An approach based slack variables in network data envelopment analysis to incorporate dynamic effects

Senior managers are the customers of organizational performance measurement methods to help them make better decisions at the firm level. One of the most applicable methods is Network Data Envelopment Analysis (DEA). Network DEA models consider systems that have a network structure in which system inputs, after passing several intermediate interactions, are transformed into intermediate productions and finally leave the system as output products. However, many real-world cases do not necessarily conform to this network structure, which is related to the system outputs during multiple time periods or the same “dynamic” impacts. These structures cannot handle dynamic impacts. Therefore, this paper presents a novel structure that can consider the dynamic impacts and influences of sub-units on each other at various time periods. Besides, two models based on slack variables are proposed which can consider dynamic effects and calculate the efficiency of such networks. Using these models, the overall efficiency of networks is calculated for the whole time period. Finally, these models are applied to two examples, and the results obtained are compared with other methods.