Constraint learning approaches to improve the approximation of the capacity consumption function in lot-sizing models

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.