Mixed-Integer Linear Programming Models for Coordinated Train Timetabling with Dynamic Demand

In this paper, we study the optimization of coordinated train timetable in an urban rail network under the consideration of time-dependent passenger demands. This problem arises in large urban rail networks with multiple lines that the passengers may transfer among different lines to arrive at their destinations. We propose an exact formulation to generate the optimal train timetables of all the involved lines in a rail transit network synchronously, and our objective is to minimize the maximal level of crowdedness of stations. In particular, we introduce several sets of passenger flow variables that enable to model this complex problem as a mixed-integer linear programming (MILP) that is possible to be solved to the optimal solution. By considering the number of boarding and alighting passengers as passenger flow variables, we explicitly incorporates the number of in-vehicle passengers in the modelling framework to capture the train carrying capacity constraints. The formulated models first extend the passenger-oriented train timetabling models in existing literature from a single transit line to a whole connected network. Case studies are conducted to verify the effectiveness of the proposed model.