Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation

In the last 10 years, sustainable supply chain management (SSCM) has become one of the important topics in business and academe. Sustainable supplier performance evaluation and selection play a significant role in establishing an effective SSCM. One of the techniques that can be used for evaluating sustainable supplier performance is data envelopment analysis (DEA). The conventional DEA methods require accurate measurement of both input and output variables present in the problem. In practice, the observed values of the input and output data present in real-world problems are often imprecise. To cope with this situation, fuzzy DEA models were constructed for expressing relative fuzzy efficiencies of decision-making units (DMUs). However, fuzzy DEA is still limited to fuzzy input/output data while some inputs and outputs might be affected by various factors of uncertainty and information granularity, meaning that they could be better modeled in terms of fuzzy sets of type-2. In this paper, we develop a multi-objective DEA model in a setting of type-2 fuzzy modeling to evaluate and select the most appropriate sustainable suppliers. In the proposed model, both efficiency and effectiveness are considered to describe the integrated productivity of suppliers. In sequel, chance constrained programming, critical value-based reduction methods and equivalent transformations are considered to solve the problem. A detailed case study is employed to show the advantages of the proposed model in terms of measuring effectiveness, efficiency and productivity in an uncertain environment expressed at different confidence levels. At the same time, the results demonstrate that the model is capable of helping decision makers to balance economic, social, and environmental factors when selecting sustainable suppliers.