Abstract We study an Inventory Routing Problem at the tactical planning level, where the initial inventory levels at the supplier and at the customers are decision variables and not given data. Since the total inventory level is constant over time, the final inventory levels are equal to the initial ones, making this problem periodic. We propose a class of matheuristics, in which a route-based formulation of the problem is solved to optimality with a given subset of routes. Our goal is to show how to design effective subsets of routes. For some of them, we prove effectiveness in the worst case, i.e., we provide a finite worst-case performance bound for the corresponding matheuristic. Moreover, we show they are also effective on average, in a large set of instances, when some additional routes are added to this subset of routes. These solutions significantly dominate, both in terms of cost and computational time, the best solutions obtained by applying a branch-and-cut algorithm we design to solve a flow–based formulation of the problem.