A fast solution method for the Dynamic Flexible Pickup and Delivery Problem with task allocation fairness for multiple vehicles

The Dynamic Flexible Pickup and Delivery Problem (DFPDP) originates from the actual needs of multi-warehouse management strategies and is one of the important challenges currently facing the field of logistics and distribution. In DFPDP, it is necessary to address dynamic order fluctuations, quickly plan heterogeneous fleet routes, ensure fairness in task allocation, and minimize total travel time under time window constraints. However, there is currently little research on this issue, and traditional heuristic algorithms make it difficult to quickly find a solution to this problem. First, we propose a Multimodal Constraint Dynamic Scheduling Mechanism (MCDSM) to select a vehicle with the lowest current time consumption to make task allocation between vehicles as fair as possible. Second, we propose a Parallel Encoder-Serial Decoder model integrating Variable-length Sequences (PESDVS), in which the variable-length sequences designed can effectively handle the generation of dynamic orders and the changes in the number of pickup and delivery locations, while the trained model can adapt itself to different order scenarios. In addition, the model improves the quality of order decisions through a parallel encoder and serial decoder structure to minimize the total traveling time of the fleet. Extensive experimental results demonstrate that our method has excellent performance and good generalization ability under different order sizes. At the same time, compared with heuristic algorithms, our method can quickly find a feasible solution to the problem and the task allocation between vehicles is relatively fair.