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First, this paper proposes the definition of directional congestion in certain input and output directions in the framework of data envelopment analysis (DEA). Second, two methods from different viewpoints are also proposed to estimate the directional congestion in a DEA framework. Third, we address the relations among directional congestion and classic congestion and strong (weak) congestion. Finally, we present a case study investigating the analysis of the research institutes in the Chinese Academy of Sciences (CAS) to demonstrate the applicability and usefulness of the methods developed in this paper.Keywords: data envelopment analysis; directional returns to scale; directional congestion see the point on the curve is an efficient production process. Congestion represents the falling portion of the curve, i.e., the (y1-y2) segment. Thus, the definition of congestion in economics is as follows (Cooper et al., 2001a;Brockett et al., 2004):Definition 1 (Congestion): Evidence of congestion is present when the reductions in one or more inputs can be associated with the increases in one or more outputs without worsening any other input or output.Proceeding in reverse, congestion occurs when the increases in one or more inputs can be associated with the decreases in one or more outputs without improving any other input or output. Cooper et al. (2004) noted that the research on congestion in classic economics is insufficient, partly due to the comments put forward by the Nobel laureate Stigler (1976) on the "X-Efficiency" proposed by Leibenstein (1966Leibenstein ( , 1976 questioning whether congestion should be a research topic in economics. However, Färe and Svensson (1980) redefined the concept of congestion. Subsequently, Färe and Grosskopf (1983) proposed the operational concept of congestion. Färe et al. (1985) first proposed the corresponding DEA (data envelopment analysis) model to explore the congestion effect. Subsequently, Cooper et al. (1996) proposed an alternative DEA approach to investigate the congestion effect. Cooper et al. (2001b) compared the similarities and differences between these two models. Based on the weak disposal assumption, Wei and Yan (2004) and Tone and Sahoo (2004) rebuilt the production possibility set (PPS) and the corresponding DEA model to determine the congestion effect of the DMUs. Kao (2010) investigated three types of models prevalent in the DEA literatures for measuring the congestion effect and utilized the model proposed by Wei and Yan (2004) on Taiwan forests. Based on the measurement and reorganization, he gave some interesting findings on how to alleviate the congestion in Taiwan forests. Brockett et al. (1998) used the model proposed by Cooper et al. (1996) to identify congestion inputs in Chinese industries. Shortly afterward, Cooper et al. (2001a) examined the problem of inefficiency in the Chinese automobile and textile industries. Using the annual data for the period 1981 to 1997, they found the evidence of congestion in both industries. Jahanshahloo and Khodabakhsh...

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