Bi-objective optimization for last-train coordination planning with dwell time adjustment strategy

In the design of last-train coordination plan, adjusting (extending/reducing) dwell time can balance economic and service goals for operation company and late-night passengers, especially when transfer-passenger flow is uncertain. For this purpose, we first develop a bi-objective scenario-based stochastic programming model for last-train coordination planning problem combined with the dwell time adjustment strategy. Then, we develop a two-phase approach, wherein the first phase we adopt the varepsilon-constraint method to reformulate the original model to a modified single-objective one. This is followed by the second phase using the branch-and-bound algorithm implemented by the CPLEX solver to obtain Pareto-optimal solutions (frontier). Finally, we demonstrate the advantage of the proposed model through comparison with the corresponding model without dwell time strategy and the max-min robust model over a randomly generated small-scale network. Moreover, we also illustrate the application of the proposed model by a real-world case study on the large-scale Beijing subway network.