Data envelopment analysis in the absence of convexity: Specifying efficiency status and estimating returns to scale

• A DEA method for identifying FDH-efficient DMUs.
• Two DEA models for the estimation of right and left RTS of FDH-efficient DMUs.
• A DEA method for determining MPSS in FDH models.
• Presentation of two examples to illustrate the use of our proposed approach.
• Making comparisons among our RTS method and other RTS methods in FDH models.

The first purpose of this study is to present new DEA (data envelopment analysis) approaches that distinguish the efficiency status (efficient or inefficient) of decision-making units (DMUs) and estimate right- and left-hand returns to scale (RTS) of efficient DMUs in free disposal hull (FDH) models. The second one is to estimate most productive scale size (MPSS) in FDH models. The proposed RTS method has three preferences with respect to the previous RTS methods in this context. First one is that it is capable of identifying all FDH-efficient DMUs, whereas the previous methods may not be able to specify all FDH-efficient DMUs. Besides, the second one is to estimate right- and left-hand RTS of FDH-efficient DMUs, while the former methods are only capable of estimating RTS of FDH-efficient DMUs. Moreover, the third one is that it is always able to estimate right- and left-hand RTS, correctly, whereas the previous methods are sometimes capable of estimating RTS, correctly. These issues are the motivations for creating this current research. Finally, a numerical example and an empirical application are exhibited for illustrating and comparing the proposed method with the former methods. Then, some consequences are provided based upon the obtained results and also some suggestions for future works are presented. Proofs of some theorems and lemmas are given in the Appendix.