Abstract

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.

摘要

在这项研究中，我们开发了多变量规模报酬率 (MRTS)，并说明了 MRTS 相对于现有标准规模报酬率 (RTS) 的优势，例如：恒定 RTS (CRS)、可变 RTS (VRS)、非递减 RTS (NDRS)、非增加 RTS (NIRS) 和混合 RTS (HRS)。我们解释了在评估具有多个输入和多个输出的数据集时引入 MRTS 的理论推理。我们演示了如何生成 MRTS 生产可能性集 (PPS) 并展示其与现有标准 RTS PPS 的差异。提出了一种线性规划模型来估计MRTS PPS的边界并测量相应的单元径向效率得分。每个单元的建议分数既不低于标准径向 CRS 模型的相应分数，也不大于标准径向 VRS 模型的相应分数。我们提出了一种从特定到通用的方法，用户在评估其数据集时应考虑该方法。