One of the challenges in medical decision making is the complexity, variability and uncertainty that exist in both patients and different treatment methods. In real practice, patients are different in their personal characteristics, drug response and treatment compliance. In this dissertation, we focus on developing mathematical foundation and computational tools that extract and utilize personalized information to improve the decision-making process for physicians (and patients). We first focus on the management of diabetes mellitus and develop a pharmacokinetic and pharmacodynamics (PK/PD) drug effect model to characterize the personalized dose response of patients receiving anti-diabetic drug therapy. Such personalized information is then incorporated in a first-of-its-kind mixed-integer program to quantitatively optimize each patient’s dose regimen. In a retrospective study, the optimized regimen gives better glycemic control with less drug used than the original regimen prescribed. The second part of the thesis focuses on the optimization of external radiotherapy. We developed a multi-objective direct aperture model that optimizes clinical objectives based on their personalized clinical priorities. A heuristic column generation algorithm that does not require dose information is developed and greatly reduces the total solution time. Moreover, a mixed-integer beam selection model is incorporated into this model to produce plans with better dose distribution than those with beam manually selected by human planner.
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