A note on the zero-sum gains data envelopment analysis model

In the case of proportional output reduction strategy with a single output, Variable-Returns-to-Scale (VRS) Zero-Sum Gains Data Envelopment Analysis (ZSG-DEA) efficiency scores can be obtained from VRS conventional DEA by means Target’s Assessment Theorem (TAT). Using TAT as departure point, two relations for computing ZSG-DEA appear in literature. Our objective this note is to compare, contrast and challenge them on both theoretical empirical grounds. For latter, three different data sets are used.