A response to comments on modeling undesirable factors in efficiency evaluation

F€are and Grosskopf (2004) address the approach of Seiford and Zhu (2002) where undesirable input and output measures are treated in data envelopment analysis (DEA). One key feature of Seiford and Zhu s (2002) approach is that the bad outputs are treated as outputs in DEA model but are reduced when DEA efficiency is evaluated. F€are and Grosskopf (2004) suggest an alternative approach in treating the undesirable measures by distinguishing between weak and strong disposability and using a directional distance function. F€are and Grosskopf (2004) point out that the two approaches do not give the same results, and mention the possible causes. We further investigate the approach of F€are and Grosskopf (2004) and show that their directional distance function can be linked to the additive DEA model (Charnes et al., 1985). We further extend their model. Use the notions in Seiford and Zhu (2002), we suppose we have n decision making units (DMUs), each DMUj produces s good outputs y g rj ðr 1⁄4 1; . . . ; sÞ and d bad outputs yb tj ðt 1⁄4 1; . . . ; dÞ using m inputs xij ði 1⁄4 1; . . . ;mÞ. The model suggested in F€are and Grosskopf (2004) can be expressed as