Vehicle routing problem with time windows and simultaneous pickups and deliveries

This paper focuses on the time windows factor in vehicle routing problem with simultaneous pickups and deliveries. In vehicle routing problem with time windows and simultaneous pickups and deliveries (VRPTWSPD), vehicles must wait and can not start service immediately if they arrive earlier ahead of the time when pickup goods are ready. Meanwhile, tardiness may cause penalty cost. We propose a mathematical model for VRPTWSPD and develop a genetic algorithm to solve it. The results for the numerical experiments validate the effectiveness of the algorithm proposed in this paper, and demonstrate the significance of introducing time windows. Moreover, we discuss the algorithm performance under varying penalty values of tardiness through sensitivity analysis.