Study on Returns to Scale Consistency Between the Weak BCC Inefficient DMUs and Their Projection in DEA

This paper discusses estimation of returns to scale (RTS) of Weak BCC inefficient DMUs in DEA. RTS generally has an ambiguous meaning if DMU is not on Weak BCC efficient frontier. Researchers adopt projection method for this problem. Theoretically, a Weak BCC inefficient DMU and its projection should exhibit the same RTS nature. Banker et~al. (Eur J Oper Res 88:583–585, 1996b)’s projection, however, may give inconsistent estimation of RTS in some cases. For accurate RTS estimation of Weak BCC inefficient DMUs, this paper establishes Weak BCC projection and strong BCC projection. It is proved that, for a Weak BCC inefficient DMU, it is its Weak BCC projection that always exhibits the same RTS nature as itself while its strong BCC projection is not in some cases. In addition, Weak BCC projection is the most representative point among all frontier points for Weak BCC inefficient DMU. Therefore the projection should be Weak BCC projection, not strong BCC projection, when estimating RTS of Weak BCC inefficient DMUs.