Analyzing closed Kanban-controlled assembly systems by iterative aggregation-disaggregation

In recent years, many companies have begun using WIP-limiting strategies such as CONWIP, Kanban or drum-buffer-rope to control parts flows in complex production systems. This paper analyzes assembly systems with a tree structure, random processing times and a constant WIP control system. We present heuristic version of the exact aggregation-disaggregation theory for finite Markov chains to evaluate the performance of these closed Kanban-controlled assembly systems. Because the approximation is theory based, it provides a framework for further model development, with some possible extensions described in the paper. The approximation has the novel feature of doing simultaneous multiple partitions of the state space, in such a way that the associated aggregate transition rates are mutually consistent. The methodology is a novel approach towards extending aggregation ideas to fork-and-join queueing networks, and it provides several useful operational and analytical insights. Numerical comparisons with simulation show that the proposed approximation computes accurate estimates of the plant throughput. It provides a fast way to assess the performance and economic impact of changes in the total WIP level (or the number of Kanbans), or in the part routes, on the throughput rate of the assembly system.