A neural branch-and-price for truck scheduling in cross-docks

In this paper, we address the complex problem of dock-door assignment and truck scheduling within cross-docking operations. This is a problem that requires frequent resolution throughout the operational day, as disruptions often invalidate the optimal plan. Given the problem's highly combinatorial nature, finding an optimal solution demands significant computational time and resources. However, the distribution of data across problem instances over a lengthy planning horizon remains consistently stable, with minimal concern regarding distribution shift. These factors collectively establish the problem as an ideal candidate for a learn-to-optimize solution strategy. We propose a Dantzig-Wolfe reformulation, solving it via both a conventional branch-and-price approach and a neural branch-and-price approach, the latter of which employs imitation learning. Additionally, we introduce some classes of valid inequalities to enhance and refine the pricing problem through a branch-and-cut scheme. Our computational experiments demonstrate that this methodology is not only feasible but also presents a viable alternative to the traditional branch-and-price algorithms typically utilized for such challenges.