Convective weather is a major contributor to air traffic delays. There is much uncertainty associated with weather predictions so stochastic models are necessary to effectively assign ground delay and route adjustments to flights. We describe a two-stage stochastic integer program for this problem. We then compare the results of this formulation to algorithms already in the literature.

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

This thesis develops integer linear programming models for and studies the complexity of problems in the areas of maintenance optimization and location–routing. We study how well the polyhedra defined by the linear programming relaxation of the models approximate the convex hull of the integer feasible solutions. Four of the papers consider a series of maintenance decision problems whereas the ...