Tractable Approximation of Dynamic Decision Making Models Under Uncertainty

该奖项的目标是为一大类不确定情况下的动态决策模型提出一个实用、高效、健壮和可扩展的建模框架。针对数据分布信息有限的多阶段随机规划问题，提出了一种凸逼近方法。将开发出从理论上和计算上衡量结果近似质量的机制。还将探讨它们与稳健优化方法的关系。提出的可处理近似方法将被用于建模和解决从供应链管理、医疗保健、金融工程和水资源管理在内的各种重要的大规模实际问题。如果该项目成功，将极大地提高我们对不确定情况下的动态决策问题建模的能力，并为解决大规模随机规划问题提供计算工具。它将允许将随机规划应用于大规模的实际动态决策模型，这些模型以前由于计算复杂而无法实现。该项目还将展示将不确定性纳入企业面临的实际决策问题的潜力，并为拥有模型和计算工具的公司提供便利，以开发能够高效率和有效地处理不确定性的急需的决策支持系统。

The objective of this award is to propose a practical, efficient, robust and scalable modeling framework to a broad class of dynamic decision making models under uncertainty. Convex approximation approaches will be proposed to solve multi-stage stochastic program problems with limited data distributional information. Mechanisms to measure the quality of the resulting approximations, both theoretically and computationally, will be developed. Their relationship with robust optimization methodology will also be explored. The proposed tractable approximation approach will be applied to model and solve a variety of important large scale practical problems ranging from supply chain management, healthcare, financial engineering and water resource management. If successful, this project would greatly enhance our capabilities to modeling dynamic decision making problems under uncertainty and provide computational tools to solving large scale stochastic programming problems. It would allow the application of stochastic programming to large scale practical dynamic decision making models which were previously out of reach due to their computational complexity. The project would also demonstrate the potential of incorporating uncertainty into practical decision making problems faced by enterprises and facilitate firms with models and computational tools to develop much-needed decision support systems that can handle uncertainty efficiently and effectively.