Optimal Control of Service Rate and Preventive Maintenance Rate for a Failure-prone Manufacturing System
有故障制造系统的服务率和预防维护率的最优控制

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.