Some alternative DEA models for two-stage process

Two-stage data envelopment analysis (DEA) has been researched by a number of authors. In a recent paper by Kao and Hwang (2008), the overall efficiency of two-stage process was defined as the product of the efficiencies of two individual stages. In a more recent paper by Chen, Cook, Li, and Zhu (2009), the overall efficiency of two-stage process was modeled as a weighted sum of the efficiencies of two individual stages. This paper looks into further two-stage DEA and proposes some alternative DEA models for two-stage process to show that (i) the overall efficiency of two-stage process can also be modeled as a weighted harmonic mean of the efficiencies of two individual stages; (ii) the two-stage DEA model of Kao and Hwang (2008) can be easily extended to variable returns to scale (VRS) assumption; and (iii) the additive efficiency decomposition model of Chen et al. (2009) can be generalized to taking into account the relative importance weights of two individual stages. Numerical illustrations are provided to show the potential applications of the proposed new DEA models.