Mixed integer programming for minimizing the period of a cyclic railway timetable for a single track with two train types

Heydar, Mojtaba; Petering, Matthew E. H.; Bergmann, Dietrich R.

doi:10.1016/j.cie.2013.06.003

Cited by 45 publications

(26 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Some studies on the periodical timetable include Odijk [16], Peeters and Kroon [12], Kroon and Peeters [17], Liebchen [18], Shafahi and Khani [5], Heydar et al [19], Kang et al [8], etc.…”

Section: Literature Reviewmentioning

confidence: 99%

A simulated annealing algorithm for first train transfer problem in urban railway networks

Kang

Zhu

2016

Applied Mathematical Modelling

View full text Add to dashboard Cite

a b s t r a c tPassengers often have to transfer between different subway lines to reach their destinations. Time coordination of first trains between feeder and connecting lines plays an important role in reducing passenger transfer waiting time. This paper addresses the first train synchronization problem, and proposes a first train coordination model which aims at minimizing total passenger transfer waiting time. Taking into account the specification of the first train problem, we use mixed-integer variables to enable the correct calculation of the waiting time for the ''first available'' train at each transfer station. In addition, we develop a simulated annealing algorithm to deal with a case study of the Beijing subway network. Results indicate that the proposed approach reduces the passenger waiting time from 705.1 min of the original first train timetable to 567.42 min of the scheduled one.

show abstract

“…Some studies on the periodical timetable include Odijk [16], Peeters and Kroon [12], Kroon and Peeters [17], Liebchen [18], Shafahi and Khani [5], Heydar et al [19], Kang et al [8], etc.…”

Section: Literature Reviewmentioning

confidence: 99%

A simulated annealing algorithm for first train transfer problem in urban railway networks

Kang

Zhu

2016

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…It is assumed that in (1) both terms have equally important. However, in order to create a pool of optimal solution, one can consider a multiple objective model and use the weighted sum approach . The new objective function will be converted to

a_{1} true {true\sum}_{i \in N} true {true\sum}_{\begin{matrix} left \\ j \in N \\ j \neq i \end{matrix}} true {true\sum}_{b \in B} t_{i j b} x {}_{i j b} + a_{2} true {true\sum}_{l \in L} true {true\sum}_{p \in P} w_{l p} z_{l p}

, where a 1 and a 2 are weights for the routing part and the assignment part, respectively, and a 1 + a 2 = 1.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

Heydar

Liu

et al. 2016

J of Advced Transportation

Self Cite

View full text Add to dashboard Cite

Summary This paper presents a mathematical model to plan emergencies in a densely populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features an integrated operational framework, which simultaneously guides evacuees through urban streets and crosswalks (referred to as “the pedestrian network”) to designated pickup points (e.g., bus stops), and routes a fleet of buses at different depots to those pick‐up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so‐called “vehicular network.” An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in two networks. Because the large instances of the proposed model are mathematically difficult to solve to optimality, a two‐stage heuristic is developed to solve larger instances of the model. Results from hundreds of numerical examples analysis indicate that proposed heuristic works well in providing (near) optimal or feasibly good solutions for medium‐scale to large‐scale instances that may arise in real transit‐based evacuation situations in a much shorter amount of computational time compared with cplex (can find optimal/feasible solutions for only five instances within 3 hours of running). Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

“…one hour, then the schedule is repeated for the total scheduling time window e.g. one day (Vromans, 2005;Erol, 2009 Caprara et al (2007), Kroon et al (2008a), Liebchen et al (2010), Heydar et al (2013). We also refer to Robenek et al (2014) for a literature review on cyclic and non-cyclic models.…”

Section: Different Types Of Ttpmentioning

confidence: 99%

Optimization-Based Methods for Revising Train Timetables with Focus on Robustness

Khoshniyat¹

2016

View full text Add to dashboard Cite

With increase in the use of railway transport, ensuring robustness in railway timetables has never been this important. In a dense railway timetable even a small disturbance can propagate easily and aect trains' arrival and departure times. In a robust timetable small delays are absorbed and knock-on eects are prevented eectively.The aim of this thesis is to study how optimization tools can support the generation of robust railway trac timetables. We address two Train Timetabling Problems (TTP) and for both problems we apply Mixed Integer Linear Programming (MILP) to solve them from network management perspectives. The rst problem is how robustness in a given timetable can be assessed and ensured. To tackle this problem, a headway-based method is introduced. The proposed method is implemented in real timetables and evaluated from performance perspectives. Furthermore, the impact of the proposed method on capacity utilization, heterogeneity and the speed of trains, is monitored.Results show that the proposed method can improve robustness without imposing major changes in timetables. The second problem addressed in the thesis is how robustness can be assessed and maintained in a given timetable when allocating additional trac and maintenance slots. Dierent insertion strategies are studied and their consequences on capacity utilization and on the properties of the timetables are analyzed. Two dierent insertion strategies are considered: i) simultaneous and ii) stepwise insertion. The results show that inserting the additional trains simultaneously usually results in generating more optimal solutions. However, solving this type of problem is computationally challenging. We also observed that the existing robustness metrics cannot capture the essential properties of having more robust timetables. Therefore we proposed measuring Channel Width, Channel Width Forward, Channel Width Behind and Track Switching. This thesis contains three papers which are appended. The results of this thesis are of special interests for railway trac planners and it would support their working process. However, railway trac operators and passengers also benet from this study.iii

show abstract

Mixed integer programming for minimizing the period of a cyclic railway timetable for a single track with two train types

Cited by 45 publications

References 48 publications

A simulated annealing algorithm for first train transfer problem in urban railway networks

A simulated annealing algorithm for first train transfer problem in urban railway networks

Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

Optimization-Based Methods for Revising Train Timetables with Focus on Robustness

Contact Info

Product

Resources

About