This paper addresses a production scheduling problem derived from an industrial use case, focusing on unrelated parallel machine scheduling with the personnel availability constraint. The proposed model optimizes the production plan over a multi-period scheduling horizon, accommodating variations in personnel shift hours within each time period. It assumes shared personnel among machines, with one personnel required per machine for setup and supervision during job processing. Available personnel are fewer than the machines, thus limiting the number of machines that can operate in parallel. The model aims to minimize the total production time considering machine-dependent processing times and sequence-dependent setup times. The model handles practical scenarios like machine eligibility constraints and production time windows. A Mixed Integer Linear Programming (MILP) model is introduced to formulate the problem, taking into account both continuous and district variables. A two-step solution approach enhances computational speed, first maximizing accepted jobs and then minimizing production time. Validation with synthetic problem instances and a real industrial case study of a food processing plant demonstrates the performance of the model and its usefulness in personnel shift planning. The findings offer valuable insights for practical managerial decision-making in the context of production scheduling.

翻译：本文针对工业实际案例中的生产调度问题，聚焦于考虑人员可得性约束的非相关并行机调度。所提模型在多时段调度期内优化生产计划，并适应各时段内人员轮班工时的变化。该模型假设多台机器共享操作人员，每台机器在作业处理期间需要一名操作人员进行设置和监督。可用操作人员数量少于机器数量，从而限制了可并行运行的机器数量。模型以最小化总生产时间为目标，考虑与机器相关的加工时间和与顺序相关的设置时间。模型还处理了实际场景中的机器资格约束和生产时间窗口。采用混合整数线性规划模型对问题建模，同时考虑连续变量和离散变量。通过两步求解方法提高计算速度：首先最大化被接受作业数量，然后最小化生产时间。基于合成问题实例和某食品加工厂的实际工业案例验证表明，该模型在人员排班中具有良好的性能及实用性。研究结果为生产调度中的管理决策提供了有价值的实践参考。