This paper considers an integrated one-vendor multi-buyer production-inventory model where the vendor manufactures multiple products in lot at their associated finite production rates. In the model, it is allowed for each product to be shipped in lot to the buyers even before the whole product production is not completed yet. Each product lot is dispatched to the associated buyer in a number of shipments. The buyers consume their products at fixed rates. The objective is to the production and shipment schedules in the integrated system, which minimizes the total cost per unit time. The total cost consists of production setup cost, inventory holding cost and shipment cost. For the model, an iterative optimal solution procedure with shipment consolidation policy incorporated. It is then tested through numerical experiments to show how efficient and effective the shipment consolidation policy is.