Two-Stage Hybrid Optimization Algorithm for Silicon Single Crystal Batch Scheduling Problem under Fuzzy Processing Time

Table 4

Fuzzy processing time of each process.

Process and processing time	Size	22 inch	24 inch	28 inch	32 inch
	(Charging amount)	(120 kg)	(150 kg)	(250 kg)	(400 kg)
Charging fuzzy processing time	6	[0.6, 0.9, 1.2]	[0.7, 1, 1.2]	—	—
	8	[0.6, 0.9, 1.2]	[0.7, 1, 1.2]	[1.2, 1.5, 1.7]	—
	10	[0.6, 0.9, 1.2]	[0.7, 1, 1.2]	[1.2, 1.5, 1.7]	—
	12	—	—	[1.2, 1.5, 1.7]	[1.7, 2, 2.2]
Melting fuzzy processing time	6	[6, 7, 8]	[8, 9, 10]	—	—
	8	[6, 7, 8]	[8, 9, 10]	[14, 15, 16]	—
	10	[6, 7, 8]	[8, 9, 10]	[14, 15, 16]	—
	12	—	—	[14, 15, 16]	[19, 20, 21]
Seeding fuzzy processing time	6	[2, 3, 6]	[2, 3, 6]	—	—
	8	[2, 3, 6]	[2, 3, 6]	[2, 3, 6]	—
	10	[2, 3, 6]	[2, 3, 6]	[2, 3, 6]	—
	12	—	—	[2, 3, 6]	[2, 3, 6]
Shouldering fuzzy processing time	6	[1.1, 1.2, 1.3]	[1.1, 1.2, 1.3]	—	—
	8	[1.4, 1.5, 1.6]	[1.4, 1.5, 1.6]	[1.4, 1.5, 1.6]	—
	10	[1.7, 1.8, 1.9]	[1.7, 1.8, 1.9]	[1.7, 1.8, 1.9]	—
	12	—	—	[2.2, 2.3, 2.4]	[2.2, 2.3, 2.4]
Equal diameter growth fuzzy processing time	6	[51, 53, 55]	[64, 66, 68]	—	—
	8	[28, 30, 32]	[35, 37, 39]	[59.9, 61.9, 63.9]	—
	10	[30, 32, 34]	[38.5, 40.5, 42.5]	[65.5, 67.5, 69.5]	—
	12	—	—	[78, 80, 82]	[126, 128, 130]
Ending fuzzy processing time	6	[2.5, 3, 3.5]	[2.5, 3, 3.5]	—	—
	8	[3.5, 4, 4.5]	[3.5, 4, 4.5]	[3.5, 4, 4.5]	—
	10	[5, 6, 7]	[5, 6, 7]	[5, 6, 7]	—
	12	—	—	[9, 10, 11]	[9, 10, 11]
Cooling down the furnace fuzzy processing time	6	[5, 5.5, 6]	[5, 5.5, 6]	—	—
	8	[6, 7, 8]	[6, 7, 8]	[6, 7, 8]	—
	10	[8, 9, 10]	[8, 9, 10]	[8, 9, 10]	—
	12	—	—	[13, 14, 15]	[13, 14, 15]
Total fuzzy processing time	6	[68.2, 73.6, 81]	[83.3, 88.7, 96]	—	—
	8	[47.5, 53.4, 61.3]	[56.6, 62.5, 70.3]	[88, 93.9, 101.7]	—
	10	[53.3, 59.7, 68.1]	[63.9, 70.3, 78.6]	[97.4, 103.8, 112.1]	—
	12	—	—	[119.4, 125.8, 134.1]	[172.9, 179.3, 187.6]