Extending the zero-sum gains data envelopment analysis model

Abstract

In this paper, we adapt the ZSG-DEA model to the case of a reverse output, whose larger (smaller) values reflect lower (higher) achievements. Then, we introduce the zero-sum reverse output redistribution strategies, state the resulting Target’s Assessment Theorem for both the proportional and the equal expansion strategy, and confirm that the Benchmarks’ Contribution Equality Theorem is also applicable to these cases. We also apply the ZSG-DEA model with a forward and a reverse output to estimate respectively teams’ offensive and defensive efficiency in Greek premier soccer league.