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

Table 7

Computation results of medium-sized instances with |N| = 60.

|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
60 × 2	0.2	0.2	4.67	12.95	18.48	0	0	0	0	5	3600	103.26	0.14	6.28	93.93	2.91
		0.6	6.32	13.39	20.34	0	0	0	0	5	3600	121.10	0.25	6.70	110.34	3.81
		1	10.33	12.06	13.15	0	0	0	0	5	3600	80.23	0.27	5.95	70.30	3.71
	0.6	0.2	15.68	18.95	24.54	0	0.88	2.11	0	2	3600	180.37	0.12	4.95	83.44	91.86
		0.6	12.57	15.97	20.85	0	0.41	2.07	0	4	3600	144.27	0.08	4.41	125.42	14.36
		1	9.86	14.31	17.82	0	0	0	0	5	3600	20.02	0.12	9.54	5.09	5.27
	1	0.2	0	0	0	0	0	0	5	5	417.89	107.97	0.05	69.93	6.67	31.32
		0.6	0	21.28	31.61	0	1.03	2.50	1	1	3600	59.8	0.05	12.19	3.91	43.65
		1	7.03	16.55	25.46	0	0.52	1.32	0	3	3600	23.33	0.08	10.40	5.51	7.34
60 × 3	0.2	0.2	0	0	0	0	0	0	5	5	971.81	11.61	0.17	5.53	2.31	3.60
		0.6	0	5.64	8.69	0	0	0	1	5	2961.22	12.63	0.17	6.70	1.87	3.89
		1	0	6.62	17.39	0	0	0	2	5	2287.86	10.53	0.11	4.77	2.03	3.62
	0.6	0.2	0	0	0	0	0	0	5	5	221.21	28.93	0.05	5.68	19.88	3.32
		0.6	0	13.71	26.03	0	0	0	1	5	2926.07	10.19	0.08	5.14	1.73	3.24
		1	0	14.28	33.12	0	0	0	2	5	2328.03	12.19	0.05	6.46	1.79	3.89
	1	0.2	0	0	0	0	0	0	5	5	228.09	18.75	0.02	9.63	0.69	8.41
		0.6	0	0	0	0	0	0	5	5	235.21	10.96	0.03	5.46	1.24	4.23
		1	0	2.75	13.77	0	0.26	1.33	4	4	935.25	8.39	0.04	3.83	0.80	3.72
Average	—	—	3.69	9.36	15.07	0	0.17	0.52	—	—	2350.70	53.59	0.10	10.20	29.83	13.45