A ranking for the Olympic Games with unitary input DEA models

There is no official method to establish a final ranking for the Olympic Games. The usual ranking is based on the lexicographic multicriteria method, the main drawback of which is to overvalue gold medals. Furthermore, it does not take into account that the various sports may be of different importance. This work proposes a ranking model to eliminate those drawbacks. We use firstly a modified cross-evaluation data envelopment analysis model with weighted restrictions for each cluster. The outputs are the number of gold, silver and bronze medals and the input is a unitary constant for all countries. After obtaining a rank for each and every cluster, we build a general ranking by aggregation of the partial ones. Our model uses the results of the Athens Olympic Games.