The presence of uncertainty complicates planning decisions in all industries and sectors. In an operations context, failure to acknowledge and incorporate the unknowns in the decision-making process may lead to undesirable outcomes including reduced profitability and customer dissatisfaction. This dissertation considers three problems that incorporate risk and uncertainty in production scheduling, surgical scheduling, and supply chain risk management. The first problem involves scheduling products in a parallel, non-identical machine environment subject to sequence dependent setup costs, sequence dependent setup times, where production waste and processing time of a product depend on feasible machine assignments. A new metric for schedule quality is introduced that considers the tradeoff between the risk of imperfect production and overall production time requirements. We develop a mathematical model and two solution approaches that determine schedules that are superior to schedules found using more traditional scheduling measures with respect to waste and overtime costs. The second problem presents a novel, scenario-based model for incorporating the inherent uncertainty of the operating theater (OT) environment into elective operation scheduling decisions. Specifically, the model allows the time requirements of elective operations to be uncertain and explicitly accounts for the service of urgent patients by requiring opportunities (i.e., break-in-moments) to perform urgent operations before a specified duration elapses. We develop a two step-solution procedure that demonstrates that the scenario-based approach is effective at capturing the uncertainty in the OT environment. The third problem examines mitigation strategies with respect to supply and demand uncertainties in a supply chain. In addition to typical mitigation strategies, such as inventory holding and sourcing from multiple suppliers, we investigate alternate strategies, namely concurrent sourcing and downward substitution. We develop an analytical model for a single period, two-product setting. Analysis of first order optimality conditions reveals several insights into environment characteristics that influence the optimal actions of the manufacturer. Most notably, in contrast to works considering infinite capacity, we find that cost is not the sole driver for strategy selection. Each problem considered is a significant extension of previous works in the respective area that is motivated by industry experience, empirical research, or interaction with practitioners. Mathematical models are presented for each problem and used to develop efficient solution approaches, and provide managerial insights. The modeling techniques and solution approaches developed are applicable to problem domains beyond those considered.