Detecting congestion in DEA by solving one model

Presence of input congestion is one of the key issues that results in lower efficiency and performance in Decision Making Units (DMUs). So, determination of congestion is of prime importance, and removing it improves performance of DMUs. One of the most appropriate methods for detecting congestion is Data Envelopment Analysis (DEA). Since the output of inefficient units can be increased by keeping the input constant through projecting on the weak efficiency frontier, it is unnecessary to determine the congested inefficient DMUs. Therefore, in this case we solely determine congested vertex units. Towards this aim, only one LP model in DEA is proposed and the status of congestion (strong congestion and weak congestion) obtained. In our method, a vertex unit under evaluation is eliminated from the production technology, and then, if there exists an activity that belongs to the production technology with lower inputs and higher outputs compared with omitted unit, we say vertex unit evidences congestion. One of the features of our model is that by solving only one LP model and with easier and fewer calculations compared to other methods, congested units can be identified. Data set obtained from Japanese chain stores for a period of 27 years is used to demonstrate the applicability of the proposed model and the results are compared with some previous methods.