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A model to evaluate the effects of the returns to scale on the inverse data envelopment analysis
Mathematical Sciences ( IF 1.9 ) Pub Date : 2021-01-20 , DOI: 10.1007/s40096-020-00353-6
M. Ebrahimzade Adimi , M. Rostamy-Malkhalifeh , F. Hosseinzadeh Lotfi , R Mehrjoo

The concept of return to scale is the ratio of proportional variations in outputs to proportional variations in inputs. A decision maker by determining the returns to scale of a unit can made a decision to limitation or extension of it. The radial models cannot determine the output changes after applying variations in the input vector. So far, the amount of input changes, output changes and efficiency of decision-making units should be available for estimating returns to scale. So several models need to be solved. This paper describes a single model-mode method that is not required to information of inputs, outputs, or efficiency values. The proposed model provides the conditions for stability or improvement of the returns to scale of the under evaluation decision-maker unit. This model reduces computation volume. This model can find MPSS units, which is the one of important purpose in solving a model, but it usually needs complex computation heretofore. In this article, all MPSS units are introduced by solving one model, so decision maker can use all of them as a target. In this paper, input changes, output changes, efficiency, RTS, BCC-CCR and CCR-BCC efficiency, MPSS units are calculated just by one powerful model. So far, no definitive model has been proposed for evaluating RTS in inverse data envelopment analysis. The purpose of this multistage model is to provide a one linear model to evaluate the rate of change in inputs and outputs, while maintaining efficiency and RTS. Given that none of the inverse data envelopment analysis models have not shown the input and output’s changes with respect to the type of returns, this model can be a starting point for investigating changes in inputs and outputs while maintaining efficiency and RTS. This specific advantage makes this model operational. This information improves managerial decisions and increases the accuracy studies on the system. Estimating outputs (or inputs) and the type of RTS, by using efficiency amount, shows the flexibility of the model. This feature of the model improves inverse data envelopment analysis models.



中文翻译:

用于评估规模报酬率对逆数据包络分析的影响的模型

规模收益的概念是输出的比例变化与输入的比例变化之比。决策者可以通过确定单位的规模收益来决定限制或扩展单位。应用输入向量的变化后,径向模型无法确定输出变化。到目前为止,输入变化量,输出变化量和决策单位的效率应可用于估算规模收益。因此,需要解决几种模型。本文描述了输入,输出或效率值信息不需要的单一模型模式方法。所提出的模型为稳定或改善被评估决策者单位的规模收益提供了条件。该模型减少了计算量。该模型可以找到MPSS单位,这是求解模型的重要目的之一,但迄今为止通常需要复杂的计算。在本文中,所有MPSS单元都是通过求解一个模型来介绍的,因此决策者可以将它们全部用作目标。在本文中,仅通过一种强大的模型即可计算出输入变化,输出变化,效率,RTS,BCC-CCR和CCR-BCC效率,MPSS单位。迄今为止,尚未提出用于在逆数据包络分析中评估RTS的确定模型。此多阶段模型的目的是提供一个线性模型,以评估输入和输出的变化率,同时保持效率和RTS。鉴于没有一个逆向数据包络分析模型没有显示输入和输出相对于收益类型的变化,该模型可以作为调查投入和产出变化同时保持效率和RTS的起点。这种特定的优势使该模型可以运行。该信息可改善管理决策并增加对系统的准确性研究。通过使用效率量来估计输出(或输入)和RTS的类型,显示了模型的灵活性。该模型的功能改进了逆数据包络分析模型。

更新日期:2021-01-20
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