A simplification generalized returns to scale approach for selecting performance measures in data envelopment analysis

Abstract

Toloo and Tichy (2015) with the aim of holding the rule of thumb in data envelopment analysis, developed a pair of models which optimally chooses some inputs and outputs among selective measures under variable returns to scale assumption. Their approach involves a lower bound for the input and output weights in the multiplier model and a penalty term in the objective function of envelopment model. These models possess an epsilon which on the one hand turns the selecting envelopment model non-linear and on the other hand increases the required computational burden for solving the selecting multiplier models. Selecting an improper value for the epsilon may cause the infeasibility and unboundedness issues for the multiplier and envelopment model, respectively. This paper demonstrates that the method of Toloo and Tichy (2015) is valid even with excluding the epsilon. The method is extended to generalized returns to scale model which considers other returns to scale assumptions, i.e. non-increasing, constant, and non-decreasing. The obtained results point out that the simplified approach is more stable and more reliable and substantially reduces the required calculations.