Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

•Optimization models for train scheduling problem for minimizing passenger waiting time.•Quadratic functional form for computing waiting time under time-dependent OD demand.•Reformulations for linking train inter-arrival events under skip-stop patterns.•Implemented and efficiently solved by general...

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Bibliographic Details
Published in:Transportation research. Part B: methodological Vol. 76; pp. 117 - 135
Main Authors: Niu, Huimin, Zhou, Xuesong, Gao, Ruhu
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2015
Subjects:
Demand
Mathematical models
Nonlinear mixed integer programming
Nonlinearity
Passenger trains
Passenger waiting time
Passengers
Rails
Scheduling
Skip-stop pattern
Stations
Time-varying demand
Train timetable
Nonlinear mixed integer programming
Time-varying demand
Passenger waiting time
Train timetable
Skip-stop pattern
ISSN:0191-2615, 1879-2367
Online Access:Get full text
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Summary:•Optimization models for train scheduling problem for minimizing passenger waiting time.•Quadratic functional form for computing waiting time under time-dependent OD demand.•Reformulations for linking train inter-arrival events under skip-stop patterns.•Implemented and efficiently solved by general purpose high-level optimization solvers. This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.
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ISSN:0191-2615
1879-2367
DOI:10.1016/j.trb.2015.03.004