On constructing a composite indicator with multiplicative aggregation and the avoidance of zero weights in DEA

Recently there has been interest in combining the use of multiplicative aggregation together with data envelopment analysis (DEA). For example Blancas et al (2013), Cook and Zhu (2013), Giambona and Vassallo (2013); the first two of these are JORS papers. The purpose of this note is to highlight differences in the way multiplicative DEA is being applied and to draw attention to the fact that a units-invariant (i.e. scale-invariant) form is available. Moreover, this model avoids the ‘zero weight problem’ in DEA (where criteria are effectively ignored).