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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 9470236, 12 pages
Research Article

Incorporation of Inefficiency Associated with Link Flows in Efficiency Measurement in Network DEA

1Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Correspondence should be addressed to Seyed Mohammad Hadjimolana

Received 11 June 2017; Revised 19 September 2017; Accepted 5 November 2017; Published 4 January 2018

Academic Editor: M. L. R. Varela

Copyright © 2018 Abolghasem Shamsijamkhaneh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Data Envelopment Analysis (DEA) is a mathematical programming approach to measure the relative efficiency of peer decision making units (DMUs) which use multiple inputs to produce multiple outputs. One of the drawbacks of traditional DEA models is the neglect of internal structures of the DMUs. Network DEA models are able to overcome the shortcoming of the traditional DEA models. In network DEA a DMU is made up of some divisions linked together by intermediate products. An intermediate product has the dual role of output from one division and input to another one. Improving the efficiency of one process may reduce the efficiency of another process. To address the conflict caused by the dual role of intermediate measures, this paper presents a new approach which categorizes the intermediate measures into either input or output type endogenously, while keeping the continuity of link flows between divisions. This categorization allows us to measure the inefficiencies associated with intermediate measures and account their indirect effects on the objective function. In this paper we propose a new Slacks-based measure which includes any nonzero slacks identified by the model and inherits the properties of monotonicity in slacks and units invariance from the conventional SBM approach.