Research Article Measurement of Congestion in the Simultaneous Presence of Desirable and Undesirable Outputs H. Zare-Haghighi, M. Rostamy-Malkhalifeh, and G. R. Jahanshahloo Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran Correspondence should be addressed to M. Rostamy-Malkhalifeh; mohsen rostamy@yahoo.com 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. Tis 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. Te 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, frms in the real world unavoidably generate undesirable outputs (such as pollutants or wastes) along with desirable outputs. Terefore, a new scheme is required for measuring congestion in the simultaneous presence of both desirable and undesirable outputs. Tis paper develops a nonradial efciency measure for including undesirable outputs into the environmental performance. Based on the proposed model, a new defnition and a new approach are presented to deal with congestion in the simultaneous presence of desirable and undesirable outputs. Ten, this paper uses the presented method to study the pollutants (waste gas emission and waste discharge) of 31 administrative regions of China. Te fnding 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. 1. Introduction Te concept of congestion, which is mainly applied in economics, refers to a situation where inputs are overinvested [1]. A typical example of congestion is the case where too many men in an underground coal mine may reduce the output of coal. Te topic of congestion was initially defned and extended by the essay of Fare and Svensson [2] in 1980. Aferwards, it was examined by Fare and Grosskopf [3] within the data envelopment analysis framework. Tey imposed the assumptions of weak and strong disposability on the pro- duction possibility set to identify the evidence of congestion. Besides, their approach sufers from some weaknesses in treating congestion [4]. In addition, a slacks-based measure was presented by Cooper et al. [5] that has some strong points compared to the previous method and can identify the congested inputs and the amount of congestion in each input. Moreover, Jahanshahloo and Khodabakhshi [6] developed an input relaxation model for improving outputs and, accord- ingly, calculated the input congestion based on the proposed model. Wei and Yan [7] estimated congestion by the ratio of technical efciency to pure technical efciency. However, their approach shows only existence or nonexistence of congestion and cannot provide a value for measuring the amount of congestion in each input. Indeed, the investigations into congestion within the DEA framework have received considerable attention in the last few decades. Some of the other investigations in this feld include Asgharian et al. [8], Flegg and Allen [9], Khodabakhshi [10], Sueyoshi and Sekitani [11], and Tone and Sahoo [12], to name a few. According to Cooper et al. [1], the common understand- ing of congestion is that a decrease (increase) in one or more inputs results in an increase (decrease) in one or more outputs. From this viewpoint, all outputs are expected to rise. Outputs of this kind are called desirable outputs. However, an important issue is that, in the real world, undesirable outputs (such as pollutants or wastes) are unavoidably gen- erated along with desirable outputs. Terefore, a new scheme is required for measuring congestion in the simultaneous presence of both desirable and undesirable outputs. In recent years, many researchers have been trying to model undesirable outputs within the DEA framework. Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 512157, 9 pages http://dx.doi.org/10.1155/2014/512157