Recognizing strong and weak congestion slack based in data envelopment analysis

The common concept of congestion is that a decrease (increase) in one or more inputs of a decision making unit (DMU) causes an increase (decrease) in one or more outputs (Cooper, Gu, & Li, 2001a). So far several congestion approaches have been proposed in DEA (data envelopment analysis) literature by many authors, such as Fare's et al. (FGL), Brockett's et al. (BCSW), and Tone and Sahoo's congestion approaches (Fare, Grosskopf, & Lovell, 1985, 1994; Brockett, Cooper, Shin, & Wang, 1998; Tone & Sahoo, 2004). Tone and Sahoo's approach (Tone & Sahoo, 2004) is one of the most robust congestion approaches in DEA literature. Moreover, Tone and Sahoo's approach has some advantages with respect to FGL and BSCW congestion approaches. However, the proposed approaches have many difficulties to treat congestion. For instance, in the presence of alternative optimal solutions, the approach proposed by Tone and Sahoo is unable to detect congestion (strong and weak). Moreover, in Tone and Sahoo's approach, all inputs and outputs of decision making units (DMUs) have been considered positive, while in real world, data is often non-negative. In this research, a slack-based DEA approach is proposed to recognize congestion (strong and weak) for the target DMUs. One of the advantages of our proposed approach is capable of detecting congestion (strong and weak) for evaluating the DMUs in the presence of alternative optimal solutions. Other advantage of our research is capable of identifying congesting (strong and weak) DMUs with non-negative inputs and outputs. However in these situations, Tone and Sahoo's congestion approach is incapable of identifying congestion. Lastly, we apply the approach to the data sets for making comparisons between the proposed approach and Tone and Sahoo's approach then some conclusions are drawn and directions for future research are suggested.