A Branch-and-Cut Algorithm for the Multi-Product Multi-Vehicle Inventory- Routing Problem

The combined operation of distribution and inventory control achieved through a vendor-managed inventory strategy creates a synergetic interaction which benefits supplier and customers. Inventory-Routing Problems (IRPs) arise when inventory and routing decisions must be taken simultaneously, which yields a difficult combinatorial optimization problem. While most IRP research deals with a single product, there are often several products involved in distribution activities. In this paper, we propose a branch-andcut algorithm for the solution of IRPs with multiple products and multiple vehicles. We formally define and model the problem, and we solve it exactly. We also consider the inclusion of consistency features which are meaningful in a multi-product environment and help improve the quality of the service offered.