| We present a robust optimization approach with multiple ranges and chance constraints.;The first part of the dissertation focuses on the case when the uncertainty in each objective coefficient is described using multiple ranges. This setting arises when the uncertain coefficients, such as cash flows, depend on an underlying random variable, such as the effectiveness of a new drug. Traditional one-range robust optimization would require wide ranges and lead to conservative results. In our approach, the decision-maker limits the numbers of coefficients that fall within each range and that deviate from the nominal value of their range.;We show how to develop tractable reformulations to this mixed-integer problem and apply our approach to a R&D project selection problem. Furthermore, we develop a robust ranking heuristic, where the manager ranks projects according to densities (ratio of cash flows to development costs) or Net Present Values. While both heuristics perform well in experiments, the NPV-based heuristic performs better; in particular, it finds the optimal solution more often.;We show the how to use multi-range robust optimization approach to have a robust project selection problem. While this approach can imitate the stochastic optimization's scenario settings, our problem is significantly faster than stochastic optimization, since we do not have the burden of having many scenarios. We also develop a robust approach to price optimization in presence of other retailers.;The last part of the dissertation connects robust optimization with chance constraints and shows that the Bernstein approximation of robust binary optimization problems leads to robust counterparts of the same structure as the deterministic models, but with modified objective coefficients that depend on a single new parameter introduced in the approximation. |
