Classical capacitated lot-sizing models include capacity constraints relying on a rough estimation of capacity consumption. The plans resulting from these models are often not executable on the shop floor. This paper investigates the use of constraint learning approaches to replace the capacity constraints in lot-sizing models with machine learning models. Integrating machine learning models into optimization models is not straightforward since the optimizer tends to exploit constraint approximation errors to minimize the costs. To overcome this issue, we introduce a training procedure that guarantees overestimation in the training sample. In addition, we propose an iterative training example generation approach. We perform numerical experiments with standard lot-sizing instances, where we assume the shop floor is a flexible job-shop. Our results show that the proposed approach provides 100% feasible plans and yields lower costs compared to classical lot-sizing models. Our methodology is competitive with integrated lot-sizing and scheduling models on small instances, and it scales well to realistic size instances when compared to the integrated approach.

中文翻译：

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用于改进批量调整模型中容量消耗函数近似的约束学习方法


经典的有容量批次大小模型包括容量约束，这些限制依赖于对容量消耗的粗略估计。这些模型生成的计划通常无法在车间执行。本文研究了使用约束学习方法将批次大小模型中的容量约束替换为机器学习模型。将机器学习模型集成到优化模型中并不简单，因为优化器倾向于利用约束近似误差来最大限度地降低成本。为了克服这个问题，我们引入了一个训练过程，保证训练样本中的高估。此外，我们提出了一种迭代训练示例生成方法。我们使用标准批量调整实例进行数值实验，其中我们假设车间是一个灵活的加工车间。我们的结果表明，与传统的地块大小模型相比，所提出的方法提供了 100% 可行的计划并产生了更低的成本。我们的方法与小型实例上的集成批次大小和调度模型相比具有竞争力，并且与集成方法相比，它可以很好地扩展到实际大小的实例。