Measuring fair efficiency decomposition in network DEA model under uncertainty: modeling and computational aspects for sustainable supply chain performance assessment

With the emergence of the concept of sustainability and the intensification of social pressures to reduce the negative effects of industrial activities on the environment and society, it is almost impossible to design the supply chain network without considering these considerations. Hence, appraising the efficiency of the supply chain with sustainability considerations can play a significant role in designing a sustainable supply chain (SSC). Network data envelopment analysis (NDEA) is a prevalent mathematical method for appraising the performance of the supply chain with a multi-stage structure. Producing multiple optimal weights by NDEA models has always been a controversial challenge, as it produces different efficiency scores and rankings for network stages. This study suggests a novel NDEA model for assessing the fair efficiency of the network stages. Then, to deal with uncertainty in input, intermediate outputs, and final output criteria, the proposed NDEA model is developed in a fuzzy setting. The suggested fuzzy NDEA (FNDEA) model can provide a fair efficiency decomposition score for series multi-stage structures at different levels of uncertainty. In addition to managing conflict between stages in the network structures, the presented approach proves that the achieved efficiency decomposition shows a fair trade-off between the stages because it is as close as possible to the highest possible efficiency score and as far as possible from the lowest possible efficiency score obtained for each stage. The applicability of the presented approach is confirmed with a numerical example and a case study involving ten fruit juice supply chains. Finally, several strategic implications are suggested to improve the efficiency of supply chains with poor performance.