The kanban production authorization system has been widely implemented as a control scheme for just-in-time manufacturing. This system is normally applied in systems with reliable processes, low setup times, static demand and excess capacity. The use of kanbans avoids the need for complex information and hierarchical control systems on the shop floor. Kanban control also has the advantage of reacting quickly to minor demand changes. In this paper we investigate the use of kanban control at workcentres which produce multiple items with dynamic, random demand. The dynamic aspects of demand may cause temporary capacity shortages. The kanban control system automatically reacts quickly to the random aspects of demand. Selection of the number of kanbans will accommodate the dynamic aspect. We assume an environment with low setup times and a desire for rapid adjustment in production rates to match demand. A mathematical model for the problem is defined and shown to reduce to a simpler problem. Using the simpler problem, we investigate necessary and sufficient conditions for feasibility of the problem and specific choices of kanban levels. These conditions are used to define upper and lower bounds on the optimal number of kanbans which, in turn, are employed for developing optimal and near-optimal, heuristic algorithms for selecting kanban levels for each item. An algorithm is also derived for finding feasible production schedules given a feasible set of kanbans. The algorithm provides a policy which is easily implemented on the shop floor for guiding production decisions when capacity is limited. The methodology is illustrated with an example and results of experimental testing of the algorithm and heuristic are presented.