A Novel Gibbs Entropy Model Based upon Cross-Efficiency Measurement for Ranking Decision Making Units

Abstract

Cross-efficiency measurement in data envelopment analysis (DEA) was developed to overcome the main disadvantage of DEA in discriminating decision making units (DMUs). However, the results obtained from each cross-efficiency model (Benevolent and aggressive models) may not generally be the same for similar problems, and each model may provide different viewpoints that we should take each model into account at the same time. Since Gibbs entropy is one of powerful tools to measure uncertainty, in this paper a novel linear programming model based on the concepts of Gibbs entropy (GE model) has been offered to combine cross-efficiency scores, which are obtained from the viewpoints of benevolent and aggressive models, for ranking DMUs. In order to validate the proposed GE model, it is tested with two examples, including the performance assessment problem and the relative efficiency of seven Thai provinces. The main advantages of the GE model are that it can be used to tackle large size problems with uncertainty, and it can be used to combine other models for ranking DMUs. In addition, the set of multiple solutions of optimal weights for each model can be ignored. By using the proposed model, decision-makers can achieve more reliable decision than individual models.