The problem of transporting vehicle components in a car manufacturer workshop can be seen as a large scale single vehicle pickup and delivery problem with periodic time windows. Our experimental evaluation indicates that a relatively simple constraint model shows some promise and in particular outperforms the local search method currently employed at Renault on industrial data over long time horizon. Interestingly, with an adequate heuristic, constraint propagation is often sufficient to guide the solver toward a solution in a few backtracks on these instances. We therefore propose to learn efficient heuristic policies via reinforcement learning and to leverage this technique in several approaches: rapid-restarts, limited discrepancy search and multi-start local search. Our methods outperform both the current local search approach and the classical CP models on industrial instances as well as on synthetic data.