Modification of the Arash Method using Facet Analysis

Data Envelopment Analysis, one of the most popular disciplines in operations research, it is a technique used to estimate the performance of Decision Making Units (DMUs). Technical efficient DMUs and Efficient DMUs are difficult to differentiate without the availability of additional information in the form of weight restrictions or the use of statistical technique and supper efficiency method. The Arash method (2013) distinguishes between Technical efficiency and Efficiency by introducing a small error in input values even if the values are accurate, the efficiency scores of the efficient DMUs does not change, only that of the technical efficient DMUs, it also establishes that, for a DMU to be efficient, technical efficiency is one of the necessary conditions. In this study we expand the Arash Method by using facet analysis to modify the PPS of the Arash method. The proposed modification places an upper bound only on the free variable of VRS Arash method. This modification on the Arash method gives the true efficiency score and rank for the weak efficient DMUs and DMUs which take their efficiency score when compared to the weak part, because, the use of facet analysis on the frontier of the Arash method deduced some essential details about the constructive hyper planes of the production possibility set (PPS), Particularly the weak part of the frontier. Keywords: Data Envelopment Analysis, Arash Method, Efficiency, Technical Efficiency, Facet Analysis, Modified Arash method, rank.