Sum-of-Processing-Times-Based Two-Agent Single-Machine Scheduling with Aging Effects and Tardiness

Table 1

Experimental results of the B&B algorithm and GA.

			B&B				Error rate of the GA								Avg. computation time of GA
			Number of nodes		Computation time (s)		GA1 (R : R)		GA2 (EDD : R)		GA3 (EDD : EDD)		GA4 (EDD : wEDD)		GA1	GA2	GA3	GA4
			Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.
8	0.2	0.2	6,355.2	938.42	1.68	0.24	0.013	0.005	0.011	0.010	0.004	0.004	0.006	0.002	0.74	0.62	0.46	0.52
		0.4	6,048.0	1,341.33	1.62	0.33	0.019	0.007	0.009	0.009	0.009	0.010	0.011	0.007	0.73	0.66	0.45	0.47
		0.6	6,713.8	2,809.12	1.93	0.83	0.018	0.009	0.013	0.011	0.007	0.002	0.006	0.006	0.75	0.64	0.49	0.48
		0.8	7,507.8	4,212.69	2.07	1.38	0.021	0.008	0.018	0.012	0.008	0.005	0.012	0.004	0.77	0.67	0.52	0.54
	0.4	0.2	2,460.4	229.00	0.58	0.03	0.011	0.004	0.012	0.011	0.005	0.002	0.007	0.003	0.73	0.68	0.53	0.57
		0.4	2,578.8	859.68	0.61	0.55	0.009	0.003	0.019	0.008	0.008	0.005	0.006	0.002	0.72	0.65	0.57	0.60
		0.6	2,872.4	1,595.51	0.78	0.85	0.012	0.006	0.014	0.005	0.011	0.008	0.010	0.004	0.73	0.69	0.59	0.58
		0.8	2,987.8	2,135.12	0.82	1.16	0.011	0.008	0.009	0.007	0.013	0.010	0.012	0.001	0.79	0.70	0.54	0.55
10	0.2	0.2	228,568.0	43,947.85	66.91	13.23	0.008	0.004	0.007	0.005	0.004	0.001	0.005	0.002	1.11	0.88	0.78	0.77
		0.4	229,012.7	52,694.14	68.84	17.61	0.005	0.002	0.009	0.003	0.008	0.004	0.006	0.001	1.20	0.89	0.76	0.77
		0.6	254,233.1	65,395.87	79.99	20.80	0.009	0.005	0.008	0.008	0.007	0.005	0.010	0.003	1.18	0.88	0.73	0.75
		0.8	252,720.4	110,233.21	80.21	34.59	0.019	0.010	0.014	0.010	0.009	0.006	0.009	0.004	1.23	0.84	0.74	0.79
	0.4	0.2	24,394.4	7,282.12	6.53	1.77	0.008	0.002	0.004	0.002	0.005	0.003	0.005	0.002	1.12	0.93	0.76	0.78
		0.4	25,259.2	9,219.01	7.30	2.14	0.007	0.004	0.011	0.003	0.007	0.002	0.009	0.003	1.22	0.88	0.74	0.75
		0.6	25,560.3	14,496.15	7.80	4.75	0.014	0.007	0.012	0.004	0.008	0.002	0.004	0.004	1.19	0.86	0.71	0.76
		0.8	26,344.11	22,289.75	9.01	5.52	0.009	0.009	0.008	0.007	0.008	0.004	0.010	0.003	1.17	0.87	0.73	0.72
12	0.2	0.2	2,266,093.2	438,187.13	978.87	162.11	0.008	0.004	0.007	0.004	0.012	0.002	0.009	0.004	2.12	1.56	1.32	1.28
		0.4	2,680,916.3	1,235,682.2	1,056.78	553.86	0.007	0.005	0.010	0.005	0.008	0.003	0.007	0.005	2.08	1.54	1.27	1.29
		0.6	2,810,094	1,960,845.3	1,147.58	828.54	0.020	0.002	0.015	0.006	0.010	0.004	0.004	0.006	2.07	1.59	1.33	1.30
		0.8	2,746,277.3	2,151,950.5	1,220.55	1,020.48	0.014	0.008	0.012	0.004	0.009	0.005	0.008	0.007	2.06	1.61	1.35	1.34
	0.4	0.2	284,563.7	156,255.3	95.77	51.40	0.004	0.004	0.004	0.002	0.009	0.004	0.005	0.002	2.03	1.60	1.28	1.32
		0.4	295,702.9	210,762.7	97.67	60.25	0.005	0.001	0.005	0.001	0.007	0.004	0.002	0.002	2.04	1.58	1.29	1.33
		0.6	295,666.3	246,098.5	104.55	71.03	0.002	0.001	0.004	0.003	0.010	0.008	0.008	0.004	2.20	1.59	1.31	1.28
		0.8	296,856.3	291,585.5	108.94	79.36	0.011	0.005	0.008	0.002	0.009	0.008	0.004	0.003	2.18	1.57	1.34	1.27