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Journal of Applied Mathematics
Volume 2014, Article ID 512157, 9 pages
Research Article

Measurement of Congestion in the Simultaneous Presence of Desirable and Undesirable Outputs

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran

Received 18 January 2014; Revised 15 March 2014; Accepted 15 March 2014; Published 15 April 2014

Academic Editor: Mohammad Khodabakhshi

Copyright © 2014 H. Zare-Haghighi 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.


The concept of congestion, which is mainly applied in economics, refers to a situation where inputs are overinvested. Many studies have focused on congestion measurement by means of data envelopment analysis (DEA). However, most of the previous investigations only considered the framework of desirable outputs. In fact, firms in the real world unavoidably generate undesirable outputs (such as pollutants or wastes) along with desirable outputs. Therefore, a new scheme is required for measuring congestion in the simultaneous presence of both desirable and undesirable outputs. This paper develops a nonradial efficiency measure for including undesirable outputs into the environmental performance. Based on the proposed model, a new definition and a new approach are presented to deal with congestion in the simultaneous presence of desirable and undesirable outputs. Then, this paper uses the presented method to study the pollutants (waste gas emission and waste discharge) of 31 administrative regions of China. The finding indicates that 7 industries pay attention to the reduction of their pollutants accompanying improvement of their commercial targets. Consequently, they do not show congestion in any input.