Decomposition Weights and Stage Efficiencies in the Additive Network DEA Model with Shared Resources.

This paper investigates issues regarding the decomposition weights in the additive two-stage network Data Envelopment Analysis model with shared resources. In the input-oriented two-stage additive NDEA model with shared resources and constant returns to scale, Wang, Wu and Chen (2019) found that the relationship between the decomposition weights is uncertain. Thus, the bias towards the first stage inherent in the elementary two-stage additive NDEA model (i.e., resources are used only in the first stage), as seen in Ang and Chen (2016) and Despotis, Koronakos and Sotiros (2016), does not exist. In this paper, we first challenge this result by providing necessary conditions for decreasing decomposition weights. However, we demonstrate that Wang, Wu and Chen (2019)’s result holds for the output-oriented model under constant returns to scale. We then examine the relationship between the decomposition weights in the case of variable returns to scale and provide sufficient conditions for non-increasing decomposition weights. In these cases, it is crucial to consider how the shadow value of resources relates to the value of the free parameter of one of the two stages. Additionally, we investigate the relation between the decomposition weights under different variants of the model, namely, (1) when both shared and dedicated resources are used at the first stage, (2) when external inputs are use in the second stage, and (3) when final outputs are produced at the first stage.