A decomposition method for multi-product kanban systems with setup times and lost sales

Abstract

We consider kanban controlled production systems with three or more different products processed on a single manufacturing facility. Customers for a product arrive according to a Poisson process. If a customer's demand cannot be met from stock, the customer leaves and satisfies his demand elsewhere (lost sales). Between the production of different products setup changes must be performed that take a significant time. Setup times and processing times are product-specific and follow exponential distributions. A production run continues until the target inventory level given by the number of kanbans for the product has been reached (exhaustive processing). Then the manufacturing facility is set up for the next product according to a fixed setup cycle. The exact model is mathematically intractable even for smaller systems. Therefore, we propose a decomposition-based approximation method for estimating steady-state performance measures.