International Association for Management of Technology IAMOT 2018 Conference Proceedings Page 1 of 8 DETERMINING THE STRONGLY AND WEAKLY MOST CONGESTED FIRMS IN DATA ENVELOPMENT ANALYSIS (Only complete the Author list after the review process has been completed) MOHAMMAD KHOVEYNI Department of Applied Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran mohammadkhoveyni@gmail.com (Corresponding) ROBABEH ESLAMI Department of Mathematics, Faculty of Technology and Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran sinhx_2002@yahoo.com ABSTRACT Determining the strongly and weakly most congested firms (or decision making units (DMUs)) is a very important issue for decision makers, however, there is no study on determining these DMUs in data envelopment analysis (DEA). Hence, to do this, we first propose a DEA approach to recognize congestion status of DMUs and then, two integrated mixed integer programming (MIP)-DEA models is presented to determine the strongly and weakly most congested DMUs. Finally, a numerical example is provided to illustrate the purpose of this research. Key words: Data envelopment analysis (DEA); Negative data in DEA; Strong and weak congestion; Slack variables; Mixed integer programming (MIP) INTRODUCTION Data envelopment analysis (DEA), which was initially introduced by Charnes et al. (CCR) (1978), is a mathematical tool for evaluating the relative efficiency of a set of decision making units (DMUs) with multiple inputs and multiple outputs. One of the important issues in the DEA literature is recognizing congestion that so far there are many studies in this context. For instance, a common concept of congestion was presented by Färe and Svensson (1980), then Färe and Grosskopf (1983) extended the topic of congestion such that they considered some inputs of the target DMU as constant values. Brockett et al. (1998) indicated that this assumption is not important and congestion of the DMU under evaluation can be removed by decreasing all its inputs. Also, Cooper et al. (1996) discussed about the treatment of congestion. In this vein, Copper et al. (2000) introduced a unified additive model approach to identify congestion. Furthermore, Tone and Sahoo (2004) proposed a unified DEA approach to specify strong and weak congestion. However, their proposed congestion approach has two problems: (1) it is not able to recognize congestion status in the presence of alternative optimal solutions and (2) it is considered that all inputs and output of DMUs are positive. To tackle these problems, Khoveyni et al. (2013) presented a slack-based DEA approach for detecting congestion status in the presence of non-negative data. In addition, since there are some DMUs including desirable and undesirable data, Wu et al. (2013) and Fang (2015) introduced some DEA approaches to identify congestion of DMUs in this case. Furthermore, Khoveyni et al. (2017) provided a DEA approach to detect congestion status of DMUs in the presence of both negative and non-negative data.