Benchmarking with network dea in a fuzzy environment
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 687-703.

Benchmarking is a powerful and thriving tool to enhance the performance and profitabilities of organizations in business engineering. Though performance benchmarking has been practically and theoretically developed in distinct fields such as banking, education, health, and so on, benchmarking of supply chains with multiple echelons that include certain characteristics such as intermediate measure differs from other practices. In spite of incremental benchmarking activities in practice, there is the dearth of a unified and effective guideline for benchmarking in organizations. Amongst the benchmarking tools, data envelopment analysis (DEA) as a non-parametric technique has been widely used to measure the relative efficiency of firms. However, the conventional DEA models that are bearing out precise input and output data turn out to be incapable of dealing with uncertainty, particularly when the gathered data encompasses natural language expressions and human judgements. In this paper, we present an imprecise network benchmarking for the purpose of reflecting the human judgments with the fuzzy values rather than precise numbers. In doing so, we propose the fuzzy network DEA models to compute the overall system scale and technical efficiency of those organizations whose internal structure is known. A classification scheme is presented based upon their fuzzy efficiencies with the aim of classifying the organizations. We finally provide a case study of the airport and travel sector to elucidate the details of the proposed method in this study.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017055
Classification : 90B50, 90C05, 90C70, 90C90
Mots-clés : Internal structure, DEA, fuzzy sets, scale and relative efficiency measure
Hatami-Marbini, Adel 1

1 
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Hatami-Marbini, Adel. Benchmarking with network dea in a fuzzy environment. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 2, pp. 687-703. doi : 10.1051/ro/2017055. http://archive.numdam.org/articles/10.1051/ro/2017055/

[1] B. Asady and A. Zendehnam, Ranking fuzzy numbers by distance minimization. Appl. Math. Model. 31 (2007) 2589–2598. | Zbl

[2] P.J. Agrell and A. Hatami-Marbini, Frontier-based performance analysis models for supply chain management: state of the art and research directions. Comput. Ind. Eng. 66 (2013) 567–583.

[3] A.I. Ali and L.M. Seiford, Translation invariance in data envelopment analysis. Oper. Res. Lett. 9 (1990) 403–405. | Zbl

[4] R.D. Banker, A. Charnes and W.W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30 (1984) 1078–1092. | Zbl

[5] J. Beasley, Determining teaching and research efficiencies. J. Oper. Res. Soc. 46 (1995) 441–452. | Zbl

[6] R.E. Bellman and L.A. Zadeh, Decision-making in a fuzzy environment. Manag. Sci. 17 (1970) B-141. | MR | Zbl

[7] L. Castelli and R. Pesenti, Network, shared flow and multi-level DEA models: a critical review. In Data envelopment analysis. Springer, USA (2014), pp. 329–376.

[8] L. Castelli, R. Pesenti and W. Ukovich, A classification of DEA models when the internal structure of the decision making units is considered. Ann. Oper. Res. 173 (2010) 207–235. | MR | Zbl

[9] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444. | MR | Zbl

[10] Y. Chen, W.D. Cook, C. Kao and J. Zhu, Network DEA pitfalls: divisional efficiency and frontier projection under general network structures. Eur. J. Oper. Res. 226 (2013) 507–515. | MR | Zbl

[11] Y. Chen, W.D. Cook, N. Li and J. Zhu, Additive efficiency decomposition in two-stage DEA. Eur. J. Oper. Res. 196 (2009) 1170–1176. | Zbl

[12] W.D. Cook and L.M. Seiford, Data envelopment analysis (DEA)-Thirty years on. Eur. J. Oper. Res. 192 (2009) 1–17. | MR | Zbl

[13] W.D. Cook, D. Chai, J. Doyle and R. Green, Hierarchies and groups in DEA. J. Prod. Anal. 10 (1998) 177–198.

[14] W.W.K. Cooper, S. Park and G. Yu, IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Manag. Sci. 45 (1999) 597–607. | Zbl

[15] D.K. Despotis, G. Koronakos and D. Sotiros, Composition versus decomposition in two-stage network DEA: a reverse approach. J. Prod. Anal. 45 (2016) 71–87.

[16] J. Ding, C. Feng, G. Bi, L. Liang and M.R. Khan, Cone ratio models with shared resources and nontransparent allocation parameters in network DEA. J. Prod. Anal. 44 (2015) 137–155.

[17] J. Du, L. Liang, Y. Chen, W.D. Cook and J. Zhu, A bargaining game model for measuring performance of two-stage network structures. Eur. J. Oper. Res. 210 (2011) 390–397. | MR | Zbl

[18] D. Dubois and H. Prade, Operations on fuzzy numbers. Int. J. Syst. Sci. 9 (1978) 613–626. | MR | Zbl

[19] H. Dyckhoff and K. Allen, Measuring ecological efficiency with data envelopment analysis (DEA). Eur. J. Oper. Res. 132 (2001) 312–325. | Zbl

[20] A. Emrouznejad, B.R. Parker and G. Tavares, Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Econ. Plan. Sci. 42 (2008) 151–157.

