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

这项教师早期职业发展（Career）计划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。这些模型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业。众所周知，在这样一个模型中引入的噪声、不确定性和高维数越多，该模型就越难以求解。该奖项支持算法和建模框架的发展，这些框架通过将随机性和不确定性作为算法和建模工具来打破这一基本障碍，将相关的困难转化为优势。该奖项还将通过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实际库存和相关模型相关的有趣的现实世界应用联系起来，从而提高教学水平。该奖项还将导致新的博士课程的发展，并将各级学生整合到所支持的研究中。该奖项将支持对两个基本库存模型家族的研究。具有正交货期的销售损失库存模型适用于许多应用程序，但由于维度的诅咒而无法解决。这导致在许多应用程序中使用了不正确的模型，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，支持的研究将创建一个算法框架和支持方法，旨在开发有效的可实现的启发式，当更多的随机性被引入到问题中，例如通过更长的前置时间，并将方法推广到相关模型中。第二个要考虑的建模框架是（分布式）鲁棒库存控制，在该框架中，在执行相关优化时将模型错误规范考虑在内。支持的研究将开发一个建模框架和解决方案方法，通过考虑有关条件分布和需求时刻的有限信息的设置，在需求预测和依赖关系存在的情况下分析此类模型。研究还将创建一个理论，解释不同的建模方法对不确定性的需求随时间的联合分布如何导致定性不同的库存控制政策，并在相关模型中探讨这些问题。

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.