An integrated inventory–targeting problem with time-dependent process mean

In this paper, the integrated inventory-targeting problem for a production process with time-dependent process mean is addressed. A lower specification limit is used to decide about the conformance of the finished product. The unit production cost is assumed to be a linear function of the amount of the single raw material used in producing the item. The formulated optimization model seeks to minimize the expected total cost which is composed of set-up cost, production cost, inventory holding cost, and raw material acquisition cost. The objective of this model is to simultaneously optimize the optimum process mean setting, raw material order quantity, and finished good production lot size. Due to the mathematical complexity of the objective function, the problem is approached heuristically by using an efficient search method.