Optimal age replacement scheduling for a random work system with random lead time
针对随机工作时间和随机交货期的系统，提出一种广义役龄更换策略，通过最小化有限时间内的平均成本率来确定最优更换时间，适用于需要同时考虑维护和备件库存的工程管理场景。
System maintenance and spare parts are two closely related logistics activities since maintenance generates the demand for spare parts. Most studies on integrated models of preventive replacement and inventory of spare parts have focused on age replacement scheduling, while random replacement policy, which is sensible and necessary in practice, is rarely discussed and applied. The purpose of this paper is to present a generalised age replacement policy for a system which works at random time and considers random lead time for replacement delivery. To model an imperfect maintenance action, we consider that the system undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the system is replaced preventively at age T or at the completion of a working time, whichever occurs first. The main objective is to determine an optimal schedule of age replacement that minimises the mean cost rate function of the system in a finite time horizon. The existence and uniqueness of optimal replacement policy are derived analytically and computed numerically. It can be seen that the proposed model is a generalisation of the previous works in maintenance theory.