A production-delivery system with volume flexibility in a single-stage supply chain is considered in this research. In this system, raw materials and/or component parts are procured from suppliers and processed into finished products, which are delivered to customers periodically at a fixed quantity with a fixed interval of time. We develop a decision-making model for optimal production rate selection. It takes into account not only raw materials' and finished goods' inventory cost but production cost as well. In this model, production rate is perceived as a decision variable and unit production cost becomes a function of production rate. A pragmatic computational approach is presented to solve the proposed model for special unit production cost functions. Finally, we conduct a numerical study to illustrate the solution.