Integrated stochastic multicriteria acceptability analysis and data envelopment analysis with fixed-sum outputs: an application for evaluating participating nations in the Winter Olympics Games

Along with the popularity of Olympic Games, evaluating and ranking participating nations has become one of the hottest issues in recent years. Data envelopment analysis (DEA) is extensively used for participating nations' performance evaluation, while the prior literature mainly addresses the maximum efficiency by ignoring the weights diversity, which might lead to unreasonable and biased results. By considering the fixed-sum medals constraint, this paper proposes an integrated approach of stochastic multicriteria acceptability analysis (SMAA) and DEA for evaluating the participating nations. The proposed approach addresses the weights diversity and multiple equilibrium efficient frontiers by investigating the overall feasible space, and two strategies are considered to guarantee the fairness concern for calculating the efficiencies. Besides, the proposed approach provides both rank acceptability and holistic acceptability index to obtain the complete ranking from the best to the worst and to get the relative ranking relationship in the overall feasible space. The proposed approach can provide more reasonable performance measurements since it explores different rank positions and improves the whole satisfaction of all participating nations. Finally, the proposed approach is applied to empirically analyze the participating nations in the Winter Olympic Games from 2010 to 2022 and some valuable analytical results are provided.