Measuring and decomposing the overall efficiency of multi-period and -division systems associated with DEA

The combination way of component efficiencies into the overall efficiency is a central topic in the efficiency modeling of network systems based on data envelopment analysis (DEA). In terms of the feature and advantage of DEA modeling as the multiplier generation on inputs/outputs, it is desirable that the combination weights are derived from the data and self-generated in calculation process. The prior weights choice makes DEA modeling lose the objectivity and generalization in efficiency measures. This study proposes a new formulating approach of dynamic network DEA (DN-DEA) models to measure and decompose the overall efficiency of multi-period and -division systems without the pre-specified weights to combine component efficiencies into the overall efficiency. In our formulating approach, the double identities of carry-overs connecting consecutive periods and linkers connecting consecutive divisions are fully accounted for. This approach is applicable for the formulations of both radial measures (DN-CCR and DN-BCC) and non-radial measures (DN-SBM). This study extends Kao’s (in press) relational approach of dynamic DEA to dynamic network systems for empirical comparison. In contrast to Kao’s (in press) approach, our approach can present a weighted average decomposition of the overall (in)efficiency score into components ones by a set of endogenous weight sets which are the most favorable for the tested multi-period and -division system. This makes sense of the comparison between overall and component (in)efficiency scores. In this context, the overall efficiency score is less or more than all component ones. We applied our models to evaluate the innovation efficiency of OECD (Organization for Economic Co-operation and Development) countries.