Correction to: An effective approach for the dual-resource flexible job shop scheduling problem considering loading and unloading

Correction to: Journal of Intelligent Manufacturing (2021) 32:707–728 https://doi.org/10.1007/s10845-020-01697-5

Due to a slip, which mixed up two folds storing data on two sets of different algorithms, the original version of this article unfortunately contained some mistakes. The original experiment results (Table 7) in Case Study were uploaded incorrectly. Algorithm C in Table 5 is obtained from the first instance in Table 7, so Table 5 needs to be revised. Figures 10, 13 and 14 are to show the Pareto solutions and the Gantt Charts of the best solution and need to be revised. Figure 17 is to show the Pareto solutions of each instance (Table 7) obtained with MODE and the improved NSGA-II, respectively and needs to be revised.

The corrected version is given below. For each item, the original and the corrected are given in the following table, respectively. From these comparisons, we can see that the corrected results support the conclusion much more.

Original article has been corrected.

Table 5	The original results	Table 5 The comparison of experimental results
			The number of Pareto solutions	Pareto solutions
		algorithm A	10	(60.8,66.8), (63.8,58), (59.8,69.2), (68,48.2), (67.2,53.2), (63.6,59.8), (59.5,73), (61.1,62.2), (67.1,54.1), (65,57.2)
		algorithm B	11	(101.2,24.7), (79.6,34.8), (85.7,29.6), (97.5,26.8), (82.8,30.8), (81.9,33.2), (82.5,31.2), (82.4,31.4), (89.2,26.9), (100.2,24.7), (83.5,29.6)
		algorithm C	10	(58.3,45.2), (63.4,42.7), (68.8,37.8), (70.9,36.9), (69.7,37.5), (63.8,40.1), (71.5,35.5), (65.6,39.5), (72.6,34.7), (62.6,45.2)
	The corrected results	Table 5 The comparison of experimental results
			The number of Pareto solutions	Pareto solutions
		algorithm A	10	(60.8,66.8), (63.8,58), (59.8,69.2), (68,48.2), (67.2,53.2), (63.6,59.8), (59.5,73), (61.1,62.2), (67.1,54.1), (65,57.2)
		algorithm B	11	(101.2,24.7), (79.6,34.8), (85.7,29.6), (97.5,26.8), (82.8,30.8), (81.9,33.2), (82.5,31.2), (82.4,31.4), (89.2,26.9), (100.2,24.7), (83.5,29.6)
		algorithm C	10	(59.5, 56.6), (69.8, 35.4), (59.2, 57.4), (67.3, 36.7), (74.1, 33.3), (66.6, 40.6), (62.1, 40.7), (71.6, 34.6), (67.1, 38.2), (59.6, 42.3)

Figure 10	The original results	Figure 10 The comparison of Pareto solutions with three algorithms
	The corrected results	Figure 10 The comparison of Pareto solutions with three algorithms

Figure 13	The original results	Figure 13 The Gantt Chart on machine resource with the SSA4STR
	The corrected results	Figure 13 The Gantt Chart on machine resource with the SSA4STR

Figure 14	The original results	Figure 14 The Gantt chart on fixture resource with the SSA4STR
	The corrected results	Figure 14 The Gantt chart on fixture resource with the SSA4STR

Table 7	The original results	Table 7. The comparison of experimental results
			min(C)		min(T)		Hypervolume		Spread
			MODE	NSGA-II	MODE	NSGA-II	MODE	NSGA-II	MODE	NSGA-II
		MKF-1	60.1	56.7	38.5	37.3	0.791	0.625	2.511	2.257
		MKF-2	39.6	39.1	15.7	13.7	0.676	0.570	1.715	1.433
		MKF-3	242.1	233.2	98.1	95.3	0.825	0.815	3.647	4.981
		MKF-4	107	107.5	99.2	84.2	0.803	0.712	3.434	2.822
		MKF-5	247.4	243.8	78.9	75.4	0.886	0.744	4.847	4.041
		MKF-6	108.9	105.6	95.2	87.7	0.865	0.813	5.386	4.265
		MKF-7	194.7	191.9	51.5	36.6	0.704	0.642	5.703	3.552
		MKF-8	634.4	638.3	313.5	296.6	0.863	0.791	10.961	5.957
		MKF-9	459.5	457.7	218.3	202.9	0.904	0.839	7.033	6.786
		MKF-10	329.7	332.7	214.2	191	0.805	0.779	5.736	5.054
	The corrected results	Table 7. The comparison of experimental results
			min(C)		min(T)		Hypervolume		Spread
			MODE	NSGA-II	MODE	NSGA-II	MODE	NSGA-II	MODE	NSGA-II
		MKF-1	60.1	59.2	38.5	33.3	0.837	0.531	3.84	1.161
		MKF-2	39.6	38.2	15.7	15.7	0.637	0.633	2.567	0.245
		MKF-3	240.6	230.6	90.1	84.2	1.129	1.331	3.923	4.027
		MKF-4	107	105.1	99.9	77.7	1.409	0.992	1.844	1.161
		MKF-5	247.4	245.4	78.9	71.1	0.654	0.473	5.035	4.319
		MKF-6	110.4	104.4	95.2	87.2	0.817	0.907	2.839	2.379
		MKF-7	194.7	192.5	51.5	36.4	0.747	0.491	1.783	4.424
		MKF-8	634.4	625.6	313.5	295.1	1.151	0.923	3.374	5.348
		MKF-9	460.2	468.3	218.3	199.2	1.043	2.483	6.406	2.825
		MKF-10	329.7	344.9	214.2	196.4	1.56	0.561	4.639	10.106

Figure 17	The original results	Figure 17 The comparison of Pareto set
	The corrected results	Figure 17 The comparison of Pareto set