Fluctuating Demand-Oriented Optimization of Train Line Planning Considering Carriage Resources Transfer under Flexible Compositions

The intercity railway is subject to variation and fluctuation in demand both in time and space over a day to a large extent. In that case, more advanced line planning techniques are practically needed to match the non-equilibrium passenger demand. We propose an integer linear programming model for adapting to the fluctuating demand and improving rail line profit, in which the multi-period planning approach and flexible train composition mode are taken into consideration. In particular, we also consider the limitations of the carriage and the dynamic transfer of resources during a finite period to ensure the better implementation of the line planning and subsequent operation plans. Our purpose is to improve on previous line planning models by integrating the multi-period strategic-level line planning decision with resource constraints. Since the problem is computationally intractable for realistic size instances, an improved round heuristic algorithm that is based on linear relaxation is proposed and we compare the round heuristic performance with the commercial solver Gurobi on artificial instances. The numerical experiments that are based on an intercity railway in China certify the effectiveness and applicability of the proposed model and algorithm. We evaluate the impact of different optimization parameters and reserved carriages and the computation results show that in comparison to the fixed composition mode, the proposed approach can improve the utilization efficiency of carriage resources and increase the line profit by 1.9% under the same carriage resource conditions