The two-echelon multi-depot inventory-routing problem

Abstract

Abstract 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 and routing improvements are performed by solving a subproblem exactly. We perform extensive computational experiments in order to evaluate the performance of our method, both by comparing the two algorithms, the effectiveness of the different inventory policies, the cost structure of the solutions, and the performance of different parts of the proposed heuristic algorithm. The results show that a more strict inventory policy leads to higher costs but fewer vehicle routes, which makes the overall problem easier to be solved by the approximated algorithm.