Right and left returns to scales in data envelopment analysis: Determining type and measuring value

This study identifies types and values of right and left returns to scales (RTSs) of efficient decision making units (DMUs) in data envelopment analysis (DEA). In this research, we first introduce a new approach to estimate types of right and left returns to scales of efficient DMUs and then, values of right and left returns to scales of these DMUs are measured by presenting two new DEA models.One of the advantages our proposed approach for determining types of right and left RTSs is that our approach is always feasible for all target DMUs while Golany and Yu’s RTS approach (Golany & Yu, 1997) is not always feasible, in this case, Golany and Yu have shown that no feasible solution means that there is no data to determine the right or left returns to scale. Other advantage is that our approach is capable of measuring values of right and left returns to scales of efficient DMUs.It is note worthy that, since an inefficient decision making unit (DMU) has more than one projection on the empirical function thus by applying our proposed approach, different types and values of right and left RTSs can be obtained for projections of the inefficient DMU.Lastly, we give an empirical example which motivates our development and contrasts the proposed approach with Golany and Yu’s approach then some conclusions are discussed based on the results and also directions for future research are suggested. Note that proofs of some theorems are presented in the Appendix.

► We propose two multiplier models for determining type of right and left RTSs of BCC-efficient DMUs. ► We introduce a method for measuring right and left RTSs of BCC-efficient DMUs. ► An empirical example highlights for illustrating the application of our proposed approach. ► We then make comparison between our approach and Golany and Yu’s approach.