Last train scheduling for maximizing passenger destination reachability in urban rail transit networks

As urban rail transit (URT) systems usually do not operate for the whole day, the last train service offers the last daily chance for late-night passengers to utilize URT services to reach their target destination stations. This paper formally introduces and models the destination-reachability based last train timetabling problem (DR-LTTP in abbreviation) in URT networks, which involves both the last train timetabling and the passenger assignment. The DR-LTTP is formulated as a mixed integer linear programming and can be solved by existing commercial optimization software. The model is illustrated with a simple numerical example on a minimum spanning tree network, and comparison experiments are conducted between DR-LTTP model and station-transferability based last train timetabling problem (ST-LTTP in abbreviation). Finally, a real case study with Beijing URT network is conducted to test the performance of our model.