Performance evaluation of two-stage multi-product kanban systems

We propose an approximate evaluation procedure for a kanban-controlled production system with two stages and multiple products. In the first stage, single-product manufacturing facilities produce items that are the input material for a single multi-product manufacturing facility in the second stage. Each manufacturing facility is controlled by a distinct kanban loop with a fixed number of kanbans. Processing and setup times are exponentially distributed, demand arrivals at the output store of the second stage are Poisson and independent for each product. If a customer's demand cannot be met from stock, the customer either waits or leaves the system, depending on the admissible number of backorders and the current number of waiting customers (partial backordering). We describe a new decomposition-based approximation method for the evaluation of such systems in steady state. We focus on the performance measures average fill rate, average fraction of served demand, and average inventory level. We report the results of several numerical tests. The results indicate that the approximation is sufficiently accurate for a large variety of systems. We also illustrate the effects of increasing the maximum number of backorders on the performance of the system.