A Lagrangian heuristic approach for the Inventory Routing Problem

The inventory routing problem (IRP) deals with the coordination of inventory replenishment and transportation. The IRP refers to the situation where the inventory replenishment at a number of locations is controlled by a central manager with a fleet of vehicles. A distribution strategy is necessary for achieving the minimization of distribution cost while satisfying the demands of the retailers are satisfied without any stock-out incident during the period of planning horizon. In this paper, we consider heterogeneous vehicles and deterministic demand rates over a planning horizon. The problem is formulated as a mixed integer program and we propose a sequential heuristic to find good feasible solutions. Computational experiments show that the proposed heuristic gives good solutions in reasonable computation time.