In this paper, we develop an efficient approach to solve a continuous review inventory system with a budget constraint when the semi-finished product and optional components are required to be assembled. We are, in particular, interested in a budget constraint that includes a service level. The service cost, such as labor and facility costs, tends to increase as the service level increase, and it makes the problem difficult to solve. Assuming that the reorder point for a semi-finished product is given, we show that the order quantity for the semi-finished product and the order quantity and reorder point for optional components can be determined by minimizing the total cost that includes setup cost, inventory holding cost, and shortage cost. The performance of the proposed approach is tested by numerical examples. By using sensitivity analysis, we conclude that, as the reorder point for semi-finished product increases, the order quantity for semi-finished product increases, whereas the order quantity and reorder point of optional components decreases.