An efficient heuristic method for joint optimization of train scheduling and stop planning on double-track railway systems

In this study, a new mathematical programming approach for solving the joint timetabling and train stop planning problem in a railway line with double-track segments is proposed. This research aims to design an optimized train timetable subject to the station-capacity and time-dependent dwell time constraints. The objective function is to maximize the railway infrastructure capacity by minimizing the schedule makespan. The problem is formulated as a particular case of blocking permutation flexible flow shop scheduling model with dynamic time window constraints. Due to the combinatorial nature of the problem, heuristic algorithm and bound tightening methods are proposed that generate approximate solutions, which are computationally efficient for large-size instances of the problem. Computational experiments based on the Iranian railway data set are conducted to examine the performance of the heuristic method. The results of the numerical experiments verified the efficiency of the heuristic method in solving moderately large instances of the problem. The outcomes show that the heuristic method works efficiently in finding high-quality solutions with optimality gaps of 2.1% on average.