  We propose a real-time decision framework for multimodal freight dispatch
through a system of hierarchical hubs, using a probabilistic model for transit
times. Instead of assigning a fixed time to each transit, we advocate using
historical records to identify characteristics of the probability density
function for each transit time. We formulate a nonlinear optimization problem
that defines dispatch decisions that minimize expected cost, using this
probabilistic information. Finally, we propose an effective homotopy algorithm
that (empirically) outperforms standard optimization algorithms on this problem
by taking advantage of its structure, and we demonstrate its effectiveness on
numerical examples.
