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

This paper develops an optimal batch size and raw material ordering policy for a two-stage production delivery system that incorporates a fixed quantity supply of finished goods to a buyer at a fixed interval of time. First, a general cost model is formulated considering both supplier (of raw material) and buyer (of finished products) sides. The model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost. Using the proposed model and its optimal solution, one can determine optimal production lot size for each stage, optimal number of transportation for semi-finished goods, and optimal quantity of semi-finished goods transported each time to meet the lumpy demand of consumers. Finally, we examine the sensitivity of raw materials ordering and production lot size to changes in ordering cost, transportation cost and manufacturing setup cost.