How to assess sustainability of suppliers in the presence of volume discount and negative data in data envelopment analysis?

Supplier selection is an important decision-making problem in supply chain management. Selecting appropriate suppliers based on sustainability criteria including economic, environmental, and social criteria can help companies move toward sustainable development. Data envelopment analysis (DEA) is applied to recognize the most sustainable supplier. However, conventional DEA models can be applied only to performance measurement systems characterized by positive input–output data. However, in real world, data can be negative. We propose a new DEA model for evaluating sustainability of suppliers in presence of negative data and volume discounts. Also, we present a super-efficiency model for ranking suppliers. In addition, we prove some main properties of our proposed method. Finally, we present a case study to demonstrate applicability of proposed model.