A new method of determining decision-making unit congestion under inter-temporal dependence

Congestion is an essential concept in data envelopment analysis (DEA). It occurs when the decrease in at least one decision-making unit (DMU) input increases at least one output without affecting the other inputs or outputs. Although various methods have discussed congestion determination in static DEA, congestion calculation in dynamic DEA under inter-temporal dependence has not been considered in the literature. This paper deals with the congested input levels in multi-period production systems under inter-temporal dependence and the inter-temporal dependence of production periods due to the stock capital. Due to the importance of evaluating DMUs in the presence of time factors, this paper expands the determination of congestion of DMUs under the time factor and dependence of input and output levels in periods. The proposed models determine the congested unit in the assessment window and characterize the extra-input and lack-output amounts in all of the congested unit components in each period of the assessment window. This paper aims to specify production system performance in different evaluation periods by determining the dynamic congestion of DMUs. This paper proposes a method to identify the congested paths. The main advantage of this method is to prevent inappropriate allocation of the resources during evaluation periods of the assessment window. The validity of the proposed method is investigated through an example in the banking sector. Moreover, this method can be utilized in other sectors to homogeneous units with the same structure.