This research deals with two variants of the Inventory Routing Problem (IRP). This problem comes from the context of a Vendor Managed Inventory (VMI) system in which the vendor is responsible for managing the customer s inventory. It is the combination of transportation and inventory management problems, which correspond to the higher costs in a logistics operation. Hence, this paper presents a mathematical model for an IRP variant, in which the vendor has customers inside and outside the VMI system. This situation is presented when it is not interesting to manage the inventories of some clients within the VMI system, resulting only in meeting their demands. In addition, the model considers three different types of stock management policies and it can comprehend multiple periods and multiple vehicles. After its modelling, the model was validated using IRP instaces, the Vehicle Routing Problem (CVRP) and specific instances for this variant. The impacts of different inventory management policies were also analyzed. In addition to the mathematical model, a hybrid meta-heuristic was developed, which solves an IRP variant considering several periods and several vehicles. Each iteration of the metaheuristic is divided into two stages: the first is modifying the position of one or more customers attended by the vehicles and periods, and a second step that solves a Maximum Flow at Minimum Cost problem, to optimally assign the load volumes transported to each customer in each vehicle in each period. Then, this approach is tested in classical instances for this IRP variant, obtaining results that prove the efficiency of the algorithm.