Congestion in multi-function parallel network DEA

Congestion is an economic phenomenon of the production process in which the excessive values of inputs lead to a reduction of the outputs. As the existence of congestion makes to increase costs and decreases efficiency, this issue is not acceptable for decision makers. Hence, many methods have been proposed to detect the congestion in the Data Envelopment Analysis framework (DEA). Most of these methods are designed to deal with the decision making units (DMUs) that have no network structure. However, in most real-world applications, some units are composed of independent production subunits. Therefore, a new scheme is required to determine the congestion of such units. A multi-function parallel system is a more common case in the real world that is composed of the same number of subunits such that each subunit has specific functions. In this paper, considering the operation of individual components of each DMU, a new DEA model is proposed to identify and evaluate the congestion of the multi-function parallel systems. It is shown that the proposed method is highly economical in comparison with the existing black-box view from a computational viewpoint. Then, the proposed model is illustrated using a numerical example along with a real case study.