CAREER: A Study of Stochastic and Robust Integer Programming: Algorithms, Computations and Applications

该学院早期职业发展(CALEAR)奖为研究和教育活动提供资金，以促进随机和稳健整数规划的理论、计算和应用。整数决策变量通常用于决策问题的模型中。此外，在实时决策问题中，实例参数通常是不确定的。这项工作将研究随机和稳健的整数规划方法来描述和解决具有整数决策变量和不确定参数的决策问题。研究活动包括：1)研究基本问题的多面体结构和多项式时间算法，2)发现将切割平面与分解算法相结合的新方法，3)探索在高性能计算设施中有效实施算法的网络基础设施，4)将理论分析与电力资产优化、联合定价和库存规划、天气预报和疏散计划中的应用问题相结合。教育活动包括1)推广随机和稳健整数规划作为解决不确定问题下决策的有效方法；2)激发学生对科学和技术研究，特别是运筹学的兴趣。研究和教育任务以一种互惠互利的方式整合在一起。如果成功，研究活动的结果将导致解决不确定问题下的大规模决策的方法论创新，并促进网络基础设施在优化中的利用。这些研究成果将提供新的方法，可用于指导下一代工程师有效的优化方法。此外，这些活动将通过向从业者传播先进的方法，并通过与工程物流和配送中心、风暴分析和预测中心以及K20中心等当地行业和研究中心的合作，向从业人员传播先进的方法，并向未被充分代表的少数族裔学生提供外联服务，对行业和社会产生重大影响。

This Faculty Early Career Development (CAREER) award provides funds for research and education activities to advance the theory, computations and applications of stochastic and robust integer programming. Integer decision variables are commonly used in models for decision making problems. Moreover, in real-time decision making problems, instance parameters are usually uncertain. This work will study stochastic and robust integer programming approaches to formulate and solve decision making problems with integer decision variables and uncertain parameters. The research activities include 1) studying polyhedral structures and polynomial time algorithms for fundamental problem formulations, 2) discovering new methods to integrate cutting planes with decomposition algorithms, 3) exploring cyberinfrastructure to implement the algorithms efficiently in high performance computing facilities, and 4) integrating theoretical analysis with application problems in power asset optimization, joint pricing and inventory planning, and weather forecasting and evacuation plans. The education activities include 1) promoting the practice of stochastic and robust integer programming as an efficient approach to solve decision making under uncertainty problems and 2) stimulating student interest in research in science and technology, especially in operations research. The research and education tasks are integrated in a way that both benefit from each other. If successful, the results of the research activities will lead to methodology innovations for solving large-scale decision making under uncertainty problems and advance the utilization of cyberinfrastructure in optimization. These research outcomes will provide new methodologies that can be used to instruct the next generation of engineers on efficient optimization methods. In addition, the activities will have big impact on industry and society by disseminating advanced methodologies to practitioners and providing outreach to underrepresented minority students, through collaborations with local industry and research centers such as Center for Engineering Logistics and Distribution, Center for Analysis and Prediction of Storms, and the K20 Center.