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

Table 4

Test results of the algorithms on the instances with the interval 𝑈[𝐷_0.5,𝐷].

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	5065	4936	97.45%	4576	90.35%	3.68	4576	90.35%	3.81
2		4	2405	2186	90.89%	2145	89.19%	3.66	2145	89.19%	3.70
3		6	1420	1298	91.41%	1296	91.27%	3.67	1296	91.27%	3.76
4		8	1172	1146	97.78%	1146	97.78%	3.73	1146	97.78%	3.75
5		10	1567	1528	97.51%	1528	97.51%	3.74	1528	97.51%	3.73
6	40	2	17081	18299	107.13%	15326	89.73%	23.57	15316	89.67%	26.33
7		4	10157	9559	94.11%	9133	89.92%	24.56	9133	89.92%	24.69
8		6	5847	5040	86.20%	4944	84.56%	24.00	4943	84.54%	23.70
9		8	3708	3376	91.05%	3334	89.91%	23.87	3334	89.91%	24.17
10		10	4141	3772	91.09%	3733	90.15%	24.67	3733	90.15%	24.67
11	60	2	37202	40606	109.15%	32409	87.12%	74.86	32406	87.11%	85.56
12		4	18904	18275	96.67%	16831	89.03%	73.84	16830	89.03%	76.31
13		6	14321	13618	95.09%	13122	91.63%	72.86	13113	91.56%	74.14
14		8	9488	8980	94.65%	8792	92.66%	77.12	8792	92.66%	75.39
15		10	10032	9203	91.74%	8991	89.62%	77.29	8988	89.59%	78.05
16	80	2	61930	68725	110.97%	54652	88.25%	163.31	54651	88.25%	205.40
17		4	27137	28577	105.31%	24790	91.35%	167.83	24776	91.30%	169.78
18		6	29003	26914	92.80%	25022	86.27%	175.63	25021	86.27%	177.12
19		8	17291	15715	90.89%	15037	86.96%	162.31	15032	86.94%	164.65
20		10	12900	12215	94.69%	11860	91.94%	168.39	11855	91.90%	169.90
21	100	2	110757	128605	116.11%	98384	88.83%	286.03	98358	88.81%	386.87
22		4	50773	49696	97.88%	44153	86.96%	310.59	44152	86.96%	315.32
23		6	30745	31697	103.10%	27834	90.53%	319.17	27833	90.53%	319.76
24		8	26562	25254	95.08%	23576	88.76%	320.56	23573	88.75%	288.13
25		10	24330	22469	92.35%	21508	88.40%	318.57	21506	88.39%	327.75
Average					97.24%		89.95%			89.93%