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

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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.