Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Data envelopment analysis (DEA) is one of the most efficient tools for efficiency measurement which can be employed as a benchmarking method with multiple inputs and outputs. However, DEA does not provide any suggestions for improving efficient units, nor does it provide any benchmark or reference point for these efficient units. Impracticability of these benchmarks under environmental conditions is another challenge of benchmarking by DEA. The current study attempts to extend basic models for benchmarking of efficient units under practical conditions. To this end, we construct the practical production possibility set (PPPS) by employing the concept of artificial decision-making units and adding these decision-making units to the production possibility set (PPS) such that these artificial units satisfy all environmental constraints. Then, the theorems related to PPPS and their proofs are provided. Moreover, as a secondary result of this study, efficient units can be ranked according to their practical efficiency scores.