This dissertation is on advanced mathematical programming with applications in portfolio optimization and supply chain management. Specifically, this research started with modeling and solving large and complex optimization problems with cone constraints and discrete variables, and then expanded to include problems with multiple decision perspectives and nonlinear behavior. The original work and its extensions are motivated by real world business problems.;The first contribution of this dissertation, is to algorithmic work for mixed-integer second-order cone programming problems (MISOCPs), which is of new interest to the research community. This dissertation is among the first ones in the field and seeks to develop a robust and effective approach to solving these problems. There is a variety of important application areas of this class of problems ranging from network reliability to data mining, and from finance to operations management.;This dissertation also contributes to three applications that require the solution of complex optimization problems. The first two applications arise in portfolio optimization, and the third application is from supply chain management. In our first study, we consider both single- and multi-period portfolio optimization problems based on the Markowitz (1952) mean/variance framework. We have also included transaction costs, conditional value-at-risk (CVaR) constraints, and diversification constraints to approach more realistic scenarios that an investor should take into account when he is constructing his portfolio. Our second work proposes the empirical validation of posing the portfolio selection problem as a Bayesian decision problem dependent on mean, variance and skewness of future returns by comparing it with traditional mean/variance efficient portfolios. The last work seeks supply chain coordination under multi-product batch production and truck shipment scheduling under different shipping policies. These works present a thorough study of the following research foci: modeling and solution of large and complex optimization problems, and their applications in supply chain management and portfolio optimization.
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