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This paper studies the application of the Vendor-Managed Inventory paradigm, when a vendor manages their own inventory in addition to those of its customers. We extend this concept by applying it to a two-echelon (2E) supply chain, in which the middle layer is responsible for managing pickups of inputs from suppliers and deliveries of final product to its customers. Inspired by a real case, we introduce 2E Multi-Depot Inventory-Routing Problem (2E-MDIRP). Different inventory policies are considered for managing the inventory of input and final products. We propose a mathematical formulation capable of handling all decisions of the system, and design a branch-and-cut algorithm to solve it. Moreover, we propose and implement a rich matheuristic algorithm to solve the problem efficiently even for very large instances. A flexible metaheuristic phase handles vehicle routes, while input pickups, product deliveries …