Determining the production lot size with a heuristic inspection policy for controlling the quality of input materials and products

This study simultaneously determines the optimal production lot size and an inspection policy for input materials and products, where an unreliable process produces products with a discrete general shift distribution. This work proposes a heuristic inspection policy for materials and products, by first obtaining the inspection range for the input material without considering product inspection, and by further determining the product inspection range based on the obtained range of the input material inspection. The optimal inspection policy shows that common policies of no or full inspection are never optimal. This study includes the optimal production lot size based on the obtained inspection policy. Numerical examples demonstrate the impacts of input quality level, process reliability and unit nonconforming cost on the optimal solution, which adopts a discrete Weibull shift distribution to model the process failure time. Finally, this study addresses the conclusions.