Performance analysis of an inventory–production system with shipment consolidation in the production facility

We consider an inventory–production system consisting of a warehouse and a production facility. The warehouse is used to store products to satisfy customer demands, and its inventory is controlled by an ( r , Q ) policy. Products ordered by the warehouse are processed in the production facility on a one-by-one basis, and finished products are consolidated into batches to be shipped from the production facility to the warehouse. Using the matrix-analytic methods, explicit solutions are obtained and computational methods are developed for analyzing system performance measures.