This paper studies the stochastic single-machine scheduling problem with workload-dependent maintenance activities, in which the processing times of all jobs are independently subject to a common discrete distribution, and the aim is to find the optimal policy so as to minimize the expected total discounted holding cost. Based on the definition of Markov process, for each of the two cases with the discount rate being zero or a positive number, we present two dynamic programming algorithms to produce the optimal static policy and the optimal dynamic policy, respectively.

中文翻译：

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具有与工作负载相关的维护活动的随机单机调度

本文研究了具有工作负载相关维护活动的随机单机调度问题，其中所有作业的处理时间独立地服从公共离散分布，目的是找到最优策略以最小化期望总时间持有成本贴现。基于马尔可夫过程的定义，对于贴现率为零或正数的两种情况，我们提出了两种动态规划算法，分别产生最优静态策略和最优动态策略。