An alternative ranking of DMUs performance for the ZSG-DEA model

Abstract

The Zero-Sum Gains Data Envelopment Analysis (ZSG-DEA) model was developed to evaluate the performance of Decision Making Units (DMUs) under output interdependency, which is evident when the total (over DMUs) observed output is a priori fixed. In this paper, we take a closer look at the derivation and interpretation of the ZSG-DEA efficiency scores and we explain why these are not really comparable across DMUs. Moreover, we verify that DMUs' ranking based on their ZSG-DEA efficiency scores is in fact incompatible with output interdependency, which requires total potential output of DMUs to be equal to their total observed output. Then, we propose an alternative metric of DMUs’ performance that is both consistent with output interdependency and comparable across DMUs. This metric is used for classifying DMUs into three (high, average or low performance) groups and for ranking them within these groups. To illustrate its empirical applicability, we use data from the Olympic Games, where output interdependency is clearly evident since the total number of awarded (gold, silver, and bronze) medals is a priori fixed.