Hybrid cluster and data envelopment analysis with interval data

Document Type : Article

Authors

1 Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

3 3Department of Management, Shahid Beheshti University, Tehran, Iran

4 Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran

Abstract

Data envelope analysis (DEA) is an approach to estimate the relative efficiency of decision making units (DMUs). Several studies were conducted in order to prioritize efficient units and some useful models such as cross-efficiency matrix (CEM) were presented.  Besides, a number of DEA models with interval data have been developed and ranking DMUs with such data was solved. However, presenting an obtained crisp data derived interval data is a critical problem, so that many researches were implemented so as to compute weights and averaging the interval data. In this paper we propose the new algorithm to find more suitable weight applying a data mining approach of DMU’s data. For this purpose, we employed clustering and pair-wise comparison matrix on given relative efficiency from CEM. Results indicate there is meaningful different between efficiency of DMUs with lower bound and that of DMUs with upper bound.

Keywords

Main Subjects

References

References
1. Lu, T. and Liu, S.T. Ranking DMUs by comparing
DEA cross-eciency intervals using entropy measures",
Entropy, 18(12), p. 452 (2016).
2. Sadeghi Gavgani, S. and Zohrehbandian, M. A Crosse
ciency based ranking method for nding the most
ecient DMU", Math. Probl. Eng., 2014, pp. 1-6
(2014).
3. Wu, J., Sun, J., Song, M., and Liang, L. A ranking
method for DMUs with interval data based on DEA
cross-eciency evaluation and TOPSIS", J. Syst. Sci.
and Syst. Eng., 22(2), pp. 191-201 (2013).
4. Mirhashemi, A. and Izadikhah, M. Ranking DMUs in
the presence of undesirable data", J. Basic. Appl. Sci.
Res., 3(4), pp. 910-919 (2013).
5. Jahanshahloo, G.R., Hosseinzadeh Lot , F., Shoja, N.,
Tohidi, G., and Razavyan, S. Ranking using l1-norm
in data envelopment analysis", Appl. Math. Comput.,
153(1), pp. 215-224 (2004).
6. Akbarian, D. Ranking all DEA-ecient DMUs based
on cross eciency and analytic hierarchy process methods",
J. Opt., 2015, pp. 1-10 (2015).
7. Zohrehbandian, M. and Sadeghi Gavgani, S. Crosse
ciency evaluation under the principle of rank priority
of DMUs", World. Appl. Sci. J., 21, pp. 46-49
(2013).
8. Yang, F., Ang, S., Xia, Q., and Yang, C. Ranking
DMUs by using interval DEA cross eciency matrix
with acceptability analysis", Eur. J. Oper. Res.,
223(2), pp. 483-488 (2012).
9. Caklovic, L. and Hunjak, T. Measuring DMUe
ciency by modi ed cross-eciency approach",
Math. Communication, 17, pp. 559-573 (2012).
10. Entani, T., Maeda, Y., and Tanaka, H. Dual models
of interval DEA and its extension to interval data",
Eur. J. Oper. Res., 136(1), pp. 32-45 (2002).
11. Sexton, T.R., Silkman, R.H., and Hogan, A.J. Data
envelopment analysis: critique and extensions" In:
Silkman, R.H. (Ed.), Measuring Eciency: An Assessment
of Data Envelopment Analysis, Jossey-Bass,
San Francisco, CA (1986).
12. Dai, X. and Kuosmanen, T. Best-practice benchmarking
using clustering methods: Application to energy
regulation", Omega, 42(1), pp. 179-188 (2014).
13. Samoilenko, S. and Osei-Bryson, K.M. Increasing the
discriminatory power of DEA in the presence of the
sample heterogeneity with cluster analysis and decision
trees", Exp. Syst. .Appl., 34(2), pp. 1568-1581 (2008).
14. Amin, G.R., Emrouznejad, A., and Rezaei, S. Some
clari cations on the DEA clustering approach", Eur.
J. Oper. Res., 215(2), pp. 498-501 (2011).
15. Jahanshahloo, G.R., Hosseinzadeh Lot , F., Rostamy
Malkhalifeh, M., and Ahadzadeh Namin, M. A generalized
model for data envelopment analysis with
interval data", Appl. Math. Model., 33(7), pp. 3237-
3244 (2009).
Scientia Iranica

Volume 25, Issue 5 - Serial Number 5
Transactions on Industrial Engineering (E)
September and October 2018
Pages 2904-2911

Files

Share

How to cite

Statistics