC, Oztaysi B (2015) Fuzzy multicriteria decisionmaking: a literature review. Int J Comput Intell Syst 8(4):637–666

    MATH  Google Scholar 

  • Kannan D, de Sousa Jabbour ABL, Jabbour CJC (2014) Selecting green suppliers based on GSCM practices: using fuzzy TOPSIS applied to a Brazilian electronics company. Eur J Oper Res 233(2):432–447

    MathSciNet  MATH  Google Scholar 

  • Karbasian M, Javanmardi M, Khabushani A, Zanjirchi M (2011) A hybrid approach using ISM for leveling agile criteria and fuzzy AHP to determine the relative weights of evaluation criteria and fuzzy TOPSIS to rank the alternatives. Prod Oper Manag 2(1):107–134

    Google Scholar 

  • Kazemi Matina R, Amin GR, Emrouznejad A (2014) A modified semi-oriented radial measure for target setting with negative data. Measurement 54:152–158

    Google Scholar 

  • Khoveyni M, Eslami R, Yang G (2017) Negative data in DEA: Recognizing congestion and specifying the least and the most congested decision making units. Comput Oper Res 79:39–48

    MathSciNet  MATH  Google Scholar 

  • Kirschstein T, Meisel F (2019) A multi-period multi-commodity lot-sizing problem with supplier selection, storage selection and discounts for the process industry. Eur J Oper Res 279:393–406

    MathSciNet  MATH  Google Scholar 

  • Kiser GE, Rao CP, Rao SR (1975) Vendor attribute evaluations of buying center members other than purchasing executives. Ind Mark Manag 4:45–54

    Google Scholar 

  • Lee ZY, Pai CC (2015) Applying improved DEA & VIKOR methods to evaluate the operation performance for world’s major TFT–LCD manufacturers. Asia-Pac J Oper Res 32(3):1550020

    MATH  Google Scholar 

  • Lehman D, O’Shaughnessy J (1982) Decision criteria used in buying different categories of products. J Purch Mater Manag 18(1):9–14

    Google Scholar 

  • Li X-B, Reeves GR (1999) Multiple criteria approach to data envelopment analysis. Eur J Oper Res 115:507–517

    MATH  Google Scholar 

  • Liao H, Mi X, Xu Z (2020) A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optim Decis Making 19:81–134

    MathSciNet  MATH  Google Scholar 

  • Lin R, Yang W, Huang H (2019) A modified slacks-based super-efficiency measure in the presence of negative data. Comput Ind Eng 135:39–52

    Google Scholar 

  • Mardani A, Jusoh A, Zavadskas EK (2015) Fuzzy multiple criteria decision-making techniques and applications: two decades review from 1994 to 2014. Expert Syst Appl 42:4126–4148

    Google Scholar 

  • Matin RK, Azizi R (2011) A two-phase approach for setting targets in DEA with negative data. Appl Math Model 35(12):5794–5803

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Mohammadnezhad Chari F, Safaei Ghadikolaei A (2017) supply chain identify and rank the criteria for selecting suppliers in the LARG (Case study: KALLEH Food Industry). J Oper Res Appl 13(4):103–120

    Google Scholar 

  • Musani M, Jemain AA (2015) Ranking schools’ academic performance using a fuzzy VIKOR. J Phys Conf Ser 622:012036

    Google Scholar 

  • Nicole A, Lea F, Zilla SS (2002) Review of ranking methods in the data envelopment analysis context. Eur J Oper Res 140:249–265

    MathSciNet  MATH  Google Scholar 

  • Opricovic S (1998) Multicriteria optimization of Civil Engineering Systems Faculty of Civil Engineering, Belgrade

  • Opricovic S, Tzeng G-H (2002) Multicriteria planning of post-earthquake sustainable reconstruction. Comput-Aided Civ Infra Eng 17(3):211–220

    Google Scholar 

  • Opricovic S, Tzeng G-H (2007) Extended vikor method in comparison with outranking methods. Eur J Oper Res 178(2):514–529

    MATH  Google Scholar 

  • Portela MS, Thanassoulis E, Simpson G (2004) Negative data in DEA: a directional distance approach applied to bank branches. J Oper Res Soc 55(10):1111–1121

    MATH  Google Scholar 

  • Rashidi K, Cullinane K (2018) A Comparison of Fuzzy DEA and Fuzzy TOPSIS in sustainable supplier selection: implications for sourcing strategy. Exp Syst Appl. https://doi.org/10.1016/j.eswa.2018.12.025

