New Exact Algorithm for the integrated train timetabling and rolling stock circulation planning problem with stochastic demand

This paper studies an integrated train timetabling and rolling stock circulation planning problem with stochastic demand and flexible train composition (TRSF). A novel stochastic integer programming model, which is formulated on a space-time underlying network to simultaneously optimize the train timetable and rolling stock circulation plan with flexible train composition, is proposed by explicitly considering the random feature of passenger distribution on an urban rail transit line. To solve this problem efficiently, the proposed model is decomposed into a master problem and a series of sub-problems regarding different stochastic scenarios. We further prove that each sub-problem model is equivalent to its linear programming relaxation problem, by proving that the coefficient matrix of each linear programming relaxation model is totally unimodular. Then, the classical Benders decomposition algorithm is applied to the studied problem. Based on the model characteristics, both single-cut and multi-cut methods with some speed-up techniques are developed to solve the proposed model in a novel and effective way. Numerical experiments are conducted on small-scale cases and large-scale cases derived from Shanghai Metro Line 17, and the results show that solving the stochastic problem can extract gains in efficiency and the value of stochastic solution tends to be high.