Cleaning debris in urban areas after major disasters is very relevant to inhabitants to recover from their effects. In natural disasters, an unexpected and large area can be affected. Moreover, the time and the costs to perform the cleaning operations can be very high. In this work, the integrated multi-period scheduling routing problem to clean debris (SRP-CD) after major disasters is investigated. The problem includes strategical (scheduling) and operational (routing) decisions and, considering complex issues such as two levels of synchronization between work-troops and dump trucks. The goal of SRP-CD is twofold: minimizing the number of days for the overall cleaning, in the strategical level; and minimizing the total costs of vehicles routes in the operational level. A new mathematical model based in a dynamic multi-flow formulation, constructive heuristics and Large Neighborhood Search (LNS)-based metaheuristics are proposed. Comparison experiments for the model and the approaches are carried out, to measure performance and robustness of the proposed methods. To the best of our knowledge, these are the first contributions in the literature for SRP-CD, including all aspects addressed here.