Sampling has become an important strategy for inference in belief networks. It can also be applied to the problem of selecting actions in influence diagrams. In this paper, we present methods with probabilistic guarantees of selecting a near-optimal action. We establish bounds on the number of samples required for the traditional method of estimating the utilities of the actions, then go on to extend the traditional method based on ideas from sequential analysis, generating a method requiring fewer samples. Finally, we exploit the intuition that equally good value estimates for each action are not required, to develop a heuristic method that achieves major reductions in required sample size. The heuristic method is validated empirically. Scheduling, routing, and layout tasks are examples of hard operations-research problems that have broad application in industry. Typical algorithms for these problems combine some form of gradient descent to find local minima with some strategy for escaping nonoptimal local minima. Our idea is to divide these two subtasks cleanly between human and computer: in our paradigm of human-guided simple search the computer is responsible only for finding local minima using a simple hill-climbing search; using visualization and interaction techniques, the human user identifies promising regions of the search space for the computer to explore, and intervenes to help it escape nonoptimal local minima. We have applied our approach to the problem of capacitated vehicle routing with time windows, a commercially important problem with a rich research history. Despite its simplicity, our prototype system is competitive with the majority of previously reported systems on benchmark academic problems, and has the added advantage of keeping a human tightly in the loop to handle the complexities of real-world applications.