Directional sustainability assessment of the two-stage processes in the presence of undesirable factors

Network data envelopment analysis (NDEA) is an appropriate technique to evaluate the sustainability of network structures. In the current paper, based on the directional distance function, a model for evaluating the sustainability of two-stage structures in several periods is introduced. The mentioned two-stage structure includes undesirable factors, consequently, the weak disposability assumption is considered to handle them. Sustainability incorporates economic, social and environmental aspects. The proposed model can evaluate sustainability in each period, in addition to the sustainability assessment of the whole system. Simultaneous with the assessing of sustainability, the efficiency of the foregoing structure is examined from three economic, social and environmental aspects in all periods, and based on it, the processes sustainability is estimated from the economic, social and environmental perspectives. To analyze and illustrate the suggested model, a real application on 19 countries is used.