Zhu, Junfeng2018-09-212018-09-212018-06https://hdl.handle.net/11299/200165University of Minnesota Ph.D. dissertation. June 2018. Major: Industrial and Systems Engineering. Advisor: Kevin Leder. 1 computer file (PDF); x, 161 pages.A major challenge in understanding tumor growth control is how to model tumor growth and how to design and solve an optimization problem which can provide an efficient treatment. In the dissertation, we aim to develop a mathematical model which describes cell dynamics under different drugs with certain toxicity restrictions. Based on the model, we can make predictions for the tumor growth, and provide a platform for designing treatment protocols which can control tumor growth. The model we developed is a hierarchy model in which we take cells at the other layers, i:e:, progenitor cells, differentiated cells and terminally differentiated cells into consideration. After solving a mixed integer nonlinear programming, we got a schedule which is more efficient compared to the general treatment protocols. As we put the toxicity constraints into the optimization problem, we make full use of it. However, in clinical application, the outcomes under the optimal protocols are sensitive to variations of parameter settings such as drug effects and the attributes of age, weight, and health conditions in human subjects. One approach to overcome this challenge is to formulate the problem of finding optimal drug delivery as a robust optimization problem (ROP).We derive the optimal protocols that minimize the cumulative tumor size. In addition, We perform sensitivity analysis on the nominal optimal solution with respect to the birth rates of mutant cells.enThesis or Dissertation