Determining the amount of the excess input and the output shortage of the congested decision-making units with negative data

Congestion is an essential concept in production systems, where the increase (decrease) of at least one of the inputs leads to the decrease (increase) of at least one of the outputs without any adverse effect on the other inputs or outputs. Various methods have been presented to calculate congestion. According to the literature, previous methods can only identify the existence of congestion of decision-making units (DMUs) with negative data without measuring its value. Due to the importance of negative data in the real world, this study determines the congestion amount of DMUs with negative data. This article aims to determine the excess amount of inputs and the lack of outputs caused by the congested DMUs with negative inputs and outputs. This study proposes two methods to specify the value of congestion of units with negative resources and products. As well as in this survey, the use of inverse DEA is employed to identify and determine the congestion amount of DMUs. The presented model prevents the inappropriate allocation of resources in an organization. Also, identifying the best and worst congestion units allows the manager to improve the performance of congested DMUs with an appropriate method. A numerical example is utilized to demonstrate the superiority of the proposed methods over the previous methods. Besides, the presented methods can be employed in various fields according to the established models.