A new ranking method based on cross-efficiency in data envelopment analysis

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 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.

Gap Minimization for Peer-Evaluation in DEA Cross-Efficiency

“…The cross-efficiency scores are determined by the profiles of weights that are used. To effectively select weights from multiple optimal solutions, goal programming formulations are considered to be an effective method in recent literature (e.g., SWAT proposed by Jahanshahloo et al [21] and the novel secondary objective function proposed by Hosseinzadeh-Lotfi et al [22]). Many alternative secondary goals for the purpose of cross-efficiency are proposed in the literature, where minimizing the summation of deviations from the ideal point and minimizing the maximum quantity among all deviation variables are typically applied in [23,24].…”

Modelos flexibles para la valoración de la eficiencia.

“…La medida de eficiencia obtenida por DEA, como ya se ha comentado, puede usarse para clasificar DMUs, pero esta clasificación no puede aplicarse para unidades eficientes (Hosseinzadeh et al 2011). Uno de los temas de investigación más interesantes, hoy en día, es discriminar entre las DMUs eficientes.…”