a new model to measuring efficiency and returns to scale on data envelopment analysis

We extend the concept of returns to scale in data envelopment analysis (dea) to the weight restriction environments. by adding weight restrictions, the status of returns to scale, i.e. increasing, constant, and decreasing, may need a change. we first define returns to scale underweight restrictions and propose a method for identifying the status of returns to scale. then, we demonstrated that this addition would usually narrow the region of the most productive scale size (mpss). finally, for an inefficient decision-making unit (dmu), we will present a simple rule for determining the status of returns to the scale of its projected dmu. here, we carry out an empirical study to compare the proposed method's results with the bcc model. in addition, we demonstrate the change in the mpss for both models. we have presented different models of dea to determine returns to scale. here, we suggested a model that determines the whole status to scale in decision-making units.