A Dynamic Inventory Routing Problem model embedded into a rolling horizon solution approach is developed, along this paper, to solve the Smart Waste Collection Routing Problem. This allows the definition of dynamic waste collection routes that explore the use of real-time information on the bins fill-level, over a medium-term horizon. Opposite to a published short-term approach, based on the solution of the Vehicle Routing Problem with Profits that maximize daily profits, the present approach leads to better results translated into higher operational profits. This evidence is shown through the comparison of the solution of both the short-term and the medium-term approaches in a set of small instances where different active rolling horizon intervals are tested. A large instance obtained from a real waste collection system case study is also studied, and the results confirm the conclusions obtained when solving smaller instances.