Fuzzy fair efficiency assessment in network data envelopment analysis models for complex system: An application in sustainable supply chain management

Network data envelopment analysis (NDEA) is a common mathematical technique to evaluate the performance of a set of homogeneous decision-making units (DMUs) with a network structure. In an open-series system with a multi-stage structure, it is crucial to determine fair efficiency for each stage when multiple optimal weights exist, so that the stages have incentives to cooperate with each other to achieve the highest possible performance of the entire system. This study suggests a novel approach based on the NDEA model to assess the fair efficiency of an open-series system with a multi-stage structure. Then, to deal with qualitative data and uncertainty in the values of some variables, the suggested NDEA model is developed in a fuzzy setting, using linguistic terms parameterized through fuzzy sets. The proposed method in this study has the following features that cannot be found in previous studies. First, the proposed method can provide a unique and fair efficiency decomposition for the stages of a system at any level of uncertainty while the overall efficiency of the system remains unchanged. Second, the proposed methodology proves that the achieved efficiency decomposition shows a fair trade-off among the stages. Third, the proposed method can provide fair efficiency decomposition in multi-stage systems in the presence of undesirable intermediate outputs, in which undesirable intermediate output can be reused as input after processing. The application of the proposed methodology is justified by two real-case studies that include performance evaluations of 9 tomato paste producer supply chains and 22 home appliance supply chains.