A Study of Flexible Flow Shop Scheduling Problem with Various Heterogeneous Labors

Table 3

The optimal solution and makespan with  = 6, n = 20.

Amount of hired heterogeneous labors (E)	Arrangement of labors	Dispatching rule						Cmax	Optimum solution	CPU time
		( = 1, m = 3)	( = 2, m = 4)	( = 3, m = 3)	( = 4, m = 3)	( = 5, m = 3)	( = 6, m = 4)		(Total cost)	(ms)
0	(20, 0, 0)	RRR	RRRR	RRR	RRR	RRR	RRRR	590.5	177150	—
1	(19, 0, 1)	ROR	RRRR	RRR	RRR	RRR	RRRR	587.29	173544.2	5315.63
	(19, 1, 0)	RDR	RRRR	RRR	RRR	RRR	RRRR	589.25	172650.25	5218.08
2	(18, 0, 2)	ROR	RRRR	RRR	RRR	RRR	RORR	605.47	176190.32	5331.14
	(18, 1, 1)	ROR	RRRR	RRR	RRR	RRR	RDRR	599.96	173087.74	5295.04
	(18, 2, 0)	RDR	RRRR	RRR	RRR	RRR	RDRR	599.43	171436.27	5376.2
3	(17, 0, 3)	ROR	RRRR	RRR	RRR	RRR	OORR	611.46	175182.57	5263.86
	(17, 1, 2)	ROR	RRRR	RRR	RRR	RRR	DORR	615.22	174721.77	5375.03
	(17, 2, 1)	ROR	RRRR	RRR	RRR	RRR	DDRR	600.21	168957.71	5302.12
	(17, 3, 0)	RDR	RRRR	RRR	RRR	RRR	DDRR	612.15	170789.15	5534.99
4	(16, 0, 4)	ROR	ORRR	RRR	RRR	RRR	OORR	613.08	172887.15	5481.58
	(16, 1, 3)	ROR	DRRR	RRR	RRR	RRR	OORR	595.37	166405.22	5319.75
	(16, 2, 2)	ROR	DRRR	RRR	RRR	RRR	DORR	602.28	166831.56	5470.35
	(16, 3, 1)	ROR	DRRR	RRR	RRR	RRR	DDRR	602.74	165450.76	5358.12
	(16, 4, 0)	RDR	DRRR	RRR	RRR	RRR	DDRR	599.82	163151.72	5531.05
5	(15, 0, 5)	ROR	ORRR	RRR	RRR	RRR	OORO	616.05	170954.57	5417.81
	(15, 1, 4)	ROR	ORRR	RRR	RRR	RRR	OORD	618.81	170172.75	5599.63
	(15, 2, 3)	ROR	DRRR	RRR	RRR	RRR	OORD	617.06	168149.53	5392.19
	(15, 3, 2)	ROR	DRRR	RRR	RRR	RRR	DORD	619.57	167282.55	5545.63
	(15, 4, 1)	ROR	DRRR	RRR	RRR	RRR	DDRD	612.53	163851.11	5641.47
	(15, 5, 0)	RDR	DRRR	RRR	RRR	RRR	DDRD	612.25	162246.25	5452.24
6	(14, 0, 6)	ROR	OROR	RRR	RRR	RRR	OORO	620.49	169393.09	5592.88
	(14, 1, 5)	ROR	ORDR	RRR	RRR	RRR	OORO	613.28	165890.89	5470.4
	(14, 2, 4)	ROR	ORDR	RRR	RRR	RRR	OORD	614.12	164584.16	5654.9
	(14, 3, 3)	ROR	DRDR	RRR	RRR	RRR	OORD	618.42	164189.18	5562.88
	(14, 4, 2)	ROR	DRDR	RRR	RRR	RRR	DORD	631.46	166073.32	5736.43
	(14, 5, 1)	ROR	DRDR	RRR	RRR	RRR	DDRD	613.77	159886.43	5522.81
	(14, 6, 0)	RDR	DRDR	RRR	RRR	RRR	DDRD	623.56	160878.48	5609.58
7	(13, 0, 7)	ROR	OROR	RRR	ORR	RRR	OORO	625.11	167842.71	5539.26
	(13, 1, 6)	ROR	OROR	RRR	DRR	RRR	OORO	625.54	166392.31	5747.1
	(13, 2, 5)	ROR	ORDR	RRR	DRR	RRR	OORO	627.68	165393.02	5707.66
	(13, 3, 4)	ROR	ORDR	RRR	DRR	RRR	OORD	622.06	162358.31	5529.52
	(13, 4, 3)	ROR	DRDR	RRR	DRR	RRR	OORD	628.93	162577.76	5670.48
	(13, 5, 2)	ROR	DRDR	RRR	DRR	RRR	DORD	634.34	162391.04	5532.89
	(13, 6, 1)	ROR	DRDR	RRR	DRR	RRR	DDRD	635.2	161023.83	5863.24
	(13, 7, 0)	RDR	DRDR	RRR	DRR	RRR	DDRD	635.44	159495.44	5635.21
20	(0, 0, 20)	OOO	OOOO	OOO	OOO	OOO	OOOO	713.87	207022.88		8159.69
	(0, 1, 19)	OOO	ODOO	OOO	OOO	OOO	OOOO	715.98	205844.25		8298.79
	(0, 2, 18)	OOO	ODOO	OOO	OOO	ODO	OOOO	713.39	203316.72		8401.87
	(0, 3, 17)	DOO	ODOO	OOO	OOO	ODO	OOOO	714.9	201958.4		8321.09
	(0, 4, 16)	DOO	ODOD	OOO	OOO	ODO	OOOO	714.99	200197.76		8190.65
	(0, 5, 15)	DOO	ODOD	OOO	OOO	DDO	OOOO	719.76	199733.96		8045.88
	(0, 6, 14)	DOO	ODOD	ODO	OOO	DDO	OOOO	721.78	256232.97		8086.76
	(0, 7, 13)	DOD	ODOD	ODO	OOO	DDO	OOOO	720.54	253990		7999.67
	(0, 8, 12)	DOD	ODOD	DDO	OOO	DDO	OOOO	722.76	252966.35		8213.06
	(0, 9, 11)	DOD	ODOD	DDO	OOD	DDO	OOOO	721.33	250662.52		8260.78
	(0, 10, 10)	DOD	ODOD	DDO	ODD	DDO	OOOO	724.77	250045.31		8469.36
	(0, 11, 9)	DOD	ODOD	DDO	ODD	DDO	OODO	725.78	248580.68		8293.31
	(0, 12, 8)	DOD	ODOD	DDO	ODD	DDD	OODO	723.89	246123.96		8562.87
	(0, 13, 7)	DOD	ODOD	DDD	ODD	DDD	OODO	722.77	243935.21		8583.97
	(0, 14, 6)	DOD	ODOD	DDD	DDD	DDD	OODO	726.89	243509.16		8756.91
	(0, 15, 5)	DOD	ODDD	DDD	DDD	DDD	OODO	725.76	241316.2		8861.01
	(0, 16, 4)	DOD	ODDD	DDD	DDD	DDD	OODD	724.35	239034.51		8684.7
	(0, 17, 3)	DOD	DDDD	DDD	DDD	DDD	OODD	727.54	238269.68		8798.53
	(0, 18, 2)	DOD	DDDD	DDD	DDD	DDD	DODD	729.49	237084.25		8689.65
	(0, 19, 1)	DOD	DDDD	DDD	DDD	DDD	DDDD	731.13	235787.81		8759.75
	(0, 20, 0)	DDD	DDDD	DDD	DDD	DDD	DDDD	730.98	233914.24		8860.41