A model to evaluate the effects of the returns to scale on the inverse data envelopment analysis

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.