Train Platforming Problem - Geoinformatics for Intelligent Transportation - page 154

For every time interval, the mathematical programming model was solved using
the lexicographic approach described in the previous section. In case that the exact
algorithm (branch and bound method) did not

finish in a predetermined computa-
tional time (30 min) then the local branching heuristic was applied.
The computational experiments were performed for a shortened change time
which is 4 min in Prague main stations, as well as for the normal change time
(8 min). The results for the shortened time are reported in Table 1 and for the
normal change time in Table 2 .
The results of computational experiments show that the timetable was not correct
with regard to safety requirements. There were some trains travelling on con icting

routes concurrently. That is why their desired arrival or departure times could not be
kept. Moreover, in some cases the original timetable did not respect desired time
passengers need to change trains. However the model respects such connections.
The best solution proposed by the model with the shortened change time delays 3
trains at arrival by 5 min and 12 trains at departure by 17 min in total, and
dispatches 31 (11 %) trains to platform tracks different from the planned ones.
Departures of 7 trains are postponed by 1 min and 5 trains by 2 min. For the normal
change time, 3 trains are delayed at arrival by 5 min and 16 trains are delayed at
departure by 27 min in total (8 trains by 1 min, 6 trains by 2 min, 1 train by 3 min
and 1 train by 4 min). 32 trains are dispatched to platform tracks different from the
planned ones.
Other experiments were performed to investigate:

fl

how decomposition of planning period in uences the computational time and

the quality of obtained solution within 30 min limit for computing,

fl

￿

how train delays in fl uence the track occupancy plan,

￿

ef ciency of the branch and bound and local branching methods.

￿

4 Conclusion

In the paper, a mixed integer programming model for the train platforming problem
at a passenger railway station is described. The model proposes a track occupancy
plan that respects safety constraints for train movements and relations between
connecting trains, minimises deviations of the arrival and departure times from the
timetable and maximises the desirability of the platform tracks to be assigned to the
trains. The model could serve as a planner ' s decision supporting tool.

Acknowledgments This research was supported by the Scienti c Grant Agency of the Ministry
of Education of the Slovak Republic and the Slovak Academy of Sciences under project VEGA 1/
0296/12 “ Public service systems with fair access to service ” and by the Slovak Research and

Development Agency under project APVV-0760-11 “ Designing of Fair Service Systems on

Transportation Networks ” .