Making a reasonable and effective production plan is always an essential and challenging task in industrial production. A joint optimization model of production and maintenance is proposed in this paper, which considers the structural relationship between production units and the influence of the unit state on demand. A three-unit series–parallel system is selected to calculate the steady-state probability density function of the system, and the model is established by dividing different maintenance situations in one cycle. By analyzing the composition of expected cost and expected time in each situation, the expected cost rate is calculated by using renewal reward theory. The objective function of the model is to minimize the expected cost rate. The genetic algorithm is improved according to the model characteristics. The application of the model is illustrated by a case, and the sensitivity analysis is set to show the influence of different parameters on the decision-making results of the system, providing ideas for decision-makers. Finally, the contrast experiments show the advantages of the proposed model and method.

中文翻译：

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具有质量或有需求的串并联系统的联合生产和维护优化

制定合理有效的生产计划始终是工业生产中一项必不可少且具有挑战性的任务。本文提出了一种生产和维护联合优化模型，该模型考虑了生产单元之间的结构关系以及单元状态对需求的影响。选取三单元串并联系统计算系统的稳态概率密度函数，并通过划分一个周期内的不同维修情况建立模型。通过分析每种情况下预期成本和预期时间的构成，利用更新奖励理论计算预期成本率。该模型的目标函数是最小化预期成本率。根据模型特点对遗传算法进行了改进。通过一个案例来说明模型的应用，并设置敏感性分析来展示不同参数对系统决策结果的影响，为决策者提供思路。最后，对比实验表明了所提模型和方法的优势。