Multivariate returns to scale production frontiers

In this study, we develop multivariate returns to scale (MRTS) and illustrate the advantages of MRTS over the existing standard returns to scale (RTS) such as: constant RTS (CRS), variable RTS (VRS), nondecreasing RTS (NDRS), nonincreasing RTS (NIRS), and hybrid RTS (HRS). We explain theoretical reasonings for introducing MRTS when evaluating datasets with multiple inputs and multiple outputs. We demonstrate how to generate an MRTS production possibility set (PPS) and show its differences with the existing standard RTS PPSs. A linear programming model is proposed to estimate the frontier of the MRTS PPS and measure the corresponding radial efficiency scores of units. The proposed score for each unit is neither less than the corresponding score of the standard radial CRS model nor greater than the corresponding score of the standard radial VRS model. We propose a specific-to-general approach that users should consider when evaluating their datasets.