Mathematical Solutions for Solving Periodic Railway Transportation

Table 3

Runtime and journey time in problems with different frequencies.

	B&B	CPLEX (B&B)				LINGO (B&B)		TOPOL.
⟨20,40,𝑓⟩		Heuristic 1.0		Heuristic 1.1		Heuristic 1.1		Heuristic 2
Frequency	Run	Run	Journey	Run	Journey	Run	Journey	Run	Journey
	time	time	time	time	time	time	time	time	time
140	15”	17”	2:16:19	15”	2:20:18	24”	2:16:19	4”	2:18:35
120	156”	16”	2:16:17	14”	2:16:17	23”	2:18:47	4”	2:18:55
100	>5 h.	18”	2:22:55	15”	2:23:10	28”	2:22:55	4”	2:19:09
90	1065”	17”	2:20:34	15”	2:26:25	28”	2:31:58	4”	2:22:08
75	>1 h.	>1 h.	2:29:18	>1 h.	—	25”	2:24:16	6”	2:23:30
60	>1 h.	>1 h.	2:21:23	>1 h.	—	>1 h.	—	46”	2:32:11