    Article  Google Scholar 

  • Raut RD, Kamble SS, Kharat MG, Joshi H, Singhal C, Kamble SJ (2017) A hybrid approach using data envelopment analysis and artificial neural network for optimising 3PL supplier selection. Int J Logist Syst Manag 26(2):203–223

    Google Scholar 

  • Rezaei J, Nispeling T, Sarkis J, Tavasszy L (2016) A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method. J Clean Prod 135:577–588

    Google Scholar 

  • Sexton TR, Silkman RH, Hogan AJ (1986) Data envelopment analysis: critique and extensions. In: Silkman RH (ed) Measuring efficiency: an assessment of data envelopment analysis, vol 32. Jossey-Bass, San Francisco, pp 73–105

    Google Scholar 

  • Sharp JA, Liu WB, Meng W (2006) A modified slacks-based measure model for data envelopment analysis with “natural” negative outputs and inputs. J Oper Res Soc 57(11):1–6

    Google Scholar 

  • Shemshadi A, Shirazi H, Toreihi M, Tarokh MJ (2011) A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst Appl 38(10):12160–12167

    Google Scholar 

  • Sinuany-Stern Z, Friedman L (1998) Data envelopment analysis and the discriminant analysis of ratios for ranking units. Eur J Oper Res 111:470–478

    MATH  Google Scholar 

  • Sinuany-Stern Z, Mehrez A, Barboy A (1994) Academic departments efficiency via data envelopment analysis. Comput Oper Res 21(5):543–556

    MATH  Google Scholar 

  • Soltanifar M, Shahghobadi S (2013) Selecting a benevolent secondary goal model in data envelopment analysis cross efficiency evaluation by a voting model. Socioecon Plann Sci 47(1):65–74

    Google Scholar 

  • Soltanifar M, Sharafi H, Zargar SM, Homayounfar M (2020). Supplier ranking using data envelopment analysis and new cross efficiency evaluation in the presence of undesirable outputs. J New Res Math (in press)

  • Sueyoshi T (1999) Data envelopment analysis non-parametric ranking test and index measurement: slack-adjusted DEA and an application to Japanese agriculture cooperatives. Omega 27:315–326

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Tone K (2017) Advances in DEA theory and applications: with extensions to forecasting models. Wiley

    Google Scholar 

  • Tone K, Chang TS, Wu CH (2020) Handling negative data in slacks based measure data envelopment analysis models. Eur J Oper Res 282:926–935

    MathSciNet  MATH  Google Scholar 

  • Torgersen AM, Forsund FR, Kittelsen SAC (1996) Slack-adjusted efficiency measures and ranking of efficient units. J Prod Anal 7:379–398

    Google Scholar 

  • Van Weele AJ (2014) Purchasing and supply chain management: Analysis, strategy, planning and practice. (6th ed.) Cengage Learning EMEA

  • Xu Z (2006) A direct approach to group decision making with uncertain additive linguistic preference relations. Fuzzy Optim Decis Making 5:21–32

    MathSciNet  MATH  Google Scholar 

  • Yager RR (2007) Centered OWA operators. Soft Comput 11:631–639

    MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zarbakhshnia N, Jaghdani J (2018) Sustainable supplier evaluation and selection with a novel two-stage DEA model in the presence of uncontrollable inputs and undesirable outputs: a plastic case study. Int J Adv Manuf Technol 97(5–8):2933–2945

    Google Scholar 

  • Zarghami M, Szidarovszky F (2009) Revising the OWA operator for multi-criteria decision-making problems under uncertainty. Eur J Oper Res 198(1):259–265

    MathSciNet  MATH  Google Scholar 

  • Zerafat Angiz M, Mustafa A, Kamali MJ (2013) Cross-ranking of decision making units in data envelopment analysis. Appl Math Model 37:398–405

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors express sincere thanks to two anonymous reviewers and the editor of JOCO for their effective comments and suggestions which have been very useful in improving the paper.

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  1. Department of Mathematics, Semnan Branch, Islamic Azad University, Semnan, Iran

    Mehdi Soltanifar

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Hamid Sharafi

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  1. Mehdi Soltanifar
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Correspondence to Mehdi Soltanifar.

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Soltanifar, M., Sharafi, H. A modified DEA cross efficiency method with negative data and its application in supplier selection. J Comb Optim 43, 265–296 (2022). https://doi.org/10.1007/s10878-021-00765-7

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