This paper presents the first optimization study of multi-site transportation in the construction industry, whichallows mutualizing building material delivery and construction waste removal. This study is inspired by a real-worldproblem encountered in the framework of the French R&D project DILC, in which a pooling platformmust centralize the delivery of building materials to the construction sites and the pickup of their waste, usinga limited and heterogeneous fleet that are allowed to perform multiple trips, under time and capacity limitationconstraints. The problem under study, called the Multi-Trip Pickup and Delivery Problem, with Split loads,Profits and Multiple TimeWindows is a new extension of the vehicle routing problem with pickup and delivery,that considers new realistic constraints specific to the construction industry such as each construction site mayhave a priority on its delivery request or its pickup request or both, with a higher priority level for deliveryrequest, and each construction site may have several time windows. To solve this problem, we propose newinsertion criteria that takes into consideration several aspects of our problem, which we have embedded in aconstruction heuristic. Experiments performed on new real instances have shown the efficiency of our method.