In pickup and delivery problems (PDPs), the aim is to transport loads from pickup locations (suppliers) to delivery locations (customers) using a set of vehicles while respecting a set of constraints. In this paper, we discuss a new variant of the PDP which has not been treated yet in the literature to our best knowledge. This new variant is the selective pickup and delivery problem with time windows and paired demands (SPDPTWPD). Its first specificity relies on the occurrence of time Windows, capacity and precedence constraints. In addition, it includes several depots and a fleet of vehicles, and the selective aspect must be taken into account. It means the choice of customers to be served when the global capacity of the vehicles is not sufficient. We proposed firstly a new mono-objective model to solve the SPDPTWPD. Then we tested our proposed algorithm on benchmark instances of near (less constrained) problems from the literature. Secondly, we have generated new instances adapted to the considered problem. Thirdly, we worked on a lexicographic approach to deal with the multi-objective aspect of our problem. The efficiency of our approaches is shown by the obtained results.
