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

Table 2

Comparison of CPLEX results with the proposed algorithms for small-sized instances.

𝑛	𝑚	CPLEX		MWCSA		VNS
		Objective	Time	Objective	RPD	Objective	RPD	Time
		value (gap)	(sec)	value		value		(sec)
6	2	582	1.48	582	0.00%	582	0.00%	0.36
	3	360	2.47	370	2.78%	360	0.00%	0.30
8	2	859	103.55	859	0.00%	859	0.00%	0.52
	3	513	122.20	513	0.00%	513	0.00%	0.46
10	2	1284	24632.09	1308	1.87%	1284	0.00%	0.72
	3	1190	144761.59	1216	1.59%	1190	0.00%	0.72
*the deteriorating date with the interval 𝑈(0,𝐷0.5]
6	2	430	1.50	430	0.00%	430	0.00%	0.30
	3	392	2.05	392	0.00%	392	0.00%	0.30
8	2	835	80.70	835	0.00%	835	0.00%	0.46
	3	590	233.25	590	0.00%	590	0.00%	0.47
10	2	1186	17676.28	1186	0.00%	1186	0.00%	0.71
	3	794	62828.11	799	0.63%	794	0.00%	0.72
*the deteriorating date with the interval 𝑈[𝐷0.5,𝐷]
6	2	446	1.63	446	0.00%	446	0.00%	0.30
	3	335	1.92	335	0.00%	335	0.00%	0.31
8	2	934	102.61	939	0.54%	934	0.00%	0.47
	3	486	205.08	491	1.03%	486	0.00%	0.47
10	2	1161	22216.36	1193	2.76%	1161	0.00%	0.72
	3	638	51367.00	638	0.00%	638	0.00%	0.70
*the deteriorating date with the interval 𝑈(0,𝐷]
Average					0.62%		0.00%