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 6 community, as gas waste, water waste, and solid wastes generated in the production process of factories. 7 Recent studies on environmental management have forced commercial organizations to re-evaluate 8 their roles and responsibilities for protecting the natural environment. This study focuses on the DEA 9 environmental assessment via the concept of congestion. Recognizing the congestion of units is one of 10 the most attractive issues in the literature of Data Envelopment Analysis (DEA), because the decision 11 maker (DM) can use this concept to decide whether to increase or decrease the size of a Decision12 Making Unit (DMU). In the DEA literature, congestion is classified into Undesirable Congestion (UC) 13 and Desirable Congestion (DC). In many real-world situations, we cannot determine the exact value for 14 all data, hence, some parameters are inevitably reported as uncertain data, e.g. stochastic data, fuzzy 15 data, interval data and so on. This study focuses on considering Returns to Damage (RTD) under UC 16 and Damages to Return (DTR) under DC in the situation that the input and desirable and undesirable 17 outputs are reported as interval data. For this purpose, some uncertain models under the different 18 production possibility sets (PPS) are formulated and then we use the robust optimization technique to 19 formulate the equivalent certain models. The potential of the proposed methods is illustrated by a 20 numerical example.
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