Cost decompositions and the efficient subset

•We introduce both an additive slack-based and a multiplicative Russell approach for decomposing cost (in)efficiency.•Focusing on the additive form, we develop a cost decomposition on the additive Russell measure.•We extend the developed additive approach into data envelopment analysis.•To show the applicability of our novel approach, we provide an illustration using data.

This paper develops two cost decompositions based on the multiplicative Russell and additive slack-based (in)efficiency measurement frameworks. While the multiplicative cost decomposition is a straightforward extension of the standard cost decomposition, the decomposition we develop in this paper incorporates slacks directly so that efficiency is measured relative to the efficient subset. To show the applicability of our novel approach, we provide an illustration using a data set used in the literature.