co-directeur de recherche

Pickup and Delivery Problems (PDPs) are a relevant class of vehicle routing problems in which objects or people need to be collected and distributed. These problems have many applications in logistics, ambulatory services and robotics. In this thesis, we survey the static and dynamic PDPs appearing in the literature, we provide a classification scheme for them, and we show the relations between these problems. We then analyze the complexity of counting the number of feasible solutions of a well known PDP, and of a related scheduling problem, and we show that both problems are hard, namely, #Pcomplete. We later introduce the Pickup and Delivery Problem with Fixed Partial Routes (PDP-FPR), in which certain fixed partial routes must be respected. We prove that determining whether an instance of the PDP-FPR is feasible is strongly NP-complete. The computational complexity of several relaxations of the PDP-FPR are also shown to be NPcomplete, whereas for others relaxations the feasibility problem is shown to be polynomial time solvable. Based on some of the results about the PDP-FPR, we then develop an exact algorithm for checking the feasibility of instances of the Dial-a-Ride Problem (DARP). The DARP is an extension of the PDP in which requests consist in transporting passengers. The main application of the DARP arises in door-to-door transportation services offered in many cities for the elderly and handicapped people. The DARP generally has tight time windows associated with the pickup and delivery vertices as well as a maximum user trip time to reduce their inconvenience. These constraints make the problem of finding a feasible solution for the DARP a challenge. The proposed exact algorithm is based on constraint programming, which is particularly effective to solve feasibility problems. To this end, we model the DARP as a Constraint Satisfaction Problem and we then develop filtering algorithms to determine whether or not a partial solution can be extended into a complete solution, taking into account different sets of constraints. Results show that the algorithm is generally able to find a feasible solution within a few seconds and that the proposed filtering algorithms are effective. Finally, we develop a hybrid algorithm for the dynamic DARP in which service request arrive in real-time. The hybrid algorithm