Joint optimization of train timetabling and rolling stock circulation planning: A novel flexible train composition mode

Document Type

Journal Article

Publication Date


Subject Area

economics - operating costs, infrastructure - rolling stock, mode - subway/metro, operations - scheduling, place - asia, place - urban, ridership - commuting, ridership - demand


Train timetable, Flexible train composition mode, Rolling stock circulation plan, VNS algorithm


The tidal traffic phenomenon is one of the most prominent problems on some metro lines, where a large number of commuters during the peak hours might cause the non-equilibrium spatial–temporal distribution of passenger flow. In order to better match the passenger demand, this study proposes a mixed-integer linear programming (MILP) model to jointly optimize the train timetable and rolling stock circulation plan, in which the flexible train composition mode is particularly taken into account by allowing rolling stocks to change their compositions through uncoupling/coupling operations at the both ends of the focused metro line. To solve the model, a customized heuristic algorithm based on the variable neighborhood search (VNS) is developed to quickly generate high-quality solutions. Based on a small example and the real-world data from Beijing metro Batong line, two sets of numerical experiments are conducted to verify the effectiveness and applicability of the proposed methodology. The computation results show that in comparison to the fixed train composition mode, the proposed approaches can bring 17.1% reduction of operation costs in morning peak periods, with no increase of passenger waiting time.


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


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