Performance Models with Data Evolution

可拓学和组合优化模型在工程设计以及制造和分销系统的操作中有许多应用。 例如，与设置时间减少，批量大小的确定，调度，路由等处理的问题，往往需要整数和组合优化模型。 解决这些问题的传统方法假设数据是确定的。 在许多实际问题中，数据不仅是不确定的，而且随着时间的推移而变化。 本研究致力于整数规划模型中允许数据演化的模型和算法。 该项目的数据演化方法借鉴了随机规划理论，主要集中在线性和凸优化模型上。 由于随机线性和凸优化问题已有有效的算法，本研究致力于发展随机整数规划的凸逼近。 要考虑的决策问题涉及决策过程和数据演化过程，它们随着时间的推移而交织在一起。在这些模型中，资源承诺和操作使用混合整数规划建模，而数据演化通过场景树捕获。 通过将混合整数规划与随机优化相结合，该项目将为不确定性下的决策提供下一代运筹学模型。

Integer and combinatorial optimization models have many applications in engineering design as well as operations of manufacturing and distribution systems. For example, issues dealing with setup timereduction, batch size determination, scheduling, routing, etc. often call for integer and combinatorial optimization models. Traditional approaches to these problems assume that data are known with certainty. In many practical problems, data are not only uncertain, but also evolve over time. This research is devotedto models and algorithms that allow data evolution within integer programming models. This project's approach to data evolution draws upon the theory of stochastic programming, which has mainly focused on linear and convex optimization models. Because there are effective algorithms for stochastic linear and convex optimization problems, this research is dedicated to developing convex approximations for stochastic integer programs. The decision making problems to be considered involve a decision process and a data evolution process that are interwoven over time. In these models, resource commitments and operations are modeled using a mixed integer program, while data evolution is captured via a scenario tree. By combining mixed integer programming with stochastic optimization, this project will provide the next generation of Operations Research models for decision making under uncertainty.