Optimal production policy for a single-product single-machine problem with intermediate machine inspection allowed

This paper considers a single-product single-machine production problem where, once the machine is setup for production operation over an interval of time, the operation quality inspection is periodically carried out at equal time intervals, since the machine is subject to operation quality defect occurring in an exponential time distribution. Once such a quality defect starts to occur, the machine keeps producing a fixed rate of imperfect items which may incur various management costs. If the machine operation is checked as being out of quality at the end of an inspection interval, the operation is stopped to do the machine restoration work for getting the next interval operation started at the original condition, and no demand is supplied until the operation is resumed. Such a machine restoration work mostly includes the machine restoration work itself and an after-service type of repair work on out-of-quality items, which requires a constant amount of time mostly for the item repair work. The paper considers various costs including lost-sales, customer goodwill loss, inventory cost, and after-service repair cost, and determines both the optimal production operation interval and the optimal number of intermediate inspections over the interval which minimizes the average expected system cost per unit time. Numerical problems are solved for illustration.