More companies choose outsourcing to gain cost advantages, focus on their core competencies and maintain competitive edge. Although outsourcing provides many benefits, it also makes the buyer more dependent to the outside firms and increases his exposure to supply chain risks. This dissertation provides quantitative techniques to measure those risks and mathematical models to incorporate risks in supply chain decision making. Outsourcing risks are grouped under two main categories: operational risks which represent risks due to day to day global supply chain operations and disruption risks which are related to rare, but catastrophic events that may disrupt supply chains and cause heavier damage than the operational risks. In this dissertation, we first present a general risk quantification scheme and a classification based on four major risk components: severity of impact, frequency of occurrence, detection time and recovery time, and implement this scheme to quantify disruption risks. Severity of impact is modeled using the Generalized Extreme Value Distribution which is appropriate for modeling minima and maxima of rare events. Frequency of occurrence is modeled as a Poisson process. A Markov chain is used to model information propagation in supply chains and detection time is modeled using the mean first passage time concept. Risk recovery time is assumed to be exponentially distributed and a conceptual model to compute the parameter of the exponential distribution is also developed. Another important issue in risk management is mitigation plans. Once a supplier faces a disruption, the buyer should have an alternative strategy to follow. In this dissertation, we propose two multiobjective mathematical models to optimally generate supplier assignment and mitigation plans under two different purchasing strategies. The first strategy, called single sourcing, assumes that the buyer assigns an order for a product to one and only one supplier; that is, order splitting among suppliers is not allowed. The second strategy, called multiple sourcing, is a generalization of the single sourcing model where the buyer can split an order among a predetermined number of suppliers. Both models consider four objectives: minimizing total cost, lead time and risk value, and maximizing quality of purchased items. The multiobjective models are solved using four variants of goal programming and their solutions are discussed. Operational risks are more common in supply chains and can be modeled using traditional probability distributions. In this dissertation, we extend the multiobjective mathematical models developed earlier to stochastic programming models. Uncertainty in customer demand and production capacity are assumed to cause operational risk. Initially, demand and capacity parameters are modeled as normal random variables and chance constraints are formed to include those stochastic data in the mathematical models. Deterministic equivalents of those chance constraints are derived to numerically solve the models. When no correlation among random variables is assumed, the deterministic equivalent models are linear mixed integer programs which can be solved efficiently using commercial optimization software. If correlation is included, deterministic equivalent models become nonlinear mixed integer programs which are computationally more challenging. Alternative linearization procedures are proposed to transform the deterministic equivalents of the nonlinear models to linear mixed integer programs. This results in an increase in the problem size. Deterministic equivalent models are also solved using goal programming techniques. It is observed that the optimal solutions to the deterministic models are infeasible to the stochastic models. This indicates that previous supply chain decisions are no longer valid when uncertainty is considered in decision making. We also present a robust model where the normality assumption on demand and capacity random variables is removed. This robust model is valuable when the decision makers have information only on the mean and the variance of demand and capacity. The robust model is more conservative and provides poorer results compared to the stochastic models under normality.