Abstract
For the train timetabling problem (TTP) in a metro system, the operator-oriented and passenger-oriented objectives are both important but partly conflicting. This paper aims to minimize both objectives by considering frequency (in the line planning stage) and train cost (in the vehicle scheduling stage). Time-varying passenger demand and train capacity are considered in a nonsmooth, nonconvex programming model, which is transformed into a mixed integer programming model with a discrete time-space graph (DTSG). A novel dwell time determining process considering congestion at stations is proposed, which turns the dwell times into dependent variables. In the solution approach, we decompose the TTP into a subproblem for optimizing segment travel times (OST) and a subproblem for optimizing departure headways from the shunting yard (OH). Branch-and-bound and frequency determining algorithms are designed to solve OST. A novel rolling optimization algorithm is designed to solve OH. The numerical experiments include case studies on a short metro line and Beijing Metro Line 4, as well as sensitivity analyses. The results demonstrate the predictive ability of the model, verify the effectiveness and efficiency of the proposed approach, and provide practical insights for different scenarios, which can be used for decision-making support in daily operations.
Highlights
With increasing concerns about urban congestion and climate change, urban metro rail transportation receives increasing attention due to its high capacity, punctuality and sustainability
Wang et al [3] only consider the objectives in one stage, that is, timetabling stage; Robenek et al [2] integrate passenger satisfaction and operating profit but do not consider frequency and energy; Schobel [8] takes into account objectives in all stages with an iterating framework; crucial factors such as passenger wait time, dwell time, and train capacity are missing
We develop a novel rolling optimization approach to solve the model, which combines the benefits of rolling horizon and iterative optimization
Summary
With increasing concerns about urban congestion and climate change, urban metro rail transportation receives increasing attention due to its high capacity, punctuality and sustainability. This paper proposes a rolling optimization algorithm to obtain noncyclic timetables considering time-varying passenger demand and the effects of congestion at stations. It integrates the objectives in the line planning (frequency), timetabling (conflicting objectives including passenger wait/in-vehicle time and energy), and vehicle scheduling (train cost). Schobel [8] considers the line planning, timetabling and vehicle scheduling in an integrated way, with passenger- and cost-oriented objectives Since his eigenmodel is general and resulting approaches are generic, important objectives described in this paper are not considered in his work, that is, passenger wait time, dwell time, and train capacity.
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