This paper deals with a real application encountered in the construction sector, which consists in a new variant of the pickup and delivery problem, including several constraints that have never been combined in the same variant, denoted MTPDSPTW. This problem is defined by a set of construction sites that have a delivery demand for construction materials and also a waste removal request. Each construction site has a certain profit which is computed according to the urgency of the pickup and delivery demand. Each site can be visited several times during the day, but the delivery must be done within a set of time windows specified by each site. Heterogeneous vehicles with di erent availability located at a massification and waste treatment platform must do multiple tours to serve the requests. The objective is to minimize the total travel distance and to maximise the profit. The developed method is based on the Iterated Local Search metaheuristic which uses a Random Variable Neighborhood Descent (RVND) in the Local Search Procedure. Di erent implementation schemes of the proposed method are tested on set of data instances provided by our industrial partner. The results show the e ectiveness of ILS-RVND compared to ILS with a single local search operator. ILS-RVND improves the results of the SBH heuristic by 13.15%.