Optimal production policy for a manufacturing system with volume flexibility in a supply chain cinder lumpy demand

A batch production system with volume flexibility in a supply chain where a manufacturer procures raw materials and/or component parts from multiple suppliers in a lot and processes them into a single product, is considered in this research. First of all, a decision-making model is developed for an optimal production rate selection in the volume-flexibility production system, where a single type of finished products is delivered periodically in fixed quantities within a fixed interval of time. In this model, the production rate is perceived as a decision variable and unit production cost becomes a function of production rate. This model takes into account not only inventory costs of raw materials and finished goods, but production costs as well. Then, a pragmatic computation approach is presented to solve the proposed model for special unit-production-cost functions. It is used to determine an optimal production rate, and thus to decide an optimal ordering policy for procurement of raw materials from suppliers and an optimal manufacturing batch size. Some observations are made for optimal production rate analysis. Finally, a numerical study is conducted to illustrate the solution and a set of data with ten problems is tested and compared.