ABSTRACT

We study a repairable production-inventory system with a constant demand rate subject to random disruptions, which supplies an assembly line according to a just-in-time configuration. Preventive maintenance (PM) actions are regularly performed on the production unit at fixed time instants. We assume that the time between breakdowns is constant and the PM and corrective actions have random durations that follow a general probability distribution. We propose the following policy to cope with production interruptions: A buffer stock is built up at the maximum production rate at the beginning of each PM cycle. At the same time, a reserve stock is maintained to hedge against random disruptions and shortages during planned maintenance. The joint convexity of the cost function is established and optimality conditions for the optimal policy parameters are derived. We perform numerical and sensitivity analyses under the exponential and Asymmetric Laplace distributions. The results suggest that: (i) The proposed policy performs better than traditional models that consider these two strategies separately; (ii) As the shortage cost increases, it is optimal to increase the reserve level; (iii) Higher reserve stock levels allow to hedge against the increased duration and rate of preventive maintenance and random disruptions.

摘要

我们研究了一种具有恒定需求率的可修复生产库存系统，该系统受到随机干扰的影响，该系统会根据即时配置提供装配线。定期在生产时间对生产单元执行预防性维护（PM）措施。我们假设故障之间的时间是恒定的，并且PM和纠正措施具有遵循一般概率分布的随机持续时间。我们提出以下政策来应对生产中断：在每个PM周期开始时以最大生产率建立缓冲库存。同时，在计划维护期间，将保留储备库存以对冲随机干扰和短缺。建立成本函数的联合凸度，并推导最优策略参数的最优条件。我们在指数分布和非对称拉普拉斯分布下进行数值和敏感性分析。结果表明：（i）拟议的政策表现优于分别考虑这两种策略的传统模型；（ii）随着短缺成本的增加，最好增加储备金水平；（iii）较高的储备库存水平可以对冲持续增加的预防性维护的持续时间和比率以及随机干扰。（ii）随着短缺成本的增加，最好增加储备金水平；（iii）较高的储备库存水平可以对冲持续增加的预防性维护的持续时间和比率以及随机干扰。（ii）随着短缺成本的增加，最好增加储备金水平；（iii）较高的储备库存水平可以对冲预防性维护的持续时间和比率以及随机中断的增加。