Directional Distance Based Efficiency Decomposition for Series System in Network Data Envelopment Analysis

The multiplier network directional distance function (DDF) model capable of handling negative data received little attention in the field of data envelopment analysis (DEA). The series system is a basic network one. Under the assumption of variable returns to scale (VRS), this paper extends the multiplier series DEA model for use with the DDF. The proposed series DDF model is non-oriented and can deal with negative data. The resulting system efficiency score can be decomposed as a weighted average of process efficiency scores. In the context of DDF, the issue of possible alternate process efficiencies is addressed. The proposed model can also be applied to the assumption of constant returns to scale (CRS). Moreover, we derive the mathematical relationship between the CRS form of our series DDF model and the series CCR model. Two empirical examples in the literature illustrate the applicability and advantages of the new model.