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.

中文翻译：

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可变需求下易于失效的制造系统中的最佳生产和纠正性维护

考虑了面临动态市场条件，导致需求变化的易于失效的制造系统。解决了单机一对产品系统的生产和纠正性维护优化组合问题。发生故障后对机器进行维修，经理必须解决难题：选择便宜（但价格较低）的维修率，或使用更高（但价格更高）的维修率。在没有库存短缺风险的情况下，前者的决定似乎是适当的，而在危急（库存短缺）的情况下必须使用后者。本文提出的精确解决此问题的方法在理论上具有指导意义，对从业者也很有价值。获得了时间依赖的汉密尔顿-雅各比-贝尔曼方程形式的最优性条件，并针对周期性时变需求的情况提出了一种新颖的数值方法来求解这些方程。最佳策略显示为对冲曲线策略，该策略将对冲点策略扩展到了不同安全库存水平的情况。仿真结果表明，最优策略具有预测未来需求变化并做出与此类动态条件相关的最优决策的重要特性。特别地，已经表明，在系统参数的大范围内，当库存接近对冲水平时，尤其是当需求水平接近其底边时，使用较低（且便宜）的维修率是有利的。