A Single-Machine Two-Agent Scheduling Problem by a Branch-and-Bound and Three Simulated Annealing Algorithms

Table 2

RPD of heuristic algorithms ( = 20~60).

	Pro		SA1				SA2				SA3
			CPU time		RPD		CPU time		RPD		CPU time		RPD
			Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.
20	0.25	25	0.0019	0.0051	0.45	1.44	0.0019	0.0051	0.41	1.19	0.0016	0.0047	0.51	1.75
		50	0.0019	0.0051	1.39	2.67	0.0019	0.0051	1.87	5.51	0.0022	0.0055	0.89	1.88
		75	0.0019	0.0051	2.86	4.81	0.0019	0.0051	4.96	6.80	0.0019	0.0051	2.01	3.66
	0.5	25	0.0019	0.0051	0.02	0.07	0.0019	0.0051	0.00	0.01	0.0016	0.0047	0.01	0.06
		50	0.0019	0.0051	0.51	0.81	0.0019	0.0051	0.39	0.67	0.0022	0.0055	0.51	0.78
		75	0.0019	0.0051	1.05	1.52	0.0022	0.0055	1.19	2.08	0.0022	0.0055	1.30	2.03
	0.75	25	0.0019	0.0051	0.00	0.00	0.0013	0.0043	0.00	0.00	0.0019	0.0051	0.00	0.00
		50	0.0019	0.0051	0.00	0.00	0.0016	0.0047	0.00	0.00	0.0019	0.0051	0.00	0.00
		75	0.0019	0.0051	0.50	0.58	0.0019	0.0051	0.58	0.75	0.0019	0.0051	0.34	0.55
Average			0.0019	0.0051	0.75	1.32	0.0018	0.0050	1.04	1.89	0.0019	0.0052	0.62	1.19
40	0.25	25	0.0066	0.0078	0.10	0.30	0.0072	0.0079	0.16	0.52	0.0066	0.0078	0.00	0.00
		50	0.0072	0.0079	0.92	1.51	0.0078	0.0079	1.22	2.09	0.0072	0.0079	0.39	1.47
		75	0.0078	0.0079	3.66	4.43	0.0084	0.0079	3.91	5.84	0.0081	0.0079	2.82	4.04
	0.5	25	0.0066	0.0078	0.02	0.06	0.0066	0.0078	0.00	0.00	0.0066	0.0078	0.00	0.00
		50	0.0075	0.0079	0.39	0.43	0.0078	0.0079	0.31	0.57	0.0078	0.0079	0.46	0.79
		75	0.0084	0.0079	0.81	0.81	0.0091	0.0078	1.03	1.69	0.0091	0.0078	0.71	1.12
	0.75	25	0.0066	0.0078	0.00	0.00	0.0063	0.0077	0.00	0.00	0.0063	0.0077	0.00	0.00
		50	0.0063	0.0077	0.00	0.00	0.0063	0.0077	0.00	0.00	0.0063	0.0077	0.00	0.00
		75	0.0072	0.0079	0.32	0.45	0.0078	0.0079	0.25	0.36	0.0081	0.0079	0.25	0.31
Average			0.0071	0.0078	0.69	0.89	0.0075	0.0078	0.76	1.23	0.0073	0.0078	0.51	0.86
60	0.25	25	0.0159	0.0022	0.07	0.20	0.0178	0.0055	0.09	0.23	0.0147	0.0037	0.02	0.11
		50	0.0175	0.0051	1.48	2.72	0.0197	0.0069	1.20	1.88	0.0163	0.0044	0.28	0.88
		75	0.0197	0.0069	2.38	2.51	0.0219	0.0077	3.74	5.10	0.0206	0.0074	2.58	4.10
	0.5	25	0.0147	0.0037	0.01	0.03	0.0147	0.0037	0.00	0.00	0.0144	0.0043	0.00	0.00
		50	0.0175	0.0060	0.39	0.57	0.0184	0.0061	0.27	0.35	0.0181	0.0066	0.23	0.42
		75	0.0209	0.0075	0.66	1.03	0.0231	0.0079	0.62	0.73	0.0222	0.0078	0.66	0.90
	0.75	25	0.0141	0.0047	0.00	0.00	0.0141	0.0047	0.00	0.00	0.0141	0.0047	0.00	0.00
		50	0.0141	0.0047	0.00	0.00	0.0141	0.0047	0.00	0.00	0.0141	0.0047	0.00	0.00
		75	0.0175	0.0051	0.21	0.27	0.0197	0.0069	0.22	0.28	0.0194	0.0067	0.21	0.25
Average			0.0169	0.0051	0.58	0.82	0.0182	0.0060	0.68	0.95	0.0171	0.0056	0.44	0.74