Optimal production and corrective maintenance in a failure-prone manufacturing system under variable demand

Failure-prone manufacturing systems facing dynamical market conditions that result in demand variations are considered. The combined production and corrective maintenance optimization problem for a one-machine-one-product system is addressed. Repairing the machine after the failure, the manager has to solve the dilemma: to choose an inexpensive (but lower) repair rate, or to use the higher, (but more expensive) repair rate. The former decision seems to be appropriate when there is no risk of inventory shortage, while the latter one has to be used in critical (stock shortage) situations. Precise solution to this problem presented in the paper is theoretically instructive and valuable for practitioners. Optimality conditions in the form of time-dependent Hamilton-Jacoby-Bellman equations are obtained and a novel numerical approach is proposed for solving these equations for the case of periodically time-varying demand. The optimal policy is shown to be the hedging-curve-policy, that extends the hedging-point-policy to the case of varying level of safety stock. The simulation results show that the optimal policies have an important property of anticipating the future demand evolutions and making the optimal decisions relevant to such dynamic conditions. In particular, it has been shown that in the large domain of the system parameters it is advantageous to use the lower (and inexpensive) repair rate when the stock is approaching the hedging level and especially when the demand level is near its bottom edge.