A Benders Decomposition Algorithm for the Passenger Train Service Planning

Table 4

Computational results for the instances.

Instance			BD & VI			BD			CPLEX
			Gap (%)	Opt	Time (s)	Gap (%)	Opt	Time (s)	Gap (%)	Opt	Time (s)
BJN-CZS	15	56	1.42	1007030.22	60.87	0.34	1007025.22	84.99	0.26	1006415.22	1161.22
BJN-JNS	16	65	0.00	1320651.85	86.81	1.84	1321351.85	119.47	–	–	1200
BJN-CZN	19	90	2.03	1428609.89	135.07	2.14	1428094.89	176.08	–	–	1200
BJN-WXE	20	100	1.86	1527330.60	238.21	10.75	1527630.60	1200	–	–	1200
BJN-SZN	21	110	1.73	1675569.06	324.06	12.82	1700734.06	1200	–	–	1200
BJN-KSS	22	121	1.40	2148337.43	350.04	33.48	2151112.43	1200	–	–	1200
BJN-SHH	23	132	2.47	2773026.40	1111.57	49.80	2801321.40	1200	–	–	1200