Joint rolling stock rotation planning and depot deadhead scheduling in complicated urban rail transit lines

This study investigates the joint rolling stock rotation planning and depot deadhead scheduling in complicated urban rail transit lines with multiple depots, multiple line services, and multiple compositions. The rotation planning aims at connecting the given train trips into train sequences (each of which is served by an individual rolling stock) and determining the routing plan of rolling stocks to pass through visited turnback stations while connecting train trips. The task of the depot deadhead scheduling is to determine conflict-free deadhead routes and deadhead timetables of rolling stocks between the origin/destination of each train sequence and corresponding depot. We formulate the studied problem as a generalized set partitioning-type model containing an exponential number of variables, by using a new time-space network representation and by proposing a novel modelling method for the departure-arrival headway requirement to control the number of constraints. Owing to the complexity of this model, a column generation-based algorithm is adopted to solve efficiently practical-size problems. We enhance a standard column generation (to compute tight lower bound) by further incorporating procedures of variable rounding and halted column generation, to strengthen the capability of searching for better quality solutions. Customized acceleration mechanisms are also explored to speed up the convergence of column generation and the computation of best-known integer solution. We compare our approach with three benchmark approaches and the trial-and-error-based empirical method used by rail dispatchers in practice. Computational results reveal that our approach outperforms these benchmark approaches by computing (near-)optimal solutions. Our optimized solution for a large real-world instance (computed within a practically reasonable computation time) is better than the empirical solution, in terms of all the considered objective function parts.