Mathematical Solutions for Solving Periodic Railway Transportation

Table 1

Runtime and journey time in problems with different number of trains.

	B&B	CPLEX (B&B)				LINGO (B&B)		TOPOL.
⟨𝑛,40,90⟩		Heuristic 1.0		Heuristic 1.1		Heuristic 1.1		Heuristic 2
Trains	Run	Run	Journey	Run	Journey	Run	Journey	Run	Journey
	time	time	time	time	time	time	time	time	time
5	6”	5”	2:19:48	4”	2:29:33	6”	2:30:54	2”	2:21:54
10	337”	8”	2:20:19	8”	2:26:04	12”	2:31:37	3”	2:22:08
15	601”	13”	2:20:29	12”	2:26:18	19”	2:31:51	3”	2:22:08
20	1065”	16”	2:20:34	16”	2:26:25	25”	2:31:58	3”	2:22:08
50	>5 h.	55”	2:20:43	43”	2:31:09	1098”	2:32:11	7”	2:22:08