Process mean determination under constant raw material supply

Setting the mean (target value) for a production process is an important decision for a producer when material cost is a significant portion of production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, production setup and raw material procurement policies. In this paper, we consider the situation in which the product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is a linear function of the amount of the raw material used in producing the item, and the supply rate of the raw material is finite and constant. Furthermore, it is assumed that quantity discounts are available in the raw material cost and that the discounts are determined by the supply rate. Two types of discounts are considered in this paper: incremental quantity discounts and all-unit quantity discounts. A two-echelon model is formulated for a single-product production process to incorporate the issues associated with production setup and raw material procurement into the classical process mean problem. Efficient solution algorithms are developed for finding the optimal solutions of the model.