Uncertain demand based integrated optimisation for train timetabling and coupling on the high-speed rail network

Transportation is an important component in the logistics and production processes. To accurately match rapidly growing demand and limited transport capacity, the goal of minimising costs while ensuring high service quality under existing infrastructure has received significant attention. This paper presents an integrated optimisation approach for the short-term operational management under daily fluctuating demand, with a focus on two key strategic decisions: train timetabling and coupling. In particular, an integrated two-stage stochastic model and a combined heuristic local search algorithm with the branch-and-bound method are developed to (1) obtain the optimal demand assignment to the rail network, (2) investigate trains' coupling plans to avoid waste of resources when demand is low, and (3) add candidate trains to generate new feasible timetables when demand surges. To verify the solving method, a lower bound algorithm is introduced. Using a hypothetical small-scale and a real-world China high-speed rail network as numerical experiments, different demand scales and critical parameters are tested to obtain optimised timetables. The results show that good solutions are achieved in several seconds, making it possible to adjust trains' schedules efficiently and effectively according to the variable demand in short-term operational management.