Cross evaluation using weight restrictions in unitary input DEA models: theoretical aspects and application to olympic games ranking

Abstract

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 the results of the Winter Games, which are also part of the Olympic Games. This paper proposes a method based on DEA, in which the outputs are the number of all three medals (gold, silver and bronze) that each country won at both the Salt Lake City and Sydney games; a constant input is considered for all countries. Theoretical aspects of this model are explained hereinbelow. Restrictions based on the importance of each medal are defined for this model. A weight average for each output, based on a modified Cross Evaluation model, is developed and is used as the coefficient in the weighted sum that establishes the final ranking.