We introduce the time-dependent capacitated profitable tour problem with time windows and precedence constraints. This problem concerns determining a tour and its departure time at the depot that maximizes the collected profit minus the total travel cost (measured by total travel time). To deal with road congestion, travel times are considered to be time-dependent. We develop a tailored labeling algorithm to find the optimal tour. Furthermore, we introduce dominance criteria to discard unpromising labels. Our computational results demonstrate that the algorithm is capable of solving instances with up to 150 locations (75 pickup and delivery requests) to optimality. Additionally, we present a restricted dynamic programing heuristic to improve the computation time. This heuristic does not guarantee optimality, but is able to find the optimal solution for 32 instances out of the 34 instances.

Additional Metadata
Keywords Transportation, Profitable tour problem, Pickup and delivery problem, Tailored labeling algorithm, Time-dependent travel times
Persistent URL dx.doi.org/10.1016/j.ejor.2017.07.004, hdl.handle.net/1765/131137
Journal European Journal of Operational Research
Organisation Department of Technology and Operations Management
Citation
Sun, P, Veelenturf, L.P, Dabia, S, & Van Woensel, T. (2018). The time-dependent capacitated profitable tour problem with time windows and precedence constraints. European Journal of Operational Research, 264(3), 1058–1073. doi:10.1016/j.ejor.2017.07.004