Estimation of Overall Returns to Scale (RTS) of a Frontier Unit Using the Left and Right RTS

Abstract

This paper introduces a proposed method for identifying the left and right Returns to Scales (RTS) and the overall RTS of frontier units based on the theoretical framework of data envelopment analysis (DEA). This paper first proposes an alternative definition for Left RTS (L-RTS) and Right RTS (R-RTS) of frontier units and then by focusing on this definition, provides two new DEA models to present a proposed method for identifying the L-RTS and R-RTS of frontier units. The major advantages of these two models include that they are feasible in all situations. Also, these models are capable to properly and accurately identify frontier units and their type of L-RTS and R-RTS, without any plurality in their judgment. The proposed method is compared -theoretically and experimentally- with other methods presented in the literature. Moreover, the theoretical correlation between the concepts of overall RTS and L&R-RTS of frontier units is analyzed. Then, this analysis is used to propose an alternative method for categorizing overall RTS of frontier units. Experimental application of this method shows that the results of evaluation of overall RTS of frontier units obtained by the proposed method is completely consistent with the results of the method presented by Banker and Thrall (Eur J Oper Res 62(1):74–84, 1992). The proposed methods in this paper can be easily used by the existing codes of DEA.