有故障制造系统的服务率和预防维护率的最优控制

考虑一类容许预防维护的制造系统的最优控制 .系统同时存在随机故障和修复、随机加工时间、随机预防维护、随机需求等多种不确定因素 .我们运用马尔可夫最优决策过程归纳方法 ,导出机器服务率和预防维护率的最优控制策略 .通过研究最优值函数的凸性、单调性和渐近性 ,证明了最优策略具有简单的阈值结构且被几个阈值参数完全刻画 .即产品库存水平小于相应的阈值时 ,最优决策是选择最大服务率或维护率 ;否则 ,停止生产或维护 .进而讨论了这些阈值之间的关系 .数值例子说明了本文的结论 .

Optimal Control of Service Rate and Preventive Maintenance Rate for a Failure-prone Manufacturing System

This paper investigates the optimal control of a manufacturing system in which the machine is allowed to be preventively maintained. The system is disturbed by many uncertainties such as machine failure and repair, random processing time, preventive maintenance, random demand and so on. The optimal control policy of machine service rate and preventive maintenance rate is derived from Markovian optimal decision process formulation. By investigating the convexity, monotonicity and asymptotic behaviour of the optimal value function, it is shown that the optimal policy is of simple hedging point structure and featured by several hedging points. That is, the optimal control should select the maximum service rate or maintenance rate if the inventory level is less than its corresponding hedging point; otherwise, select zero. The relationship of the hedging points is further discussed. Numerical examples are given to illustrate our results.