Analysis of a Kanban Discipline for Cell Coordination in Production Lines, II: Stochastic Demands

Abstract

We describe and analyze a discipline called kanban for the control and coordination of cells in large-scale manufacturing facilities. There are many cells in tandem and also a process of arriving consumers; each consumer queues as long as necessary before departing with a product finished by the last cell. The coordination scheme relies on the circulation of a fixed number of cards (or kanbans) in each cell. This paper differs from our earlier paper in that here the process of consumers modulates the production process. Our results are in three parts. First, the kanban is compared to the classical production discipline and its (sample path) dominance in terms of the consumers' waiting time is proven. Second, we give an analytic scheme for approximating the performance of the stochastic kanban system by examining a single cell in isolation and then combining these through fixed-point equations. Ergodicity is equivalent in our approximation to the existence and uniqueness of a solution to the fixed-point equations and a complete, finite procedure for its resolution is obtained. Third, we report on experiments involving simulations and our method of analysis.