Measurement of Inefficiency Slacks in Network Data Envelopment Analysis
الموضوعات :
حسین عزیزی
1
,
علیرضا امیرتیموری
2
,
سهراب کردرستمی
3
1 - گروه ریاضی، واحد پارس‌آباد مغان، دانشگاه آزاد اسلامی، پارس‌آباد مغان، ایران
2 - گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
3 - گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
الکلمات المفتاحية: optimistic and pessimistic viewpoints, inefficiency slacks, Data envelopment analysis, series systems, &lrm, overall performance,
ملخص المقالة :
The two-stage data envelopment analysis models show the performance of individual processes and thus, provide more information for decision-making compared with conventional one-stage models. This article presents a set of additive models (optimistic and pessimistic) to measure inefficiency slacks in which observations are shown with crisp numbers. In the concept of pessimistic efficiency, DMU with balanced input and output data can be scored as efficient. Since pessimistic efficiency represents the minimum efficiency that is guaranteed in any unfavorable conditions, the assessment based on this efficiency is in compliance with our natural meaning, especially in risk-averse situations. Therefore, pessimistic efficiency solely can play a useful role in the DMU ranking. However, it is not a good idea to ignore optimistic efficiency. Hence, it is an inevitable necessity to integrate different performance sizes in order to achieve an overall performance assessment for each DMU. An example of resin manufacturer companies in Iran is presented to explain how to calculate the system and process inefficiency slacks.
[1]A. Amirteimoori, S. Kordrostami, H. Azizi, Additive models for
network data envelopment analysis in the presence of shared resources,
Transportation Research Part D: Transport and Environment 48 (2016)
411-424.
[2]H. Azizi, H. Ganjeh Ajirlu, Measurement of the worst practice of decisionmaking
units in the presence of non-discretionary factors and imprecise
data, Applied Mathematical Modelling 35 (9) (2011) 4149-4156.
[3]A. Charnes, W.W. Cooper, E. Rhodes, Measuring the eciency of decision
making units, European Journal of Operational Research 2 (6) (1978) 429444.
[4]W.D. Cook, J. Zhu, G. Bi, F. Yang, Network DEA: Additive eciency
decomposition, European Journal of Operational Research 207 (2) (2010)
1122-1129.
[5]T. Entani, Y. Maeda, H. Tanaka, Dual models of interval DEA and its
extension to interval data, European Journal of Operational Research 136
(1) (2002) 32-45.
[6]R. Fare, S. Grosskopf, Network DEA, Socio-Economic Planning Sciences
34 (1) (2000) 35-49.
[7]G.R. Jahanshahloo, M. Afzalinejad, A ranking method based on a fullinecient
frontier, Applied Mathematical Modelling 30 (3) (2006) 248-260.
[8]C. Kao, Eciency decomposition in network data envelopment analysis:
A relational model, European Journal of Operational Research 192 (3)
(2009) 949-962.
[9]C. Kao, Eciency measurement for parallel production systems, European
Journal of Operational Research 196 (3) (2009) 1107-1112.
[10]C. Kao, S.-N. Hwang, Eciency decomposition in two-stage data
envelopment analysis: An application to non-life insurance companies in
Taiwan, European Journal of Operational Research 185 (1) (2008) 418-429.
[11]M. Khodakarami, A. Shabani, R. Farzipoor Saen, M. Azadi, Developing
distinctive two- stage data envelopment analysis models: An application in
evaluating the sustainability of supply chain management, Measurement
70 (2015) 62-74.
65
[12]L. Liang, W.D. Cook, J. Zhu, DEA models for two-stage processes: Game
approach and eciency decomposition, Naval Research Logistics 55 (7)
(2008) 643-653.
[13]K. Tone, M. Tsutsui, Network DEA: A slacks-based measure approach,
European Journal of Operational Research 197 (1) (2009) 243-252.
[14]Y.-M. Wang, K.-S. Chin, J.-B. Yang, Measuring the performances of
decision-making units using geometric average eciency, Journal of the
Operational Research Society 58 (7) (2007) 929-937.
