Provide a New Model for Evaluating and Ranking DMUs With Ordinal Data
الموضوعات : مجله بین المللی ریاضیات صنعتی
J. PourmahmoUd
1
(Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.)
D. Norouzi
2
(Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.)
الکلمات المفتاحية: Exact Data, Efficiency, Ranking, Evaluation, Data Envelopment Analysis, Ordinal Data, Imprecise data,
ملخص المقالة :
Classic Data Envelopment Analysis assumes that the values of inputs and outputs are exactly determined. However, in most real-life problems, the exact values of some of the inputs and outputs are imprecise. One of such imprecise data is ordinal data. In this paper, a new model is presented for measuring the efficiency evaluation of decision making units with ordinal data. The general idea of this model is assigning real values to ordinal data with new approach. Furthermore, another new model for ranking efficient units is presented with the main idea of changes in controlled efficiency. Then, the results of proposed model are compared with Cooper model. Therefore, the efficiency scores obtained from proposed model are more realistic and reasonable than the results obtained from the Cooper's model.
[1] K. Chiang Kao, Network Data Envelopment Analysis, Foundations and Extensions, ISBN 978-3-319-31718-2 (eBook).
[2] K. Chiang Kao, Interval efficiency measures in data envelopment analyze with imprecise data, Eur J Oper Res 174 (2006) 1087-1099.
[3] WD. Cook, M. Kress, LM. Seiford, On the use of ordinal data in data envelopment analysis, J. Oper. Res. Soc. 44 (1993) 133-140.
[4] WW. Cooper, KS. Park, G. Yu, IDEA and AR-IDEA: models for dealing with imprecise data in DEA". Manga. Sci. 45 (1999) 597-607.
[5] J. Zhu, Efficiency evaluation with strong ordinal input and output measures, Eur. J. Oper. Res. 146 (2003b) 477-485.
[6] DK. Despotis, YG. Smirlis YG, Data envelopment analysis with imprecise data, Eur. J. Oper. Res. 140 (002) 24-36.
[7] WW. Cooper, KS. Park, G. Yu, An illustrative application of IDEA (imprecise data envelopment analysis) to a Korean mobile telecommunication company, Oper. Res. 49 (2001) 807-820.
[8] WW. Cooper, KS. Park, G. Yu, IDEA (imprecise data envelopment analysis) with CMDs (column maximum decision making units), J. Oper. Res. Soc. 52 (2001) 176-181.
[9] J. Zhu, Imprecise data envelopment analysis (IDEA): a review and improvement with an application, J. Eur. J. Oper. Res. 144 (2003a) 513-529.
[10] J. Zhu, Imprecise DEA via standard linear DEA models with a revisit to a Korean mobile telecommunication company, Oper. Res. 52 (2004) 323-329.
[11] KS. Park, Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA), J. Oper. Res. Soc. 55 (2004) 1363-1366.
[12] YM. Wang, R. Greatbanks, JB. Yang, Interval efficiency assessment using data envelopment analysis, Fuzzy Sets and Systems 153 (2005) 347-370.
[13] WD. Cook, J. Zhu, Rank order data in DEA: a general framework, Eur. J. Oper. Res. 174 (2006) 1021-1038.
[14] RF. Saen, Technologies ranking in the presence of cardinal and ordinal data, Appl. Math. Comput. 176 (2006) 476-487.
[15] R. Farzipoor Saen, Suppliers selection in the presence of both cardinal and ordinal data, Eur. J. Oper. Res. 183 (2007) 741-747.
[16] A. Asosheh, S. Nalchigar, M. Jamporazmey, Information technology project evaluation: an integrated data envelopment analysis and balanced scorecard approach, Expert. Syst. App. l37 (2010) 5931-5938.
[17] AH. Shokouhi, A. Hatami-Marbini, M. Tavana, S. Saati, A robust optimization approach for imprecise data envelopment analysis, Comput. Ind. Eng. 59 (2010) 387-397.
[18] M. Toloo, S. Nalchigar, A new DEA method for supplier selection in presence of both cardinal and ordinal data, Expert. Syst. Appl. 38 (2011) 14726-14731.
[19] M. Toloo, Selecting and full ranking suppliers with imprecise data: a new DEA method, Int. J. Adv. Manuf. Techno. l74 (2014) 1141-1148.
[20] A. Charnes, T. Clark, WW. Cooper, B. Golany, A developmental studyof data envelopment analysis in measur-ing the efficiency of maintenance unitsin, U. S. Air Forces. In R. Thompson R.M. Thrall (Eds.), Annals of Operational Re-search 2 (1985) 95-112.
[21] P. Andersen, N. C. Petersen, A procedure for ranking efficient units in data envelopment analysis, INFORMS 39 (1993) 1261-1264.
[22] G. R. Jahanshahloo, L. Pourkarimi, M. Zarepishe, Modified MAJ model for ranking decision making units in Data Envelopment Analysis, Applied Mathematics and Computation 174 (2006) 1054-1059.
[23] G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, H. ZhianiRezai, F. RezaiBalf, Using Monte Carlo Method for ranking efficient DMUs, Applied Mathematics and Computation 162 (2005) 371-379.
[24] J. Pourmahmoud, New model for ranking DMUs in DDEA as a special case, Int. J. Industrial Mathematics 7 (2015) 187-192.
[25] J. Pourmahmoud, E. Babazadeh, A New Group Data Envelopment Analysis Method for Ranking Design Requirements in Quality Function Deployment, Int. J. Industrial Mathematics 9 (2017) 269-278.
[26] N. Adler, L. Friedman, Z. Sinuany-Stern, Review of ranking methods in data envelopment analysis context, European Journal of Operational Research 140 (2002) 249-265.
[27] J. Doyle, R. Green, Efficiency and crossefficiency in DEA; Derivations, meanings and uses, Journal of the Operational Research Society 45 (1994) 567-578.
