Improved Combinatorial Benders Decomposition for a Scheduling Problem with Unrelated Parallel Machines

Table 1

Comparison of T&B and ICBD methods using the instances from Tran and Beck (2012).

		LB		T&B			ICBD
		% gap	Time	# iter	# cut	Time	# iter	# cut	Time
10	2	0.23	0.05	1.40	2.80	0.10	1.40	2.80	0.11
	3	0.14	0.11	1.20	3.60	0.16	1.20	3.60	0.17
	4	0.44	0.23	1.10	4.40	0.30	1.10	4.40	0.29
	5	0.40	0.23	1.20	6.00	0.34	1.20	6.50	0.33
20	2	0.11	0.18	1.80	3.60	0.45	1.70	4.00	0.42
	3	0.34	0.40	2.10	6.30	0.90	2.00	8.70	0.86
	4	0.18	1.02	1.50	6.00	1.55	1.50	6.00	1.58
	5	0.31	1.85	1.50	7.50	2.79	1.40	7.00	2.59
30	2	0.07	0.33	1.70	3.40	0.71	1.60	3.40	0.66
	3	0.17	0.94	1.80	5.40	1.70	1.70	6.60	1.63
	4	0.27	2.56	1.90	7.60	7.01	1.90	10.80	6.87
	5	0.17	18.19	1.80	9.00	99.49	1.70	10.00	68.15
40	2	0.06	0.72	1.90	3.80	2.02	1.90	4.00	1.94
	3	0.05	1.57	1.60	4.80	2.77	1.50	5.40	2.73
	4	0.17	11.73	1.80	7.20	18.77	1.70	8.00	18.66
	5	0.19	41.14	1.90	9.50	102.10	1.70	12.00	99.24
50	2	0.03	0.69	1.80	3.60	2.23	1.70	4.00	2.14
	3	0.07	3.37	1.50	4.50	6.42	1.50	4.80	5.24
	4	0.12	28.65	1.70	6.80	44.32	1.70	9.20	40.59
	5	0.09	133.74	1.70	8.50	267.45	1.70	12.00	212.99
60	2	0.04	1.44	1.80	3.60	3.89	1.70	3.80	3.79
	3	0.05	5.66	1.80	5.40	8.89	1.70	5.70	8.58
	4	0.05	64.36	1.70	6.80	111.89	1.60	8.00	106.71
	5	0.13	303.25	2.30	11.50	878.30	2.10	15.00	697.76
Average		0.16	25.93	1.69	5.90	65.19	1.62	6.90	53.50