CAR: heuristics for the inventory routing problem

Vendor managed inventory (VMI) is a streamlined approach to inventory and order fulfillment and is a system in which vendors continuously and automatically replenish a trading partner’s inventory. Vendors must ensure appropriate quantities of storages at the point of demand and must ensure optimal distribution plans, including routing of the distribution vehicles. This problem is known as the inventory routing problem (IRP) and seeks to integrate the routing of vehicles used for collection and distribution, with conventional inventory management. This paper addresses an IRP with a manufacturer that supplies a product using a fleet of vehicles to a set of warehouses over a defined time horizon. We develop a mixed integer linear program to determine the optimal allocation and the routing schedule for warehouses over the defined time horizon. To solve this problem, we propose a three-phase heuristic approach, called CAR: clustering of receiver nodes, allocation of quantities to these nodes, and routing of delivery vehicles through clusters of nodes. Computational studies are carried out and experimental trials conducted over a large number of data sets provide encouraging results and show usefulness of the solution approaches. The proposed ILP would provide optimal solution to the problem but it demands huge computational effort. However, CAR2, a proposed heuristic, is able to get solutions 7.41% better than the upper bound solutions obtained from CPLEX. These approaches can easily be implemented into existing VMI systems.