Measuring efficiencies of multi-period and multi-division systems associated with DEA: An application to OECD countries’ national innovation systems

• We model for efficiencies of multi-period and multi-division systems by DEA.
• We extend Kao's (2013) formulation approach of dynamic DEA to DN-DEA.
• We propose a new formulating approach for dynamic network DEA (DN-DEA) models.
• Our formulating approach can be applicable to both radial and non-radial measures.
• We apply the DN-CCR model to evaluate OECD countries’ innovation efficiency scores.

The efficiency-oriented performance evaluation of multi-period and multi-division systems (MPMDS) becomes increasingly important for complex investment and management decisions. This paper proposes a new formulation approach for dynamic network DEA (DN–DEA) models based on system thinking to measure and decompose the overall efficiency of MPMDS. The proposed approach is general and maintains the objective property of DEA evaluation, which not only does not need the pre-specified weights to subjectively combine component efficiencies into overall efficiency, but also is applicable to both radial and non-radial measures. More attracting, it presents a weighted average decomposition of the overall efficiency score into component ones by a set of endogenous weight sets which are most favorable for the overall efficiency of the tested entire MPMDS and ensures consistency in the comparison between overall and component efficiency scores. This study makes two contributions to the existing literature. First, it not only makes the structured decision making of MPMDS possible but also helps us realize semi- and non-structural decision making from an expert and intelligent systems point of view. Second, it evaluated the innovation efficiency of OECD countries in the multi-period and multi-division context, which presents an analytical technique and some systemic evidence for national innovation investment decisions in the long run.