The two-echelon inventory-routing problem with fleet management

•We introduce fleet management in the context of inventory-routing.•We study different combinations of inventory policies and fleet management costs.•We design a matheuristic and a hybrid parallel exact algorithm based on branch-and-cut.•We validate our algorithms on a special case of our problem from the literature, obtaining all BKSs.•We show that a more complex logistics system leads to greater efficiency in logistics operations.