A BRANCH-AND-CUT ALGORITHM FOR THE ROUTING PROBLEM WITH INVENTORY AND TWO-DIMENSIONAL PACKING

The work addresses the Inventory Routing Problem with Two-Dimensional Loading Constraints, integrating decisions on item inventories, vehicle routing, and the packing of items into vehicles. Motivated by practical applications such as the transportation of palletized loads and fragile items, the problem represents customer demands and vehicle compartments as rectangles, imposing two-dimensional geometric constraints. The objective is to minimize total inventory and routing costs over a planning horizon while ensuring that demands are satisfied. An integer linear programming formulation is proposed, strengthened by valid inequalities and solved using a branch-and-cut algorithm supported by Constraint Programming to handle item packing. The results indicate that ignoring inventory decisions can increase costs by up to 70%, while disregarding packing constraints renders more than 83% of the solutions infeasible, highlighting the importance of an integrated approach for complex logistics problems.