Understanding Self and Cross-Efficiencies and Their Relations in Data Envelopment Analysis

Abstract

This paper explicitly talks about the relationship between self-efficiency and cross efficiencies. The self-efficiency and cross efficiencies are used in different research works and various secondary goals are also developed using these measurements, but there is no explicit statement or derivation found in any prior art regarding the relationship between self and best cross efficiency for a DMU. Thus, in the present work, the relationship between self and cross efficiencies is examined explicitly and established via some theorems. These relationships can be useful in DEA's further formulations like goal programming models. The paper also complements the author's previous book chapter wherein they have used these relationships. A Numerical illustration is given in the end to establish the results.