CAREER: Risk Management via Stochastic Programming: Models, Computation, and Applications

该学院早期职业发展(Career)项目的研究目标是研究新的优化模型和算法，使决策者能够在面对不确定性的情况下做出复杂决策时管理风险。具体的研究活动包括：探索具有限制坏结果概率的约束的随机规划的新的基于分解的方法；研究新的随机支配约束模型，允许决策者以可调整的方式设置最小可接受的风险分布；以及通过使用这些模型来解决诸如供应链管理、劳动力配备、财务和医疗规划等应用领域的问题，来证明这些模型的可用性和影响。这一职业项目的主要教育目标是增加在面对不确定性时使用量化工具做出决定的个人人数。具体的教育活动包括：与校园预科外展组织合作，将与优化相关的主题纳入他们的计划；为工程入门课程开发和教授不确定性下的决策模块；以及设计和实施不确定下的优化研究生课程。该项目将产生一套新的计算实用工具，决策者可以使用这些工具来找到平衡风险和效率的计划。例如，这些工具可以被企业用来以更低的成本满足客户服务目标，被政府机构用来选择具有成本效益的疾病控制政策，或者被医生用来设计放射治疗计划。该提案的教育方面将通过向研究生提供应用这些方法所需的技能，并让广泛的本科生接触到优化的使用，从而促进这些方法的采用。大学预科教育活动将通过覆盖威斯康星州不同经济背景的大学预科学生来促进数学科学的多样性。

The research objective of this Faculty Early Career Development (CAREER) project is to investigate new optimization models and algorithms that enable decision-makers to manage risk when making complex decisions in the face of uncertainty. Specific research activities include: explore new decomposition-based methods for stochastic programs having constraints limiting the probability of a bad outcome; study new stochastic dominance constrained models that allow decision-makers to set a minimally acceptable risk profile in an adjustable manner; and prove the usability and impact of these models by using them to solve problems in application areas such as supply chain management, workforce staffing, finance, and medical treatment planning. The overarching educational objective of this CAREER project is to increase the population of individuals who use quantitative tools to make decisions in the face of uncertainty. Specific educational activities include: work with a campus precollege outreach organization to incorporate optimization-related topics into their programs; develop and teach a decision-making under uncertainty module for an introductory engineering course; and design and implement a graduate course on optimization under uncertainty.This project will lead to a new set of computationally practical tools that decision-makers can use to find plans that balance risk and efficiency. For example, these tools could be used by businesses to meet customer service targets at lower cost, by government agencies to choose cost-effective disease control policies, or by physicians to design radiation treatment plans. The educational aspect of the proposal will facilitate adoption of the methods by giving graduate students the skills needed to apply them, and by exposing a wide range of undergraduate students to the use of optimization. Precollege educational activities will promote diversity in the mathematical sciences by reaching an economically diverse range of precollege students across Wisconsin.