We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete time horizon. The goal is to minimize the total cost of the distribution that comprises the inventory cost at the supplier and at the customers and the routing cost. We present a matheuristic that combines a tabu search and mathematical programming formulations. When compared with two exact methods on 640 small instances, the matheuristic finds 192 (48%) optima over the 402 instances with known optima and improves 125 upper bounds. Tested on 240 large instances (with up to 200 customers) for which no optimal solutions are known, it improves the best solution for 220 (92%) of the 240 instances. The online supplement is available at https://doi.org/10.1287/ijoc.2016.0737 .