A note on some alternative DEA models for two-stage process

In a recent paper in this journal by Wang and Chin (2010), they transformed a two-stage process into a single process. However, we find that Fig. 2 in Wang and Chin (2010) ignored the relationship between two processes when the single process was treated as a black box, which can misguide the decision maker. In this paper, the Fig. 2 in Wang and Chin (2010) is corrected, and a new transformation is proposed which transforms a two-stage process to a single process with two independent parallel sub-processes. The relationship between Chen, Cook, Li, and Zhu (2009)’s model and models (22) in Wang and Chin (2010) is also discussed.