Developing new robust DEA models to identify the returns to damage under undesirable congestion and damages to return under desirable congestion measured by DEA environmental assessment

In recent years, the environmental issue has attracted widespread concern from the international community, as gas waste, water waste, and solid wastes generated in the production process of factories. Recent studies on environmental management have forced commercial organizations to re-evaluate their roles and responsibilities for protecting the natural environment. This study focuses on the DEA environmental assessment via the concept of congestion. Recognizing the congestion of units is one of the most attractive issues in the literature of Data Envelopment Analysis (DEA), because the decision maker (DM) can use this concept to decide whether to increase or decrease the size of a Decision Making Unit (DMU). In the DEA literature, congestion is classified into Undesirable Congestion (UC) and Desirable Congestion (DC). In many real-world situations, we cannot determine the exact value for all data, hence, some parameters are inevitably reported as uncertain data, e.g. stochastic data, fuzzy data, interval data and so on. This study focuses on considering Returns to Damage (RTD) under UC and Damages to Return (DTR) under DC in the situation that the input and desirable and undesirable outputs are reported as interval data. For this purpose, some uncertain models under the different production possibility sets (PPS) are formulated and then we use the robust optimization technique to formulate the equivalent certain models. The potential of the proposed methods are illustrated by a numerical example.