The classic version of the Inventory Routing Problem considers a system with one supplier that manages the stock level of a set of customers. The supplier defines when and how much products to supply and how to combine customers in routes while minimizing storage and transportation costs. We present a new version of this problem that considers a two-echelon system with indirect deliveries and routing decisions at both levels. In this variant, the products are delivered to customers through distribution centers to meet demands of customers with minimum total cost, where the total cost is composed by ordering costs, inventory costs, vehicle fixed costs and transportation costs. We introduce a mathematical formulation and a branch-and-cut algorithm to solve the proposed Two-Echelon Inventory Routing Problem for different inventory policies and routing configurations. Intrinsic new valid inequalities to the two-echelon system are introduced. We analyze the impact of the new inequalities, as well as the already known valid inequalities on the efficiency of the proposed algorithm. Computational experiments are presented for a set of randomly generated instances. The results show that, for the simplest variant of the problem, the proposed method is able to solve medium-scale instances up to the problem optimality.
Working Paper, February, 2019.