CAREER: Embracing Randomness and Uncertainty in Inventory Problems: Algorithms and Insights

这项学院早期职业发展(Career)计划拨款将为库存控制问题开发算法和建模工具和方法。需求随机时的库存管理问题是运筹学的核心问题之一。这种模式有许多对美国经济至关重要的应用，包括：供应链、医疗保健、能源、云计算、军事行动和先进制造。人们普遍认为，在这样的模型中引入的噪声、不确定性和高维越多，该模型就变得越难求解。该奖项支持算法和建模框架的开发，通过将随机性和不确定性作为算法和建模工具，将相关的困难转化为优势，从而打破了这一根本障碍。该奖项还将促进教育学的发展，将本科工程专业学生在高级设计项目中的经验整合到他们的运筹学和工业工程入门课程中，使学生能够将他们的课程直接与与实际库存和相关模型有关的有趣的现实世界应用程序联系起来。该奖项还将导致新的博士课程的开发，并将所有级别的学生纳入支持的研究。该奖项将支持对两个基本的清单模型家族的研究。具有正提前期的销售损失库存模型适用于许多应用，但由于维度诅咒而无法求解。这导致在许多应用中使用不正确的模型，例如，当丢失的销售模型更合适时，使用具有积压需求的模型。如果成功，得到支持的研究将创建一个算法框架和辅助方法，旨在开发有效实施的启发式方法，随着问题中引入更多的随机性，例如通过更长的准备时间，这种启发式方法被证明是近乎最佳的，并将该方法推广到相关模型。第二个要考虑的建模框架是(分布式)稳健库存控制框架，其中在执行相关优化时考虑了模型的错误指定。支持的研究将开发一个建模框架和解决方案方法，通过考虑关于需求随时间的条件分布和时刻的有限信息的设置，在存在需求预测和相关性的情况下分析此类模型。这项研究还将创建一种理论，解释不同的建模方法如何对需求随时间的联合分布的不确定性进行建模，从而导致不同的库存控制政策，并在相关模型中探索这些问题。

This Faculty Early Career Development (CAREER) Program grant will develop algorithmic and modeling tools and methodologies for inventory control problems. The problem of managing inventory when demand is stochastic is one of the core problems of Operations Research. Such models have many applications critical to the American economy, including: supply chains, healthcare, energy, cloud computing, military operations, and advanced manufacturing. It is common wisdom that the more noise, uncertainty, and high-dimensionality that one introduces into such a model, the more difficult that model becomes to solve. This award supports the development of algorithmic and modeling frameworks which break this fundamental barrier by embracing randomness and uncertainty as an algorithmic and modeling tool, turning the associated hardness into an advantage. The award will also advance the state of pedagogy, by integrating undergraduate engineering students' experiences in senior design projects into their introductory Operations Research and Industrial Engineering courses, enabling students to connect their coursework directly to interesting real-world applications pertaining to actual inventories and related models. The award will also lead to the development of new Ph.D. courses, and the integration of students at all levels into the supported research.The award will support research into two fundamental families of inventory models. Lost sales inventory models with positive lead times are appropriate for many applications, but have resisted solution due to the curse of dimensionality. This has led to the use of incorrect models in many applications, for example the use of models with backlogged demand when lost sales models are more appropriate. If successful, the supported research will create an algorithmic framework and supporting methodologies aimed at developing efficiently implementable heuristics which provably perform nearly optimally as more randomness is introduced into the problem, for example through longer lead times, and generalize the approach to related models. The second modeling framework to be considered is that of (distributionally) robust inventory control, in which one takes model misspecification into consideration when performing the relevant optimizations. The supported research will develop a modeling framework and solution methodology for analyzing such models in the presence of demand forecasting and dependencies, by considering settings in which one has limited information regarding the conditional distribution and moments of demand over time. The research will also create a theory explaining how different approaches to modeling uncertainty in the joint distribution of demand over time lead to qualitatively different inventory control policies, and explore these questions in related models.