Bus schedule coordination for the last train service in an intermodal bus-and-train transport network

Only when a designated bus arrives at a particular bus stop (that connects to a rail station) earlier than the departure time of the associated last train by at least the necessary transfer walking time can passengers on the designated bus successfully access the rail network and finish the remainder of their trips by train. This paper first proposes an optimal bus schedule coordination problem for last train service in an intermodal bus-and-train transport network by offsetting and perturbing the original bus schedules to reduce transfer failures from bus service to train service based on the given last train schedules. The proposed problem is then formulated as a mixed integer nonlinear programming (MINLP) model. The MINLP model is equivalently transformed into a mixed integer linear programming (MILP) model that can be exactly solved by any optimization solvers, such as CPLEX. A case study based on eight real bus lines and the mass rapid transit (MRT) system in Singapore is conducted, and it shows that the bus schedule coordinated by the developed model is able to improve operational intermodal connectivity substantially.