In this paper, we study several coordinated production-delivery scheduling problems with potential disruption motivated by a supply chain in the manufacturing industry. Both single-machine environment and identical parallel-machine environment are considered in the production part. The jobs finished on the machines are delivered to the same customer in batches. Each delivery batch has a capacity and incurs a delivery cost. There is a situation that a possible disruption in the production part may occur at some particular time and will last for a period of time with a probability. We consider both resumable case and nonresumable case where a job does not need (needs) to restart if it is disrupted for a resumable (nonresumable) case. The objective is to find a coordinated schedule of production and delivery that minimizes the expected total flow times plus the delivery costs. We first present some properties and analyze the NP-hard complexity for four various problems. For the corresponding single-machine and parallel-machine scheduling problems, pseudo-polynomial-time algorithms and fully polynomial-time approximation schemes (FPTASs) are presented in this paper, respectively.

中文翻译：

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在具有批量交付和潜在中断的单机和并行机上进行调度

在本文中，我们研究了制造业中供应链引起的潜在生产中断的协调生产交付计划问题。生产部分同时考虑了单机环境和相同的并行机环境。机器上完成的作业将分批交付给同一位客户。每个交货批次都有一定的生产能力，并产生一定的交货成本。存在这样的情况，在某个特定时间可能会在生产部件中发生中断，并有可能持续一段时间。我们考虑可恢复性情况和不可恢复性情况，其中，如果一个工作因可恢复性（不可恢复性）情况而中断，则不需要（需要）重新启动该作业。目的是找到协调的生产和交货时间表，以最大程度地减少预期的总生产时间加上交货成本。我们首先介绍一些性质，并分析四个问题的NP难解性。针对相应的单机和并行机调度问题，分别提出了伪多项式时间算法和完全多项式时间逼近方案（FPTAS）。