Average lexicographic efficiency decomposition in two-stage data envelopment analysis: an application to China's regional high-tech innovation systems

This paper proposes a lexicographic decomposition strategy for the two-stage network DEA model. Instead of assigning a priority over the two component stages, our proposed approach employs a lexicographic algorithm in such a way that the system efficiencies of the DMUs are lexicographically computed for each of their possible sequences while maintaining the efficiencies of those units already investigated unchanged. In particular, the system efficiency and the two component efficiencies can be uniquely determined under our proposed decomposition approach. Besides, prior to implement the proposed lexicographic evaluation procedure, we also highlight a potential infeasibility problem arising from the normalization constraint, and develop a modified iterative approach that facilitates us to guarantee a feasible search procedure. Finally, we use a numerical example to illustrate the effectiveness of the proposed approach, and conduct an empirical study to analyze China's regional high-tech innovation systems for the period of 12th Five-Year Plan (2011-2015).