Measurement of Inefficiency Slacks in Network Data Envelopment Analysis

Subject Areas : Applied Mathematics

حسین  عزیزی ¹ (گروه ریاضی، واحد پارس‌آباد مغان، دانشگاه آزاد اسلامی، پارس‌آباد مغان، ایران)
علیرضا  امیرتیموری ² (گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران)
سهراب  کردرستمی ³ (گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران)

Received: 2018-12-04 Accepted : 2019-03-04 Published : 2019-05-01

Keywords: optimistic and pessimistic viewpoints, inefficiency slacks, Data envelopment analysis, series systems, &lrm, overall performance,

Abstract :

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.‎

References:

[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.