Optimal Inspection, Lot Sizing and Setup Reduction

Porteus, and Rosenblatt and Lee have recently developed models in which process quality and lot sizing interact. Lot sizes should be reduced to compensate for poor quality. Investment in setup time reduction leads to even smaller lot sizes and increased quality output. Lee and Rosenblatt extended the models by allowing for inspection during production. If inspection results are known immediately, then the problem reduces essentially to two separate lot sizing problems: the classical EOQ lot sizing problem and an inspection lot sizing problem. This paper incorporates an inspection delay time, measured in units production and inspection lot sizes. Numerous possible process improvements are proposed and optimal solutions determined. A numerical example illustrates the results. The value of automated defect control (with 100% inspection and immediate production stoppage upon decision of a defect) is examined.