Distributionally robust optimization for minimizing price fluctuations in quota system

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.