The effects of inspection delay and restoration cost on the optimal inspection and production policy

Economic production lot size models with a process inspection delay have been studied over several decades in the literature. When an imperfect process is assumed to have a given probability to run from an in-control state to an out-of-control state each time an item is produced, an inspection schedule is arranged to monitor the process reliability; however, a time delay to obtain the inspection results exists. This study further includes process restoration cost in the inspection/production model to study its effects on the optimal production lot size and the economic inspection lot under the consideration of minimizing the approximated total cost per week. For the case of multiple inspections, when the restoration cost is considered, the resulting the economic inspection lot may depend on the production lot size, especially when the fixed part of the restoration cost is large.