Abstract In production lines, several factors contribute to the manufacturing of final products. Among these factors, the production time, machine status, and energy consumption, before and during production, need to be investigated further. In this paper, we present a mathematical model which jointly optimizes production scheduling and maintenance planning in a single-machine production environment. The performance of the machine deteriorates with time, and the machine is subject to stochastic deterioration-based failures. We assume that the transitions between the machine’s deterioration states follow an exponential distribution. We consider that processing times and energy consumption are affected by machine deterioration and failures. The main contribution of the paper is that maintenance and scheduling decisions are made based on the machine’s degradation level (i.e., the machine’s condition). We address the machine’s deterioration as a discrete multi-state degradation process; and model the effects of the machine’s deterioration and failures on the duration of job processing and the machine’s energy consumption. Then, we develop a stochastic mixed-integer programming model that integrates decisions about maintenance and production scheduling. The model generates the optimal maintenance action for each degradation state, as well as the optimal inspection policy and job sequence, with the overall aim being to minimize the total cost, including: inspection costs, repair costs, machine energy consumption costs, and the makespan penalty for exceeding a predetermined threshold. Due to the complexity of the developed model, an effective genetic algorithm (GA) based on the properties of the considered problem is proposed. Finally, through a comparative numerical study, we show that making decisions according to the deterioration level of the machine results in more integrated and cost-effective plans compared to the current method of repairing the machine only once it has reached its failure state.

中文翻译：

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具有劣化故障的单一劣化机器中的集成生产和维护计划

摘要 在生产线中，有几个因素会影响最终产品的制造。在这些因素中，生产时间、机器状态和能源消耗，在生产之前和生产过程中，需要进一步调查。在本文中，我们提出了在单机生产环境中联合优化生产调度和维护计划的数学模型。机器的性能会随着时间的推移而恶化，并且机器会受到基于随机恶化的故障的影响。我们假设机器退化状态之间的转换遵循指数分布。我们认为加工时间和能源消耗会受到机器老化和故障的影响。该论文的主要贡献是根据机器的退化水平（即机器的状况）做出维护和调度决策。我们将机器的退化视为一个离散的多状态退化过程；并对机器老化和故障对作业处理持续时间和机器能耗的影响进行建模。然后，我们开发了一个随机混合整数编程模型，该模型集成了有关维护和生产调度的决策。该模型为每个退化状态生成最优的维护动作，以及最优的检查策略和作业顺序，总体目标是最小化总成本，包括：检查成本、维修成本、机器能耗成本和制造周期超过预定阈值的惩罚。由于所开发模型的复杂性，提出了一种基于所考虑问题的特性的有效遗传算法（GA）。最后，通过比较数值研究，我们表明，与当前仅在机器达到故障状态后才维修机器的方法相比，根据机器的退化程度做出决策会产生更完整和更具成本效益的计划。