This paper studies the effects of work-in-process (WIP) inventory on the simultaneous determination of the optimal production batch sizes of the single product and its component parts, where the component parts, processed in manufacturing cells, are assembled into the product. We develop a procedure to simultaneously find the optimal lot size for the product and its component parts and the total relevant cost. The effect of setup reduction is considered. A numerical example demonstrates that, in the lot size computation, the WIP inventory costs and the relationship between the product and its component parts should all be taken into account.