The inventory routing problem (IRP) integrates two operational problems of the supply chain: inventory management and routing. The objective of the decision-maker is to decide, for each period of the time horizon, whether a client should be replenished, with which quantity and following which route, optimising both the inventory and transportation costs.

When evolving in an urban logistics context, one problem that can be faced is the volatility of the travelling times between locations. This volatility is represented in this paper by considering the travelling times as time dependent. As time-dependent problems tend to be harder to solve than their basic counterpart \cite{Gendreau2015}, it is necessary to propose new efficient algorithms. In this paper, a matheuristic that decomposes the problem into first assigning the clients to visit at each period and then solving a time-dependent travelling salesman problem (TD-TSP) is proposed.