A Temporal-Network Constraint Programming Model for the Pickup and Delivery Problem with Time Windows

This paper studies the single-vehicle pickup and delivery problem with time windows (PDPTW). We present a constraint programming formulation that models routing decisions using a global circuit constraint and arrival times using conditional difference constraints. The resulting temporal constraint structure can be interpreted as a dynamic simple temporal network (STN). We analyse propagation properties of this model and compare it with a baseline mixed-integer linear programming formulation. A fully auditable empirical instance is constructed and analysed through enumeration and sensitivity experiments on time windows.