A two-step linear programming model for energy-efficient timetables in metro railway networks

Document Type

Journal Article

Publication Date


Subject Area

place - asia, mode - subway/metro, mode - rail, operations - scheduling


Railway networks, Energy efficiency, Regenerative braking, train scheduling, Linear programming


In this paper we propose a novel two-step linear optimization model to calculate energy-efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and maximizes the utilization of regenerative energy produced by braking trains, subject to the constraints in the railway network. In contrast to other existing models, which are NP-hard, our model is computationally the most tractable one being a linear program. We apply our optimization model to different instances of service PES2-SFM2 of line 8 of Shanghai Metro network spanning a full service period of one day (18 h) with thousands of active trains. For every instance, our model finds an optimal timetable very quickly (largest runtime being less than 13 s) with significant reduction in effective energy consumption (the worst case being 19.27%). Code based on the model has been integrated with Thales Timetable Compiler - the industrial timetable compiler of Thales Inc that has the largest installed base of communication-based train control systems worldwide.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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