arXiv:2608.10245v1 Announce Type: new Abstract: Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared o...