Performance evaluation of two-stage network structures with fixed-sum outputs: An application to the 2018winter Olympic Games

In many applications of performance evaluation based on data envelopment analysis (DEA), it is often found that decision-making units (DMUs) have two-stage network structures, and the sum of these DMUs’ outputs is fixed. For example, in the Olympic Games, each participant country has two stages—the preparation of athletes and competition of athletes—and at a single game the total numbers of gold, silver, and bronze medals (the DMU outputs) are fixed. Such an evaluation scenario is very common in practice, but none of the existing approaches adequately analyze this kind of situation. This paper addresses this scenario and proposes a two-stage DEA approach with fixed-sum final outputs. The approach has two steps: constructing a common efficient frontier and evaluating the DMUs based on that frontier. To illustrate the proposed approach, we apply it to a real dataset for the 2018 PyeongChang Winter Olympic Games. Our results show that: (1) countries with high latitudes and a developed economy had much better efficiency; (2) the efficiency of the whole two-stage Olympic process is much more correlated with competition stage efficiency than with preparation stage efficiency; and (3) there are few DMUs whose efficiency in both stages is better than average. Finally, policy suggestions are made to help inefficient nations to win more Olympic medals.