Analysis of multi-product kanban systems with state-dependent setups and lost sales

We propose a decomposition-based approximation method that generates fairly accurate estimates for steady-state performance measures of a kanban-controlled production system. The manufacturing facility of this system can process items of several different products. Setup and processing times are assumed to be exponentially distributed. Customers arrive according to mutually independent Poisson processes. A customer whose demand cannot be met from stock leaves the system and satisfies his demand elsewhere (lost sales). The manufacturing facility processes items of a product until a target inventory level given by the number of kanbans has been reached. Then the manufacturing facility is set up for the next product according to a fixed setup sequence if the next product's inventory level is below target. Otherwise, this product is skipped (cyclic-exhaustive processing with state-dependent setups). The manufacturing facility idles when the inventory levels of all products are at their target levels.