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

Table 5

Computation results of small-sized instances with |N| = 20.

|N| × |M|	TF	R	Gap (%)						No. of optimal solutions		CPU(s)
			MILP			CG			MILP	CG	MILP			CG
			Min	Ave	Max	Min	Ave	Max	MILP	CG	Total	Total	CH	LP	MILP	DE
20 × 2	0.2	0.2	0	0	0	0	0	0	5	5	119.14	3.24	0.03	1.08	0.68	1.45
		0.6	0	0	0	0	0	0	5	5	68.63	4.49	0.03	1.91	0.64	1.91
		1	0	0	0	0	0	0	5	5	32.27	3.58	0.03	1.30	0.28	1.97
	0.6	0.2	0	0	0	0	0	0	5	5	45.83	6.11	0.04	1.90	2.25	1.92
		0.6	0	0	0	0	0	0	5	5	22.23	4.88	0.02	2.46	0.77	1.63
		1	0	0	0	0	0	0	5	5	42.65	5.05	0.02	2.04	0.46	2.53
	1	0.2	0	0	0	0	0	0	5	5	20.60	6.55	0.02	2.46	0.05	4.02
		0.6	0	0	0	0	0	0	5	5	19.86	7.19	0.02	2.74	0.42	4.01
		1	0	0	0	0	0	0	5	5	29.80	5.83	0.02	2.23	0.32	3.26
20 × 3	0.2	0.2	0	0	0	0	0	0	5	5	45.21	5.24	0.07	1.53	0.54	3.10
		0.6	0	0	0	0	0	0	5	5	39.03	5.28	0.12	1.74	0.32	3.10
		1	0	0	0	0	0	0	5	5	71.07	6.27	0.03	1.95	0.61	3.68
	0.6	0.2	0	0	0	0	0	0	5	5	48.03	6.03	0.03	1.95	0.78	3.27
		0.6	0	0	0	0	0	0	5	5	57.81	6.75	0.02	2.05	0.51	4.17
		1	0	0	0	0	0	0	5	5	45.02	5.71	0.02	1.58	0.57	3.54
	1	0.2	0	0	0	0	0	0	5	5	36.20	6.82	0.02	2.10	0.15	4.55
		0.6	0	0	0	0	0	0	5	5	37.69	3.19	0.02	0.68	0.11	2.38
		1	0	0	0	0	0	0	5	5	42.03	3.32	0.13	0.61	0.18	2.40
Average	—	—	0	0	0	0	0	0	—	—	45.73	5.31	0.04	1.80	0.54	2.94