Train platforming problem

Ľudmila Jánošíková Michal Krempl

University of Žilina, VŠB-Technical University of Ostrava,

Slovak Republic Czech Republic

Train platforming problem

The train platforming problem consists in the allocation of passenger trains to platforms in a railway station.

The solution is a track occupancy plan.

The plan is a dispatcher’s decision support tool.

It specifies for each arriving or departing train the platform track the time slot during which the track will be occupied by the

train.

Track occupancy plan

Benefits

better management of train operation

• train routes are occupied shorter time

• workload of the infrastructure elements, such as tracks, switches, and platforms is more uniform

higher service quality perceived

by passengers

• shorter distances needed for changing trains

• less probability of changing the planned platform when the train delays

• regular platforms for the same direction

meeting train operators’

requirements

• on arrival and departure times and platforms

Problem description

Given list of the trains arriving, departing, or travelling through the

station network timetable safety rules for train movements layout of the station

The train platforming problem: assign a route through the station to each of the trains, adjust the arrival and departure times due to safety or

capacity reasons.

Track layout

Problem description

Criteria:

1. minimise deviations from the planned arrival and departure times

2. maximise preferences of trains for platforms

Mathematical programming model

Variables

adjust the arrival and departure timesui real arrival time of train i at a platform, i Uvi real departure time of train i from a platform, i U

assign a route through the station to each of the trains

otherwise0

train toassigned is track if1:,for

ikxiKkUi ik

Notation

U set of all arriving, departing, and transit trains

K(i) set of feasible platform tracks for train i

Mathematical programming model

and similar variables for combinations arrival – departure, departure – arrival, departure – departure.

Auxiliary variables - model safety headways between conflicting trains:

otherwise0

arrives trainbefore arrives trainif1:,,for

jiyjiUji aa

ij

Solution method

Mathematical programming MIP model with a huge number of variables (> 45 000) and constraints (> 700 000)

Decompositiono 0:00 – 5:00o 5:00 – 8:00o 8:00 – 10:00o 10:00 – 12:00o 12:00 – 15:00o 15:00 – 18:00o 18:00 – 24:00

Local branching metaheuristics

Prague main station Timetable 2004/2005, 4 min change time

Period No. of trains

Deviation (min) Different platform assignmentsarrival departure

0:00 - 5:00 20 0 0 0

5:00 - 8:00 56 2 2 5

8:00 - 10:00 45 0 5 8

10:00 - 12:00 37 0 2 5

12:00 - 15:00 52 1 2 9

15:00 - 18:00 54 0 2 0

18:00 - 24:00 77 2 4 4

Total 5 17 31 (11%)

The model proposes a feasible track occupancy plan that: respects safety constraints for train movements minimises deviations of the arrival and departure times

from the timetable maximises preferences for the platform tracks respects relations between connecting trains:

ensures that passengers have enough time to change trains

minimises distance between connecting trains

Conclusions