Integrated lot-sizing and scheduling problem with a period-based learning effect

This research investigates a multi-product capacitated lot-sizing and scheduling problem incorporating a novel learning effect, namely the period-based learning effect. This is inspired by a real case in a core analysis laboratory under a job shop setting. Accordingly, a Mixed-Integer Linear Programming (MILP) model is extended based on the big-bucket formulation, optimizing the total tardiness and overtime costs. Given the complexity of the problem, a cutting plane method is employed to simplify the model. Afterward, three matheuristic methods based on the rolling horizon approach are devised, incorporating two lower bounds and a local search heuristic. Furthermore, a post-processing approach is implemented to incorporate lot-streaming possibility. Computational experiments demonstrate: 1) the simplified model performs effectively in terms of both solution quality and computational time; and 2) although the model encounters challenges with large-scale instances, the proposed matheuristic methods achieve satisfactory outcomes; and 3) it can be inferred that the complexity of the models and solution methods are independent of the learning effect; however, the value of learning effect may impact the performance of the lower bounds; 4) in manufacturing settings, where the lot-streaming is possible, incorporating post-processing can drastically improve the objective function; 5) the impact of the period-based learning effect in the results is significant, and the model’s sensitivity to time-based parameters (e.g., learning rate) is more than cost-based ones (e.g., tardiness cost).

本研究针对一类引入新型学习效应的多产品容量受限批量调度问题展开探讨，该学习效应即基于周期的学习效应（period-based learning effect）。本研究的问题灵感来源于单件车间（job shop）环境下岩心分析实验室的真实生产场景。据此，本文基于大桶建模框架（big-bucket formulation）拓展了混合整数线性规划（Mixed-Integer Linear Programming, MILP）模型，以最小化总拖期惩罚成本与加班总成本为优化目标。鉴于该问题的复杂性，本文采用割平面法（cutting plane method）对模型进行简化。随后，本文基于滚动时域法（rolling horizon approach）设计了三类数学启发式方法（matheuristic methods），融合了两类下界求解策略与一种局部搜索启发式算法。此外，本文还引入后处理方法以支持批量拆分流转的可行性。计算实验结果表明：
1. 简化后的模型在求解质量与计算耗时两方面均表现出色；
2. 尽管原模型在处理大规模算例时存在一定挑战，但本文提出的数学启发式方法可获得令人满意的求解结果；
3. 可推断模型与求解方法的复杂度与学习效应无关，但学习效应的取值会对下界的求解性能产生影响；
4. 在支持批量拆分流转的制造场景中，引入后处理方法可显著优化目标函数值；
5. 基于周期的学习效应对求解结果具有显著影响，且模型对基于时间的参数（如学习率）的灵敏度高于基于成本的参数（如拖期惩罚成本）。