A decomposition-based heuristic for the multiple-product inventory-routing problem

The inventory-routing problem is an integrated logistics planning problem arising in situations where customers transfer the responsibility for inventory replenishment to the vendor. The vendor must then decide when to visit each customer, how much to deliver and how to sequence customers in vehicle routes. In this paper, we focus on the case where several different products have to be delivered by a fleet of vehicles over a finite and discrete planning horizon. We present a three-phase heuristic based on a decomposition of the decision process of the vendor. In the first phase, replenishment plans are determined by using a Lagrangian-based method. These plans do not specify delivery sequences for the vehicles. The sequencing of the planned deliveries is performed in the second phase in which a simple procedure is employed to construct vehicle routes. The third phase incorporates planning and routing decisions into a mixed-integer linear programming model aimed at finding a good solution to the integrated problem. Computational experiments show that our heuristic is effective on instances with up to 50 customers and 5 products.