Training Demand Prediction Models by Decision Error for Two-Stage Lot-Sizing Problems

Demand prediction to support appropriate production decisions is being actively studied. Many prediction models are designed to minimize the prediction error, which is measured by determining the difference between the predicted and ground-truth demand. However, these models ignore the effect of the prediction error on downstream production decisions. This prompts our study, which focuses on demand prediction models for two-stage uncapacitated lot-sizing problems. In this paper, we present a linear prediction model that minimizes the decision error, which is measured by the optimization objective of lotsizing problems. Our model mitigates the impact of prediction errors by leveraging the structure of the lot-sizing problems. We subsequently extend the prediction model to a distributionally robust version. A cutting-plane method is proposed to solve the resulting model under the L_{1} and  L_{infinity} norms. The decision errors are used as loss functions to construct decision treeand neural network-based prediction models, respectively. The corresponding training methods are proposed as well. Numerical experiments demonstrate that the proposed prediction models are significantly superior to traditional prediction methods for small samples and high-dimensional data. In addition, the performance of the robust model is highly tolerant to model misspecification and imperfect data.</p