Determination of optimal lot sizing parameters and a controllable process mean for a production system

Several mathematical models have been developed separately for determining production and recycled lot quantities to minimize total production cost and the determination of optimal process mean setting to minimize total quality cost. For a single stage discrete part production system, this paper presents a mathematical model that combines these two inter-related aspects. The production process has a controllable parameter, the process mean, which determines the output lot quality. One-sided tolerance is used to decide the quality of finished goods. Bad units are reworked before they can be reprocessed with the fresh input. For such a situation, the model determines production lot size, recycling lot quantity, and a process mean while minimizing total system cost. The model has been validated using sample data from a pharmaceutical company. Results indicate that the production lot size and the recycled quantity have an inverse relationship with process mean and, a direct relationship with process variance.