Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction

This paper seeks to demonstrate that lower setup costs can benefit production systems by improving quality control. It does so by introducing a simple model that captures a significant relationship between quality and lot size: while producing a lot, the process can go "out of control" with a given probability each time it produces another item. Once out of control, the process produces defective units throughout its production of the current lot. The system incurs an extra cost for rework and related operations for each defective piece that it produces. Thus, there is an incentive to produce smaller lots, and have a smaller fraction of defective units. The paper also introduces three options for investing in quality improvements: (i) reducing the probability that the process moves out of control (which yields fewer defects, larger lot sizes, fewer setups, and larger holding costs); (ii) reducing setup costs (which yields smaller lot sizes, lower holding costs, and fewer defects); and (iii) simultaneously using the two previous options. By assuming a specific form of the investment cost function for each option, we explicitly obtain the optimal investment strategy. We also briefly discuss the sensitivity of these solutions to changes in underlying parameter values. A numerical example illustrates the results.