A Decomposition-Based Heuristic Method for Inventory Routing Problem

The inventory routing problem (IRP) arises in a broad spectrum of real-life applications related to joint decisions of inventory and routing. In the basic IRP, a supplier has to make decisions about the delivery timing, delivered quantity of a single product and routing with a single vehicle to a set of retailers without backlog. It poses computational challenge due to its natural complexity. To tackle this problem, we propose a two-phase decomposition-based heuristic method. In Phase 1, a logic-based Benders like decomposition method is employed to first determine the retailers' replenishments, followed by the routing decisions individually for each period. Valid cuts, inequalities for diversification constraints and for greedy search are employed. Then, the solutions obtained in Phase 1 are improved with a restricted mixed integer linear programming (MILP) model in Phase 2. Computational experiments are conducted on 220 benchmark problem instances with up to 200 retailers and 6 periods. The results show the high performance of the proposed method and it is comparable to the state-of-the-art heuristics in terms of both efficiency and effectiveness.