This paper presents a model that analyzes the impact of uncertainties in demand and processing times on the production lead time of a Kanban system. We consider the waste associated with under-production as well as over-production when we measure the production lead time. We set up an optimization model to minimize the production lead time. A simple heuristic procedure is developed to determine solutions in terms of the size of containers and the number of Kanban cards. In addition, we numerically examine the behavior of the optimal Kanban system.