Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 253-260.

Ranking all of the decision making units (DMUs) is one of the most important topics in Data envelopment analysis (DEA). Provided methods for ranking often rank the efficient units. Ranking inefficient units by early DEA models has some weaknesses since slacks are ignored. One of the methods presented in the ranking of all DMUs is Khodabakhshi and Ariavash’s method [M. Khodabakhshi and K. Ariavash, Appl. Math. Lett. 25 (2012) 2066–2070.] in this method, the maximum and minimum efficiency values of each DMU are measured by considering the sum of all efficiencies equal one. Finally, the rank of each DMU is determined in proportion to a convex combination of its minimum and maximum efficiency values. But optimistic and pessimistic weights of the other DMUs are not considered in ranking of the evaluated DMU. In this paper, a fair method to rank all DMUs, using Khodabakhshi and Ariavash’s method is proposed. In the proposed method optimistic and pessimistic efficiency values will be assessed, not only by the optimal weights of evaluated DMU but also by considering the optimistic and pessimistic optimal weights of all DMUs. The obtained optimistic and pessimistic efficiency values are supposed as criterion for the ranking. The proposed method is illustrated by a numerical example.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016023
Classification : 90B99, 90c05, 90c90
Mots-clés : Data envelopment analysis, ranking, optimistic efficiency, pessimistic efficiency
Jahanshahloo, Gholam Reza 1 ; Sadeghi, Jafar 1 ; Khodabakhshi, Mohammad 2

1 Faculty of Mathematical Sciences and Computer, Kharazmi university, Tehran, Iran.
2 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran.
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     title = {Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {253--260},
     publisher = {EDP-Sciences},
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Jahanshahloo, Gholam Reza; Sadeghi, Jafar; Khodabakhshi, Mohammad. Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 253-260. doi : 10.1051/ro/2016023. http://www.numdam.org/articles/10.1051/ro/2016023/

P. Andersen and N.C. Petersen, A procedure for ranking efficient units in data envelopment analysis. Manage. Sci. 39 (1993) 1261–1264. | DOI | Zbl

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

I. Bardhan, et al., Models for efficiency dominance in data envelopment analysis. Part I: Additive models and MED measures. J. Oper. Res. Soc. Jpn. 39 (1996) 322–332. | MR | Zbl

G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets. Fuzzy Sets Systems (1985) 15 1–19. | DOI | MR | Zbl

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

W.D. Cook, M. Kress and L.M. Seiford, A general framework for distance-based consensus in ordinal ranking models. Eur. J. Oper. Res. 96 (1997) 392–397. | DOI | Zbl

Y. Chen, Measuring super-efficiency in DEA in the presence of infeasibility. Eur. J. Oper. Res. 161 (2005) 545–551. | DOI | MR | Zbl

J. Doyle and R. Green, Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. J. Oper. Res. Soc. (1994) 567–578. | Zbl

A. Emrouznejad, A. Mustafa and A. Al-Eraqi, Aggregating preference ranking with fuzzy data envelopment analysis. Knowl.-Based Syst. 23 (2010) 512–519. | DOI

A. Foroughi and M. Tamiz, An effective total ranking model for a ranked voting system. Omega 33 (2005) 491–496. | DOI

L. Friedman and Z. Sinuany−Stern, Scaling units via the canonical correlation analysis in the DEA context. Eur. J. Oper. Res. 100 (1997) 629–637. | DOI | Zbl

B. Golany, An interactive MOLP procedure for the extension of DEA to effectiveness analysis. J. Oper. Res. Soc. (1988) 725–734. | Zbl

G.R. Jahanshahloo, A new DEA ranking system based on changing the reference set. Eur. J. Oper. Res. 181 (2007) 331–337. | DOI | Zbl

M. Khodabakhshi and K. Aryavash, Ranking all units in data envelopment analysis. Appl. Math. Lett. 25 (2012) 2066–2070. | DOI | MR | Zbl

S. Li, G.R. Jahanshahloo and M. Khodabakhshi, A super-efficiency model for ranking efficient units in data envelopment analysis. Appl. Math. Comput. 184 (2007) 638–648. | MR | Zbl

L. Liang, Alternative secondary goals in DEA cross-efficiency evaluation. Int. J. Prod. Econ. 113 (2008) 1025–1030. | DOI

C.K. Lovell and J.T. Pastor, Radial DEA models without inputs or without outputs. Eur. J. Oper. Res. 118 (1999) 46–51. | DOI | Zbl

L.-C. Ma and H.-L. Li, A fuzzy ranking method with range reduction techniques. Eur. J. Oper. Res. 184 (2008) 1032–1043. | DOI | MR | Zbl

S. Mehrabian, M.R. Alirezaee and G.R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment. Anal. Comput. Optim. Appl. 14 (1999) 261–266. | DOI | MR | Zbl

H. Noguchi, M. Ogawa and H. Ishii, The appropriate total ranking method using DEA for multiple categorized purposes. J. Comput. Appl. Math. 146 (2002) 155–166. | DOI | MR | Zbl

T.R. Sexton, R.H. Silkman and A.J. Hogan, Data envelopment analysis: Critique and extensions. New Directions for Program Eval. 1986 (1986) 73–105. | DOI

A.M. Torgersen, F.R. Fãrsund, and S.A. Kittelsen, Slack-adjusted efficiency measures and ranking of efficient units. J. Productivity Anal. 7 (1996) 379–398. | DOI

D.D. Wu, Performance evaluation: an integrated method using data envelopment analysis and fuzzy preference relations. Eur. J. Oper. Res. (2009) 194 227–235. | DOI | MR | Zbl

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