Optimal investment in setup reduction in manufacturing systems with work-in-process inventories

A number of models have been proposed to predict optimal setup times, or optimal investment in setup reduction, in manufacturing cells. These have been based on the economic order quantity (EOQ) or economic production quantity (EPQ) model formulation, and have a common limitation in that they neglect work-in-process (WIP) inventories, which can be substantial in manufacturing systems. In this paper a new model is developed that predicts optimal production batch sizes and investments in setup reduction. This model is based on queueing theory, which permits it to estimate WIP levels as a function of the decision variables, batch size and setup time. Optimal values for batch size and setup time are found analytically, even though the total cost model was shown to be strictly non-convex.