Process mean determination with quantity discounts in raw material cost

Setting the mean (target value) for a container-filling process is an important decision for a producer when the material cost is a significant portion of the production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, the production setup and raw material procurement policies. In this paper, we consider the situation in which quantity discounts exist in the raw material acquisition cost, and incorporate the quantity-discount issue into an existing model that was developed for simultaneously determining the process mean, production setup, and raw material procurement policies for a container-filling process. 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 proportional to the amount of the raw material used in producing the item. A two-echelon model is formulated for a single-product production process, and an algorithm is developed for finding the optimal solution. A sensitivity analysis is performed to study the effects of the model parameters on the optimal solution.