Stability of pull production control methods for systems with significant setups

In manufacturing, a pull production control method is a method of authorizing production based on replenishing current and past consumption, as opposed to forecasts or orders for future consumption. We consider special classes of pull systems for operations that involve significant setup times. In particular, we present a model for variations of the signal Kanban method and the pattern production method, each of which is used in industry when conventional Kanban methods are inappropriate. The paper examines such systems under demands with unpredictable load content but an upper bound on the total load. It is shown that, under appropriate conditions, such systems are stable in the sense that cumulative production at any time trails cumulative demand by no more than a constant. We determine buffer parameters under each protocol (including reorder points in the signal Kanban case) such that the backorder queue will clear to zero and remain empty thereafter. The results are then extended to consider multiple machines fulfilling production authorizations in parallel.