Finding stability regions for preserving efficiency classification of variable returns to scale technology in data envelopment analysis


1 Faculty of Engineering, Qom Branch, Islamic Azad University, Qom, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


This paper addresses issue of sensitivity of efficiency classification of variable returns to scale (VRS) technology for enhancing the credibility of data envelopment analysis (DEA) results in practical applications when an additional decision making unit (DMU) needs to be added to the set being considered. It also develops a structured approach to assisting practitioners in making an appropriate selection of variation range for inputs and outputs of additional DMU so that this DMU be efficient and the efficiency classification of VRS technology remains unchanged. This stability region is simply specified by the concept of defining hyperplanes of production possibility set of VRS technology and the corresponding halfspaces. Furthermore, this study determines a stability region for the additional DMU within which, in addition to efficiency classification, the efficiency score of a specific inefficient DMU is preserved and also using a simulation method, a region in which some specific efficient DMUs become inefficient is provided.