Joint determination of process mean, production run size and material order quantity for a container-filling process

Selection of the mean (target value) for a container-filling process is an important decision to a producer especially 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. It is evident that these decisions should be made jointly in order to control the production, inventory and raw material costs. In this paper, we incorporate the issues associated with production setup and raw material procurement into the classical process mean problem. 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. A two-echelon model is formulated for a single-product production process, and an efficient algorithm is developed for finding the optimal solution.