Abstract

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 cross-efficiency 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.

Key words: Data envelopment analysis (DEA), ranking, cross-efficiency.