We develop and analyze an algorithm to maximize the throughput of a serial kanban-based manufacturing system with arbitrary arrival and service process distributions by adjusting the number of kanban allocated to each production stage while maintaining the total work-in-process inventory at any desired level. The optimality properties of the algorithm are proved under a necessary and sufficient "smoothness condition". The algorithm is driven by throughput sensitivities which, in general, can only be estimated along an observed sample path of the system. It is shown that the algorithm converges to the optimal allocation in probability and, under additional mild conditions, almost surely as well. Finally, it is shown that Finite Perturbation Analysis (FPA) techniques can be used to obtain the sensitivity estimates in order to reduce the amount of simulation required in either on-line or off-line simulation-based optimization.