In this book, we study optimization models for health care under uncertainty and resource constraints. In particular, we study two problems. The first problem is the multi-shift Vehicle Routing Problem (MSVRP) with overtime to meet around-the-clock demand. We use insertion to create the initial routes and then use tabu search to improve the routes. We show that our algorithm can find high-quality solutions for very large problems. The second problem is a multi-city resource allocation model to distribute the medical supplies in order to minimize the total number of fatalities in an infectious disease outbreak. We consider the problem with uncertainty in the initial number of cases and transmission rate, and build a two-stage stochastic programming model. To solve instances of realistic size we use a heuristic based on Benders decomposition. Finally, we use sample average approximation (SAA) to get confidence intervals on the optimal solution. We illustrate the use of the model and the solution technique in planning an emergency response to a hypothetic national smallpox outbreak. Computations show that the algorithm is efficient and can obtain near-optimal solution.