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.

Data envelopment analysis (DEA) models compute efficiency score for decision making units (DMUs) and discriminate between efficient and inefficient DMUs. Therefore, they rank DMUs except when multiple DMUs have an efficiency score of 1. This paper proposes a new method for complete ranking of DMUs that is based on cross-efficiency evaluation method. One of the drawbacks of the crossefficiency evaluation method is the existence of multiple cross-efficiency scores due to the presence of alternative optimal solutions of the dual multiplier model. Hence choosing weights between alternative optimal solutions as part of a procedure for ranking DMUs is problematic. Liang et al. (2008) introduced alternative secondary goals in cross-efficiency evaluation. However, this paper finds that their approach is problematic in some situations. As a result, this paper seeks to introduce a new secondary objective function in cross-efficiency evaluation for removing their difficulties. Numerical demonstration reveals the validity of the proposed method by using a real data set of a case study which consists of 20 Iranian bank branches.

Data envelopment analysis (DEA) is a mathematical programming technique for identifying efficiency scores of decision making units (DMUs). Since DEA models cannot present efficient frontiers of PPS, in order to do this, we introduce a method for identifying efficient frontier for DMUs with interval data.

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