Peyrache, AntonioSilva, Maria C. A.2024-06-052024-06-052024-090305-0483http://hdl.handle.net/10400.14/45410Kao (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 recognize 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.engData envelopment analysisDirectional distance functionFree disposal hullInefficiencyNetworksjournal article10.1016/j.omega.2024.10308485190243258001229691700001