Efficiency decomposition of the network DEA in variable returns to scale: An additive dissection in losses

Abstract

Kao and Hwang [10] proposed a model based on the multiplier form for two-stage network under constant returns to scale. Their model assumes that the system efficiency is the product of the efficiencies of the two stages. That is, the system operates in a multiplicative way. Alternatively, we define loss to be equal to the aggregated input (cost) minus the aggregated output (revenue). Based on the notion of the loss, we dissect a system in a way that the system loss is the sum of the losses of the subsystems. That is, a system operates in an additive way. We find that the model in [10] can be decomposed in this additive way. We further develop the multiplier form under VRS for the two-stage network based on losses, whose dual form is the VRS extension of the CRS envelopment model in [10]. Based on losses, an alternative definition of efficiency other than ratio efficiency is provided. Based on the additivity of losses, the two-stage VRS model is further extended to a general network structure.