### Abstract

We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. examined the optimal way to allocate the running time supplement. The uncertain disturbances in a railway were modeled using random variables. In their model, it was assumed that there was an upper limit to the total supplement, but its allocation was not restricted. In this paper, we suggest an improvement to the previous model and present a new stochastic programming model in which there is a constraint on the running time supplement allocated to each trip to minimize the expected delay. Then a solution algorithm to solve the problem is developed. In the previous model, allocation of the running time supplement was biased because it was not allocated to all trips. We balance the amounts of supplements for trips by adding upper and lower bounds. The fluctuations of the supplements for trips become small, and the probability of a delay decreases using our new model. Then the calculation times using the L-shaped algorithm and the former method solving a deterministic equivalent of large-scale problems are compared. It is shown that the large-scale problems can be solved effectively by using the L-shaped method.

Original language | English |
---|---|

Journal | Journal of Advanced Mechanical Design, Systems and Manufacturing |

Volume | 10 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

- L-shaped method
- Multistage stochastic programming
- Optimization
- Railway timetable
- Running time supplement

### ASJC Scopus subject areas

- Mechanical Engineering
- Industrial and Manufacturing Engineering

### Cite this

**Multistage stochastic programming model for optimizing allocation of running time supplements.** / Shiina, Takayuki; Morito, Susumu; Imaizumi, Jun.

Research output: Contribution to journal › Article

*Journal of Advanced Mechanical Design, Systems and Manufacturing*, vol. 10, no. 3. https://doi.org/10.1299/jamdsm.2016jamdsm0043

}

TY - JOUR

T1 - Multistage stochastic programming model for optimizing allocation of running time supplements

AU - Shiina, Takayuki

AU - Morito, Susumu

AU - Imaizumi, Jun

PY - 2016

Y1 - 2016

N2 - We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. examined the optimal way to allocate the running time supplement. The uncertain disturbances in a railway were modeled using random variables. In their model, it was assumed that there was an upper limit to the total supplement, but its allocation was not restricted. In this paper, we suggest an improvement to the previous model and present a new stochastic programming model in which there is a constraint on the running time supplement allocated to each trip to minimize the expected delay. Then a solution algorithm to solve the problem is developed. In the previous model, allocation of the running time supplement was biased because it was not allocated to all trips. We balance the amounts of supplements for trips by adding upper and lower bounds. The fluctuations of the supplements for trips become small, and the probability of a delay decreases using our new model. Then the calculation times using the L-shaped algorithm and the former method solving a deterministic equivalent of large-scale problems are compared. It is shown that the large-scale problems can be solved effectively by using the L-shaped method.

AB - We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. examined the optimal way to allocate the running time supplement. The uncertain disturbances in a railway were modeled using random variables. In their model, it was assumed that there was an upper limit to the total supplement, but its allocation was not restricted. In this paper, we suggest an improvement to the previous model and present a new stochastic programming model in which there is a constraint on the running time supplement allocated to each trip to minimize the expected delay. Then a solution algorithm to solve the problem is developed. In the previous model, allocation of the running time supplement was biased because it was not allocated to all trips. We balance the amounts of supplements for trips by adding upper and lower bounds. The fluctuations of the supplements for trips become small, and the probability of a delay decreases using our new model. Then the calculation times using the L-shaped algorithm and the former method solving a deterministic equivalent of large-scale problems are compared. It is shown that the large-scale problems can be solved effectively by using the L-shaped method.

KW - L-shaped method

KW - Multistage stochastic programming

KW - Optimization

KW - Railway timetable

KW - Running time supplement

UR - http://www.scopus.com/inward/record.url?scp=84977106583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977106583&partnerID=8YFLogxK

U2 - 10.1299/jamdsm.2016jamdsm0043

DO - 10.1299/jamdsm.2016jamdsm0043

M3 - Article

AN - SCOPUS:84977106583

VL - 10

JO - Journal of Advanced Mechanical Design, Systems and Manufacturing

JF - Journal of Advanced Mechanical Design, Systems and Manufacturing

SN - 1881-3054

IS - 3

ER -