This dissertation develops a mixed integer linear program to establish the upper and lower bounds of the Alphorn of Uncertainty. For a project manager, planning for uncertainty is a staple of their jobs and education. But the uncertainty associated with a catastrophic event presents difficulties not easily controlled with traditional methods of risk management. This dissertation brings and modifies the concept of a project schedule as a bounded “Alphorn of Uncertainty” to the problem of how to reduce the risk of a catastrophic event wreaking havoc on a project and, by extension, the company participating in that project. The dissertation presents new mathematical models underpinning the methods proposed to reduce risk as well as simulations to demonstrate the accuracy of those models. The dissertation further assesses the complexity of the models and thus their practical application. Finally, the dissertation presents strategies to reduce the risk to a project of a catastrophic event using the upper bound of the Alphorn as the measure of risk.