Evaluating sustainability of supply chains by two-stage range directional measure in the presence of negative data

Assessing sustainability of supply chains is a critical and increasingly complex problem. In recent years sustainability has received more attention in supply chain management (SCM) literature with triple bottom lines including social, environmental, and economic factors. Conventional data envelopment analysis (DEA) models consider decision making units (DMUs) as black boxes that consume a set of inputs to produce a set of outputs and do not take into consideration internal interactions of DMUs. Two-stage DEA models deal with such DMUs. However, existing two-stage DEA models are applicable only in technologies characterized by positive inputs/outputs. This paper aims to build and present a new two-stage DEA model considering negative input-intermediate-output data. Some numerical examples along with some theorems and properties are given to show capability of proposed method. The proposed ideas are used in a case study where 29 Iranian supply chains producing equipment of expendable medical devices are evaluated in terms of sustainability.