Table 2: Sets defined for modeling.

Set nameDescriptionSizeIndex
of set

TrnAll the trains
SegAll the segments
All the stations
All the sectionsSN
ItvAll the intervals where an interval is the possession of a segment by a train with specified start and end timesp
The ordered set of intervals for train according to the original timetable
The ordered set of intervals associated with stopping at stations for trains
The ordered set of intervals for segment according to the original timetable
All the tracks of station

Remarks: for the ease of understanding, we use p as the index for every interval-related set (i.e., Itv, , , and ). In each of the interval-related sets, p + 1 indicates the first subsequent interval of p, and indicates all the subsequent intervals of p.