Solving a mathematical model integrating unequal-area facilities layout and part scheduling in a cellular manufacturing system by a genetic algorithm

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Table 8 Comparison of GA solutions and exact solutions

Problem no.	No. of machines	No. of parts	No. of operations per part	No. of processing positions per machine	No. of cells	Sequential approach					Solution GAP
						B&B		GA
						OFV	Time (s)	Best OFV	Average OFV	Time (s)
1	3	4	2	4	2	1292.5*	16	1292.5	1292.5	1.6	–
2	4	4	3	3	2	3474.5*	276	3474.5	3474.5	3.9	–
3	4	4	3	4	2	3132*	20,350	3132	3132	14.6	–
4	4	5	3	4	2	3688.5*	38,405	3688.5	3700.5	15.4	–
5	5	6	3	4	2	5010.5	43,200	4798	4851.7	18.5	−3.3
6	6	8	3	4	2	6490.7	43,200	6206.5	6456.5	23.3	−4.6
7	8	10	4	5	3	13,728.6	43,200	12,802	13,588.4	33.8	−7.2
8	10	12	5	6	3	22,347.4	43,200	20,997	21,190.8	42.4	−6.4
9	15	25	3	5	4	NA	43,200	30,677	30,152.7	61.1	NA
10	20	40		6	6	NA	43,200	86,110	77,090.3	102.5	NA

Problem no.	No. of machines	No. of parts	No. of operations per part	No. of processing positions per machine	No. of cells	Concurrent approach					Solution GAP	OFV Improvement B&B (%)	OFV Improvement GA (%)
						B&B		GA
						OFV	Time (s)	Best OFV	Average OFV	Time (s)
1	3	4	2	4	2	1135*	185	1135	1112.5	2.9	–	13.9	13.9
2	4	4	3	3	2	3089*	1203	3089	3089	7.6	–	12.5	12.5
3	4	4	3	4	2	2911*	29,900	2911	2911	18.2	–	7.6	7.6
4	4	5	3	4	2	3557.3	43,200	3520	3691.7	19.2	−1.1	3.7	4.8
5	5	6	3	4	2	4556.7	43,200	4323.5	4482.7	23.3	−5.4	10	11
6	6	8	3	4	2	5764.2	43,200	5486	5543.9	31.4	−5.1	12.6	13.1
7	8	10	4	5	3	10,582.5	43,200	9957.5	10,233.8	56.7	−6.3	29.7	28.6
8	10	12	5	6	3	18,632.4	43,200	17,453	18,255.6	68.47	−6.8	19.9	20.3
9	15	25	3	5	4	NA	43,200	23,543	24,040.3	108.3	NA	NA	30.3
10	20	40		6	6	NA	43,200	67,872	68,253.6	221.1	NA	NA	26.9