A Branch and Bound Algorithm and Iterative Reordering Strategies for Inserting Additional Trains in Real Time: A Case Study in Germany

Table 2

Results of inserting additional trains to a fixed order timetable (subproblem 1).

Number of additional trains	Lower bound ()	Upper bound ()	Percentage of in	Time
1	0	0	100	0.02
2	0	0	100	0.26
3	0	0	100	0.27
4	0	0	100	0.29
5	0	0	100	1.26
6	0	0	100	1.56
7	0	0	100	1.93
8	0	0	100	2.90
9	0	0	100	3.38
10	1	143	87.22	3.67
11	1	143	87.29	4.14
12	1	143	87.37	4.62
13	1	423	93.10	16.20
14	2	423	92.91	17.82
15	2	423	93.00	24.17