[21] A. Emrouznejad, M. Rostamy-Malkhalifeh, A. Hatami-Marbini, M. Tavana and N. Aghayi, An overall profit Malmquist productivity index with fuzzy and interval data. Math. Comput. Model. 54 (2011) 2827–2838. | MR | Zbl

[22] A. Emrouznejad, M. Tavana and A. Hatami-Marbini, Art in fuzzy data envelopment analysis. Performance measurement with fuzzy data envelopment analysis. In Vol. 309 of Studies in Fuzziness and Soft Computing. Springer-Verlag (2014) 1–45.

[23] R. Färe and S. Grosskopf, Productivity and intermediate products: a frontier approach. Econ. Lett. 50 (1996) 65–70. | Zbl

[24] R. Färe and S. Grosskopf, Network DEA. Socio-Econ. Plan. Sci. 34 (2000) 35–49.

[25] R. Färe and G. Whittaker, An intermediate input model of dairy production using complex survey data. J. Agric. Econ. 46 (1995) 201–213.

[26] M.J. Farrell, The measurement of productive efficiency. J. Roy. Statis. Soc. Ser. A 120 (1957) 253–290.

[27] D. Gillen and A. Lall, Developing measures of airport productivity and performance: an application of data envelopment analysis. Transp. Res. E: Log. Transp. Rev. 33 (1997) 261–273.

[28] E.G. Gomes and M.E. Lins, Modelling undesirable outputs with zero sum gains data envelopment analysis models. J. Oper. Res. Soc. 59 (2008) 616–623. | Zbl

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

[30] A. Hatami-Marbini, P.J. Agrell, H. Fukuyama, K. Gholami and P. Khoshnevis, The role of multiplier bounds in fuzzy data envelopment analysis. Ann. Oper. Res. 250 (2017b) 249–276. | MR | Zbl

[31] A. Hatami-Marbini, A. Ebrahimnejad and S. Lozano, Efficiency measures in data envelopment analysis using lexicographic multiobjective approach. Comput. Ind. Eng. 105 (2017c) 362–376.

[32] A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur. J. Oper. Res. 214 (2011a) 457–472. | MR | Zbl

[33] A. Hatami-Marbini, A. Emrouznejad and P.J. Agrell, Interval data without sign restrictions in DEA. Appl. Math. Model. 38 (2014) 2028–2036. | MR | Zbl

[34] A. Hatami-Marbini, S. Saati and M. Tavana, An ideal-seeking fuzzy data envelopment analysis framework. Appl. Soft Comput. 10 (2010) 1062–1070.

[35] A. Hatami-Marbini, M. Tavana and A. Ebrahimi, A fully fuzzified data envelopment analysis model. Int. J. Inf. Decis. Sci. 3 (2011b) 252–264.

[36] A. Hatami-Marbini, M. Tavana, A. Emrouznejad and S. Saati, Efficiency measurement in fuzzy additive data envelopment analysis. Int. J. Ind. Syst. Eng. 10 (2011c) 1–20.

[37] A. Hatami-Marbini, M. Tavana, K. Gholami and Ghelej Z. Beigi, Bounded data envelopment analysis model in a fuzzy environment with an application to safety in the Semiconductor industry. J. Optim. Theory Appl. 164 (2015) 679–701. | MR | Zbl

[38] A. Hatami-Marbini, M. Tavana, S. Saati and P.J. Agrell, Positive and normative use of fuzzy DEA-BCC models: a critical view on NATO enlargement. Int. Trans. Oper. Res. 20 (2013) 411–433. | Zbl

[39] O. Herrera-Restrepo, K. Triantis, J. Trainor, P. Murray-Tuite and P. Edara, A multi-perspective dynamic network performance efficiency measurement of an evacuation: a dynamic network-DEA approach. Omega 60 (2016) 45–59.

[40] C. Kao, Efficiency measurement for parallel production systems. Eur. J. Oper. Res. 196 (2009) 1107–1112. | Zbl

[41] C. Kao, Efficiency decomposition for parallel production systems. J. Oper. Res. Soc. 63 (2012) 64–71.

