Modeling methods and a branch and cut algorithm for pharmaceutical clinical trial planning using stochastic programming

We discuss methods for the solution of a multi-stage stochastic programming formulation for the resource-constrained scheduling of clinical trials in the pharmaceutical research and development pipeline. First, we present a number of theoretical properties to reduce the size and improve the tightness of the formulation, focusing primarily on non-anticipativity constraints. Second, we develop a novel branch and cut algorithm where necessary non-anticipativity constraints that are unlikely to be active are removed from the initial formulation and only added if they are violated within the search tree. We improve the performance of our algorithm by combining different node selection strategies and exploring different approaches to constraint violation checking.