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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Vydané v:	Transportation research. Part B: methodological Ročník 76; s. 117 - 135
Hlavní autori:	Niu, Huimin, Zhou, Xuesong, Gao, Ruhu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.06.2015
Predmet:	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
On-line prístup:	Získať plný text
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Abstract	•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.
AbstractList	•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. 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.
Author	Gao, Ruhu Niu, Huimin Zhou, Xuesong
Author_xml	– sequence: 1 givenname: Huimin surname: Niu fullname: Niu, Huimin email: hmniu@mail.lzjtu.cn organization: School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China – sequence: 2 givenname: Xuesong surname: Zhou fullname: Zhou, Xuesong email: xzhou74@asu.edu organization: School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85287, United States – sequence: 3 givenname: Ruhu surname: Gao fullname: Gao, Ruhu email: ruhugao@hotmail.com organization: School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China
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ContentType	Journal Article
Copyright	2015 Elsevier Ltd
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Keywords	Nonlinear mixed integer programming Time-varying demand Passenger waiting time Train timetable Skip-stop pattern
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Snippet	•Optimization models for train scheduling problem for minimizing passenger waiting time.•Quadratic functional form for computing waiting time under... 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...
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SubjectTerms	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
Title	Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints
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