A comprehensive common weights data envelopment analysis model: Ideal and anti-ideal virtual decision making units approach

Abstract

Data envelopment analysis (DEA) calculates the relative efficiency of homogenous decision-making units (DMUs) with multiple inputs and outputs. Classic DEA models usually suffer from several issues such as: discrimination power, variable weights of inputs/outputs, inaccurate efficiency estimation for small number of DMUs, incapability in working with zero and negative data, and not having exterior target. Ranking methods in DEA have been proposed to resolve such issues.In this paperan approach is proposed to overcome all of theseissues, concurrently. This approach has five main properties: 1) using common weight methodology to reduce the chance of inefficient DMUs to be evaluated as efficient; 2) defining virtual ideal and anti-ideal DMUs in a unique modelconcurrently to improve the discrimination power and to make exterior target based on observed DMUs; 3) providing full ranking for even production possibility sets (PPS) with low number of DMUs; 4) handling forzero and non-positive data; 5) Ranking all DMUs in a single run which reduces the computational efforts effectively. The properties of the model of this study including convexity, feasibility, and optimality are discussed through several theorems.The validity of the model is illustrated through solving five benchmark numerical examples adopted from the literature of past works.The results of the model are compared with those of existing methods. The results illustrate theefficacy and comparability of proposed approach among the existing methods.