Variable Neighborhood Search for Parallel Machines Scheduling Problem with Step Deteriorating Jobs

Table 3

Test results of the algorithms on the instances with the interval U(0,𝐷_0.5].

Problem; number	𝑛	𝑚	SRF	MWCSA		VNS			VNS + MWCSA
			Objective	Objective	(𝐵)/(𝐴)	Objective	(𝐶)/(𝐴)	Time	Objective	(𝐷)/(𝐴)	Time
			value (𝐴)	value (𝐵)		value (𝐶)		(sec)	value (𝐷)		(sec)
1	20	2	5859	5062	86.40%	5001	85.36%	3.71	5001	85.36%	3.90
2		4	3274	2589	79.08%	2587	79.02%	3.58	2583	78.89%	3.77
3		6	1792	1676	93.53%	1655	92.35%	3.65	1655	92.35%	3.71
4		8	1299	1247	96.00%	1199	92.30%	3.68	1199	92.30%	3.73
5		10	1324	1309	98.87%	1269	95.85%	3.71	1267	95.69%	3.76
6	40	2	17056	14013	82.16%	13361	78.34%	23.00	13307	78.02%	23.73
7		4	11530	9614	83.38%	9513	82.51%	23.57	9508	82.46%	24.38
8		6	7833	6890	87.96%	6800	86.81%	23.05	6797	86.77%	23.56
9		8	4684	4299	91.78%	4201	89.69%	23.60	4198	89.62%	23.67
10		10	3858	3465	89.81%	3434	89.01%	24.15	3428	88.85%	24.71
11	60	2	47917	41030	85.63%	39204	81.82%	73.04	39149	81.70%	71.14
12		4	28547	22651	79.35%	22234	77.89%	72.34	22184	77.71%	67.62
13		6	17378	13616	78.35%	13504	77.71%	70.08	13474	77.53%	70.38
14		8	12577	10288	81.80%	10122	80.48%	69.37	10121	80.47%	72.68
15		10	10346	8695	84.04%	8573	82.86%	71.59	8548	82.62%	68.72
16	80	2	73047	66321	90.79%	58736	80.41%	157.50	58392	79.94%	181.86
17		4	41378	33779	81.64%	32734	79.11%	160.57	32687	79.00%	132.71
18		6	27955	22144	79.21%	21679	77.55%	152.83	21671	77.52%	142.25
19		8	20569	16200	78.76%	16055	78.05%	157.20	16013	77.85%	136.14
20		10	15479	12720	82.18%	12569	81.20%	160.32	12516	80.86%	152.90
21	100	2	126101	108828	86.30%	98779	78.33%	288.47	98026	77.74%	290.95
22		4	58800	46684	79.39%	45214	76.89%	295.09	44858	76.29%	277.00
23		6	46629	35717	76.60%	34678	74.37%	307.01	34466	73.92%	240.82
24		8	35233	27602	78.34%	27275	77.41%	286.20	27143	77.04%	263.09
25		10	29084	22906	78.76%	22753	78.23%	299.92	22629	77.81%	303.41
Average					84.40%		82.14%			81.93%