[42] C. Kao, Network data envelopment analysis: a review. Eur. J. Oper. Res. 239 (2014) 1–16. | MR | Zbl

[43] C. Kao and S. Hwang, Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. Eur. J. Oper. Res. 185 (2008) 418–419. | Zbl

[44] C. Kao and P.H. Lin, Efficiency of parallel production systems with fuzzy data. Fuzzy Sets Syst. 198 (2012) 83–98. | MR | Zbl

[45] C. Kao and S.T. Liu, Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113 (2000) 427–437. | Zbl

[46] C. Kao and S.T. Liu, Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets Syst. 176 (2011) 20–35. | MR | Zbl

[47] A. Kaufmann and M.M. Gupta, Fuzzy Mathematical models in engineering and management science. North-Holland, Amsterdam (1988). | MR | Zbl

[48] S. Lertworasirikul, S.C.J. Fang, A. Joines and H.L. Nuttle, Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139 (2003) 379–394. | MR | Zbl

[49] L. Liang, F. Yang, W.D. Cook and J. Zhu, DEA models for supply chain efficiency evaluation. Ann. Oper. Res. 145 (2006) 35–49. | MR | Zbl

[50] S. Lozano, Scale and cost efficiency analysis of networks of processes. Expert Syst. Appl. 38 (2011) 6612–6617.

[51] S. Lozano, Process efficiency of two-stage systems with fuzzy data. Fuzzy Sets Syst. 243 (2014a) 36–49. | MR | Zbl

[52] S. Lozano, Computing fuzzy process efficiency in parallel systems. Fuzzy Optim. Decis. Making 13 (2014b) 73–89. | MR | Zbl

[53] S. Lozano, E. Gutiérrez and P. Moreno, Network DEA approach to airports performance assessment considering undesirable outputs. Appl. Math. Model. 37 (2013) 1665–1676. | Zbl

[54] O.B. Olesen and N.C. Petersen, Chance constrained efficiency evaluation. Manag. Sci. 41 (1995) 442–457. | Zbl

[55] O.B. Olesen and N.C. Petersen, Stochastic data envelopment analysis: a review. Eur. J. Oper. Res. 251 (2016) 2–21. | MR | Zbl

[56] A. Prieto and J. Zofio, Network DEA efficiency in input-output models: with an application to OECD countries. Eur. J. Oper. Res. 178 (2007) 292–304. | Zbl

[57] S. Reinhard, C.K. Lovell and G. Thijssen, Econometric estimation of technical and environmental efficiency: an application to Dutch dairy farms. Amer. J. Agric. Econ. 81 (1999) 44–60.

[58] S. Reinhard, C.K. Lovell and G.J. Thijssen, Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA. Eur. J. Oper. Res. 121 (2000) 287–303. | Zbl

[59] S.M. Saati, A. Memariani and G.R. Jahanshahloo, Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim. Decis. Making 1 (2002) 255–267. | Zbl

[60] S. Saati, A. Hatami-Marbini, M. Tavana and P.J. Agrell, A fuzzy data envelopment analysis for clustering operating units with imprecise data. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 21 (2013) 29–54. | MR | Zbl

[61] H. Scheel, Undesirable outputs in efficiency valuations. Eur. J. Oper. Res. 132 (2001) 400–410. | Zbl

[62] J.K. Sengupta, A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24 (1992) 259–266. | MR | Zbl

[63] M. Tavana, R.K. Shiraz and A. Hatami-Marbini, A new chance-constrained DEA model with birandom input and output data. J. Oper. Res. Soc. 65 (2014) 1824–1839.

[64] M. Tavana, R.K. Shiraz, A. Hatami-Marbini, P.J. Agrell and K. Paryab, Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC). Expert Syst Appl. 39 (2012) 12247–12259.

[65] M. Toloo, Selecting and full ranking suppliers with imprecise data: a new DEA method. Int. J. Adv. Manuf. Technol. 74 (2014) 1141–1148.

[66] M. Toloo, N. Aghayi and M. Rostamy-Malkhalifeh, Measuring overall profit efficiency with interval data. Appl. Math. Comput. 201 (2008) 640–649. | Zbl

[67] Y.M. Wang, Y. Luo and L. Liang, Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Syst Appl. 36 (2009) 5205–5211.

[68] D.D. Wu, Bilevel programming data envelopment analysis with constrained resource. Eur. J. Oper. Res. 207 (2010) 856–864. | Zbl

[69] J. Wu, B. Xiong, Q. An, J. Sun and H. Wu, Total-factor energy efficiency evaluation of Chinese industry by using two-stage DEA model with shared inputs. Ann. Oper. Res. 1–20 (2015).

[70] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1 (1978) 3–28. | Zbl

[71] Y. Zha and L. Liang, Two-stage cooperation model with input freely distributed among the stages. Eur. J. Oper. Res. 205 (2010) 332–338. | Zbl

[72] H.J. Zimmermann, Fuzzy set theory and its applications. Kluwer Academic Publishers, Boston (1996). | Zbl

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