The implementation of ‘kanban’ inventory control systems, originally developed in Japan by Toyota, in flow-line manufacture has been widely described. It is generally asserted that kanbans are an efficient method of controlling flow-line assembly systems with consistent demands. This paper describes work carried out in association with Jaguar Cars Limited to develop a steady-state Markovian model for calculating the number of kanbans required to control single-stage processes feeding assembly lines. A Markovian model of an alternative just-in-time system, in which the off-line process is triggered by the passage of vehicle bodies past a point prior to the assembly area, is also described. The use of these models has shown that the use of a trigger system leads to lower inventory levels and greater pressure for improvement than a kanban system