Evaluating efficiency and ranking of technical efficient and inefficient units

Maintaining the efficiency score of efficient units and distinguishing between technical efficiency and efficiency are very essential topics in operations research. The Arash method is a new technique in Data Envelopment Analysis (DEA) for estimating the performance of units and ranking. The Arash method is based on additive DEA model (ADD). In this study we expand the Arash method by using facet analysis to modify the production possibility set (PPS). This modification avoids the effect of the weak part of PPS frontier which can propose a bias efficiency evaluation to DMUs placed on or compared with the weak part of the frontier. We integrated the attributes of the Arash method and modified variable return to scale model, consequently showing the true efficiency score and ranks of units associated with the weak part of the frontier, also identifying “technical efficient” and “inefficient” DMUs. The efficiency score of DMUs located at the strong part of the frontier remains the same, only those associated with the weak part are modified. A numerical example is used to show the effectiveness of the proposed model in comparison with the Arash method.