Quota systems play a crucial role in regulating public-interest goods and controlling negative externalities, with a primary focus on social impacts rather than economic benefits. This paper examines the decision-making process for quota release, aiming to control growth rates and ensure price stability over time. We first develop a chance-constrained problem for quota systems, solving it using sample average approximation. Due to computational demands, alternative approximation methods are explored. We consider two types of quota systems: mature systems with known distributions and newly established systems with distributional ambiguity. For mature systems, Conditional Value-at-Risk (CVaR) is used to approximate the chance constraint, while for newly established systems, worst-case CVaR is employed within a robust optimization framework and the binary search algorithm is derived to efficiently solve the problem. The proposed models’ effectiveness is validated through computational studies using data from Singapore’s Vehicle Quota System. With known distributions, our CVaR sample average approximation (CVaR-SAA) model outperforms traditional models, reducing violation probability by more than 56.32%. With distributional ambiguity, worst-case CVaR approximation robust optimization (WCVaR-RO) model provides superior solutions, particularly in maximum violation probability (MVP). In the most notable case, WCVaR-RO reduces the MVP by over 53.37%. This research offers valuable insights into the management of quota systems.

中文翻译：

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分配稳健优化，以最大限度地减少配额系统中的价格波动


配额制度在监管公共利益商品和控制负外部性方面发挥着至关重要的作用，主要关注社会影响而不是经济利益。本文研究了配额释放的决策过程，旨在控制增长率并确保价格长期稳定。我们首先为配额系统开发了一个机会约束问题，使用样本平均近似来解决它。由于计算需求，探索了替代近似方法。我们考虑两种类型的配额系统：具有已知分布的成熟系统和具有分布模糊性的新建立的系统。对于成熟的系统，使用条件风险值 （CVaR） 来近似机会约束，而对于新建立的系统，在稳健的优化框架内采用最坏情况的 CVaR，并推导出二叉搜索算法来有效地解决问题。通过使用来自新加坡车辆配额系统的数据进行计算研究来验证所提出模型的有效性。在已知分布的情况下，我们的 CVaR 样本平均近似 （CVaR-SAA） 模型优于传统模型，将违规概率降低了 56.32% 以上。在分布模糊性下，最坏情况 CVaR 近似鲁棒优化 （WCVaR-RO） 模型提供了出色的解决方案，尤其是在最大违规概率 （MVP） 方面。在最显着的情况下，WCVaR-RO 将 MVP 降低了 53.37% 以上。这项研究为配额制度的管理提供了有价值的见解。