The decomposition of efficiency in parallel network production models
指出Kao(2012)的并行系统效率分解方法在规模报酬可变时可能产生负的子单元效率值，并提出基于方向距离函数的改进分解方法，避免该问题且适用于非凸技术。
Kao (2012) proposed a method to decompose DMU efficiency into sub-unit efficiencies for parallel production systems. We provide a numerical example showing that the proposed method can yield negative sub-unit efficiency scores under variable returns to scale, against common sense and standard postulates requiring this score to be non-negative. As a solution, we propose a decomposition based on the directional distance function that does not suffer from this problem. In particular, we recognise that the overall inefficiency of the DMU is composed of the sub-units technical inefficiencies and a reallocation inefficiency component. The proposed method can be also applied to non-convex technologies, therefore providing a more general method to implement such a decomposition. Given the connection between the directional distance function and slack-based efficiency measurement, the method can easily be extended to this case as well.