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

Table 4

Comparison of T&B and ICBD relative to traditional and proposed convergence acceleration elements.

		T&B		⁢ICBD
		# iter	# cut	# ta	# ws iter	# iter	# ws cut	# cut	ws time	Original time
20	2	4.27	0.00	0.57	5.43	1.20	22.97	3.73	1.12	0.33
	3	5.17	0.00	0.53	4.87	1.50	33.73	7.60	1.97	0.75
	4	5.77	0.00	0.50	4.90	1.20	44.13	6.83	5.09	1.93
	5	5.13	0.00	0.43	5.07	1.73	20.80	5.37	2.22	6.44
30	2	8.07	0.00	1.07	5.80	1.83	31.47	8.10	3.59	1.18
	3	10.77	0.00	1.77	7.03	1.80	62.07	10.97	23.71	6.28
	4	8.80	0.00	1.13	6.20	1.33	66.63	8.07	46.64	59.3
	5	3.90	0.00	0.23	4.37	1.53	16.47	4.90	7.91	35.07
40	2	8.57	0.00	1.70	6.33	1.90	36.17	8.13	7.43	1.84
	3	11.70	0.00	1.53	7.60	1.23	67.93	5.77	44.02	7.75
	4	9.43	0.00	2.00	6.97	1.47	88.10	10.80	347.75	45.53
	5	5.90	0.00	0.97	5.37	2.20	29.00	8.03	55.59	369.05
50	2	13.63	0.00	3.70	7.20	3.90	45.10	21.83	17.25	3.4
	3	11.97	0.00	2.60	8.47	1.97	80.27	11.33	293.77	83.28
	4	12.27	0.00	3.40	8.43	1.67	116.30	12.97	841.21	303.00
	5	8.03	0.00	1.83	6.27	2.33	49.87	11.73	307.05	947.89
60	2	12.07	0.00	3.37	7.93	2.87	50.47	16.70	42.00	8.39
	3	18.17	0.00	5.17	10.73	2.73	107.07	17.40	328.53	188.97
	4	10.40	0.00	4.40	9.00	1.53	130.63	13.80	1185.92	443.66
	5	8.20	0.00	4.40	8.60	1.20	161.00	22.00	1802.03	1179.53
Average		9.11	0.00	2.07	6.83	1.86	63.01	10.80	268.24	184.68