Optimal production policy for a two-stage production system under lumpy demand

A two-stage production-delivery system is considered in this research, where raw materials and/or components are procured from outside suppliers and processed into finished products which are delivered to customers periodically at a fixed quantity with a fixed interval of time. A decision-making model is developed for an optimal production policy under lumpy demand. a comprehensive cost function is formulated considering both supplier(of raw materials) and buyer (of finished products) sides. An optimal solution to the problem is derived on basis of the cost model. Also, we examine the sensitivity of raw materials ordering and production lot size to changes in ordering cost, transportation cost and manufacturing cost. A pragmatic computation approach for realistic operation situations is proposed to solve integer approximation solution. Finally, some numerical examples are given to illustrate the optimal solution and computational approach.