Employing Optimization and Hierarchical Decision Making for Modeling and Solving Practical ProblemsBilgic, Utku Tarik (2025) Employing Optimization and Hierarchical Decision Making for Modeling and Solving Practical Problems. Doctoral Dissertation, University of Pittsburgh. (Unpublished)
AbstractMulti-level optimization serves as a highly effective framework for modeling hierarchical decision-making processes in real-world applications. By integrating the strengths of this approach with data-driven insights, we can achieve impactful decisions. This dissertation delves into the modeling capabilities and development of solution methodologies for multi-level optimization and leveraging data to enhance decision-making across various domains. In the first study, we propose a general framework that integrates both optimistic and pessimistic optimization approaches in solving the regression problem to address outlier cleaning and robustification in a unified fashion. This multi-level optimization scheme ensures constructing robust models trained on data sets with outliers and adversarial points. In the second study, we develop a solution methodology for bilevel mixed integer linear programs, using Lagrangian relaxations and column and constraint generation algorithm framework. By using branch and bound method, the algorithm guarantees optimal solution for this challenging problem. In our next study, we develop a new scheme to handle missing values in a data set, moving beyond the common "impute first, predict after" approach. Our strategy directly incorporates incomplete data points into building a predictive model, utilizing the available data from the data with missing features. In a robust optimization framework, we define local uncertainty sets leveraging projection. In our final project, we predict length of stay of an inpatient patient, exploring the effect of nursing care and the patient characteristics, via interpretable machine learning models. We work on a novel data set with shift-level granularity to develop models that can help clinicians and hospital administrators in capacity planning. Share
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