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.

在本研究中，我们提出了一个多期调度问题的模型，该模型考虑了在每个时间段内人员排班时间的变化，同时解决了相关无关的并行机器调度问题。我们的模型旨在最小化总生产时间，考虑到各机器的处理时间和设备时间，以及各种实际情景下的约束条件和时间窗口。我们介绍了一个混合整数线性规划模型来表述这个问题，并采用了两步骤的解决方法来提高计算速度。通过合成问题实例和真实的工业案例研究，我们验证了模型的性能和在人员排班计划中的实际决策制定方面的有用性。

一种同时考虑人员轮班规划和无关并行机器调度的数学模型