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

Table 3

Results for the scenarios from Table 1 with Reordering strategy (sub-problem 2).

Number of additional trains	Total number of changed orders	Lower bound ()	Upper bound ()	Objective value^1	Time^2
10	1	0	0	0	10.00
11	2	0	0	0	12.31
12	2	0	0	0	18.65
13	3	0	75	(75)	(90)
14	3	0	75	(75)	(90)
15	3	0	75	(75)	(90)

The numbers in the parentheses refer to the current best feasible solution () found when the time limit of 90 seconds was exceeded without an optimal solution being verified.
²The numbers in the parentheses refer to exceed the time limit of 90 seconds.