A Combinatorial Benders’ Cuts Algorithm for the Local Container Drayage Problem

Table 2

Computational results.

Number		CBC				Branch-and-cut (CPLEX)				CBC without CUT_1,  2,  3				Ga	Ga
		Best^1	CPU (s)	Nodes	Cuts	Best^2	CPU (s)	Nodes	Cuts	Best^3	CPU (s)	Nodes	Cuts
1	2/2	20.5	0.2		153	20.5	15.9		12	20.5	2.7		266	0.00	0.00
2	2/3	21.4	1.1		871	21.4	4390.8		24	21.4	4.1		2117	0.00	0.00
3	3/2	23.6	10.8		2165	23.6	11343.3		23	23.6	32.2		4290	0.00	0.00
4	3/3	22.8	99.6		8107	24.1	18000		6	22.8	203.7		22447	5.70	0.00
5	3/4	38.7	1310.1		25889	39.3	18000		5	38.7	3326.0		39625	1.55	0.00
6	4/3	36.8	1289.5		20167	36.8	18000		11	36.8	4058.2		38731	0.00	0.00
7	4/4	37.9	12173.2		45063	38.5	18000		1	37.9	18000		78003	1.58	0.00
8	4/5	39.2	18000		101859	39.2	18000		0	39.2	18000		123750	0.00	0.00
9	5/4	40.8	18000		142137	45.6	18000		10	41.6	18000		152196	11.76	1.96
10	5/5	39.2	18000		143221	43.5	18000		1	41.0	18000		157769	10.97	4.59
11	2/8	38.7	18000		159763	45.3	18000		1	38.7	18000		173281	17.05	0.00
12	3/7	36.0	18000		137129	37.6	18000		2	36.6	18000		165594	4.44	1.67
13	4/6	40.6	18000		130077	47.4	18000		0	44.5	18000		161036	16.75	9.61
14	6/4	38.1	18000		121977	38.4	18000		4	38.1	18000		145782	0.79	0.00
15	7/3	39.7	18000		159195	44.7	18000		2	41.6	18000		173282	12.59	4.79
16	8/2	39.0	18000		121764	44.5	18000		20	40.6	18000		162649	14.10	4.10
Average														6.08	1.67

Gap = (Best²  − Best¹)/Best¹ (%).
Gap = (Best³  − Best¹)/Best¹ (%).