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

Table 4

Computation results of small-sized instances with |N| = 15.

|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
15 × 2	0.2	0.2	0	0	0	0	0	0	5	5	50.80	3.74	0.03	0.82	1.50	1.38
		0.6	0	0	0	0	0	0	5	5	78.68	3.46	0.03	1.33	0.51	1.59
		1	0	0	0	0	0	0	5	5	31.00	3.81	0.02	1.06	1.20	1.52
	0.6	0.2	0	0	0	0	0	0	5	5	74.30	2.20	0.03	0.67	0.25	1.25
		0.6	0	0	0	0	0	0	5	5	82.75	6.17	0.1	2.57	1.21	2.29
		1	0	0	0	0	0	0	5	5	21.00	6.42	0.02	3.50	0.45	2.45
	1	0.2	0	0	0	0	0	0	5	5	9.00	1.79	0.02	0.47	0.08	1.22
		0.6	0	0	0	0	0	0	5	5	67.52	2.94	0.02	1.09	0.05	1.78
		1	0	0	0	0	0	0	5	5	11.80	3.57	0.02	1.29	0.14	2.13
15 × 3	0.2	0.2	0	0	0	0	0	0	5	5	15.21	3.25	0.03	1.09	0.59	1.54
		0.6	0	0	0	0	0	0	5	5	9.53	2.04	0.03	0.55	0.23	1.23
		1	0	0	0	0	0	0	5	5	10.86	1.79	0.03	0.49	0.16	1.11
	0.6	0.2	0	0	0	0	0	0	5	5	12.32	1.39	0.02	0.31	0.08	0.97
		0.6	0	0	0	0	0	0	5	5	11.06	5.74	0.03	2.64	0.19	2.88
		1	0	0	0	0	0	0	5	5	18.62	1.84	0.02	0.48	0.19	1.14
	1	0.2	0	0	0	0	0	0	5	5	13.68	1.34	0.02	0.24	0.08	1.00
		0.6	0	0	0	0	0	0	5	5	10.22	1.75	0.02	0.38	0.10	1.25
		1	0	0	0	0	0	0	5	5	11.85	1.23	0.02	0.22	0.05	0.94
Average	—	—	0	0	0	0	0	0	—	—	30.01	3.03	0.03	1.07	0.39	1.54