Benchmarking of countries at Summer Olympic Games using two-stage DEA models

After important sports events as the Summer Olympic Games are, the participating countries are ranked according to the number of gold, silver and bronze medals. A lexicographic ranking is usually applied which leads to higher ranking of countries with one gold and no other medals comparing to countries without any gold but with several silver or bronze medals. Moreover, this ranking does not take into account the specific conditions of the countries (population, economic strength that is usually measured by GDP per capita, etc.). The aim of the paper is not only to evaluate the absolute achievements of the countries but evaluate their performance with respect to the resources they can use. A two-stage DEA model is formulated and solved by an original SBM procedure. The first stage evaluates the performance of the countries in training of athletes and the second stage evaluates the achievements of the nominated athletes. The models with variable returns to scale and weight restrictions are applied. The models and their results are illustrated on the case of Olympic Games 2016 and compared with results given by traditional models.