In this paper, an integrated vendor-buyer production inventory system for a single-product is studied. We assume that production rate for the vendor is less than demand rate and so the vendor may respond to the total demand simultaneously through production in the firm and ordering from the outside. We relax the assumption of stochastic demand and assume that it is deterministic. Also shortages are not allowed and the lead time is constant. The purpose of this study is to determine the three following decision variables: the quantity of each shipment from the vendor to the buyer, the quantity the vendor should order and the amount it should produce to minimize the joint total inventory costs. To solve the problem, an exact method is applied and numerical examples are proposed to illustrate the application of the model.

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