Measuring the performance of nations at the Summer Olympics using data envelopment analysis
用数据包络分析评估各国在最近五届夏季奥运会上的表现，输入为国民生产总值和人口，输出为金银铜牌数，并加入权重限制确保金牌价值高于银牌、银牌高于铜牌。
In this paper a well known tool for relative efficiency assessment, namely Data Envelopment Analysis (DEA), is used to measure the performance of the nations participating at the last five Summer Olympic games. The proposed approach considers two inputs (GNP and population) and three outputs (number of gold, silver and bronze medals won). To increase the consistency of the results, weight restrictions are included, guaranteeing a higher valuation for gold medals than for silver medals and higher for the latter than for bronze medals. Variable returns to scale are assumed. The results for the last five Summer Olympics are analysed. For each of them, a performance index as well as benchmarks are computed for each country. In addition, plotting the performance of a specific country for the different games can help identify trends as well as objective successes and disappointments.