A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

Table 6

Computation results of medium-sized instances with |N| = 40.

|N| × |M|	TF	R	Gap (%)						No. of optimal solutions		CPU(s)
			MILP			CG					MILP			CG
			Min	Ave	Max	Min	Ave	Max	MILP	CG	Total	Total	CH	LP	MILP	DE
40 × 2	0.2	0.2	0.00	2.13	10.66	0	0	0	4	5	1610.20	30.18	0.11	3.21	25.07	1.79
		0.6	0	0	0	0	0	0	5	5	134.47	10.18	0.07	3.55	4.42	2.14
		1	0	0	0	0	0	0	5	5	213.20	10.25	0.12	3.48	4.02	2.63
	0.6	0.2	0	14.68	33.19	0	1.33	3.91	2	2	2204.82	358.08	0.14	2.96	347.32	7.66
		0.6	0	3.79	17.45	0	0.35	0.88	3	3	447.67	87.96	0.07	2.59	18.79	66.52
		1	0	10.37	22.02	0	0.66	1.96	1	3	2907.40	52.63	0.07	4.18	16.70	31.68
	1	0.2	0	0	0	0	0	0	5	5	758.61	23.04	0.03	11.89	0.44	10.68
		0.6	0	0	0	0	0	0	5	5	182.65	16.58	0.03	5.29	1.13	10.13
		1	0	0	0	0	0	0	5	5	110.00	14.02	0.20	2.94	0.78	10.10
40 × 3	0.2	0.2	0	0	0	0	0	0	5	5	96.61	9.87	0.08	4.09	2.91	2.79
		0.6	0	0	0	0	0	0	5	5	92.25	5.58	0.09	2.67	0.68	2.14
		1	0	0	0	0	0	0	5	5	130.82	2.38	0.07	0.73	0.18	1.40
	0.6	0.2	0	0	0	0	0	0	5	5	107.20	10.61	0.05	4.30	3.32	2.94
		0.6	0	0	0	0	0	0	5	5	239.68	8.02	0.04	3.18	1.96	2.84
		1	0	0	0	0	0	0	5	5	75.25	14.00	0.05	7.95	1.78	4.22
	1	0.2	0	0	0	0	0	0	5	5	77.21	7.16	0.04	2.99	0.32	3.81
		0.6	0	0	0	0	0	0	5	5	96.63	52.56	0.04	6.00	1.25	45.27
		1	0	0	0	0	0	0	5	5	92.20	3.46	0.03	1.28	0.30	1.85
Average	—	—	0	1.72	4.63	0	0.13	0.38	—	—	532.05	39.81	0.07	4.07	23.97	11.70