Application du Machine Learning à la prédiction des paramètres optimaux des politiques de production d’un système manufacturier soumis à une demande périodique

Abstract

Production systems subject to time-varying demand as well as random breakdowns and repairs pose a major control challenge, as optimal decisions must adapt to uncertain and non-stationary dynamics. Stochastic dynamic programming and Hamilton–Jacobi–Bellman (HJB) equations provide a rigorous framework for determining optimal production policies. However, in non stationary settings, the numerical resolution of these equations entails significant computational effort, which makes the exploration of multiple scenarios difficult in industrial environments where responsiveness is essential. This thesis proposes the use of Machine Learning to rapidly predict the parameters of optimal production policies based on previously computed HJB solutions. The solutions obtained from the resolution of the Hamilton–Jacobi–Bellman equations are used to build a training dataset for supervised learning models, which learn the relationship between system parameters and the characteristics of optimal policies. Once trained, these models directly provide approximations of the optimal parameters without requiring further numerical resolution of the HJB equations, thereby significantly reducing computation time. To implement and validate this approach, a progressive methodology is developed on two systems of different complexity, the second representing an extension of the first. In the case of a system consisting of a single machine producing one type of part, several algorithms are compared : the k-nearest neighbors (kNN) algorithm, deep neural networks (DNN), and radial basis function (RBF) neural networks. The input space initially includes demand characteristics (mean, amplitude, and frequency) and is subsequently extended to incorporate the backlog cost and the repair rate. The results show that kNN offers an excellent trade-off between accuracy and computational efficiency, closely reproducing the solutions obtained from the HJB equations while significantly reducing computation time. This enables rapid exploration of multiple scenarios, allowing decision-makers to assess the impact of different operating conditions on the production policy. To assess the relevance of this approach on a more complex system, the study is extended to a machine producing two types of parts. This configuration also makes it possible to analyze how the increase in the number of input variables influences the choice of the learning algorithm. The results reveal that kNN performance deteriorates as the dimensionality of the input space increases, whereas deep neural networks maintain good predictive accuracy. These findings confirm that Machine Learning constitutes an effective alternative to repeated numerical solutions of the HJB equations, enabling near-instantaneous predictions while guiding the choice of the most suitable algorithm according to the complexity of the system under study.

Date	20 Mar 2026
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Pierre Kenné (Supervisor) & Ali Gharbi (Co-supervisor)