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)(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.