Question

There are 5 jobs each of which is to be processed through three machines A, B and C in the order ABC. Processing times in hours are as shown in the following table : 

Job	1	2	3	4	5
A	3	8	7	5	4
B	4	5	1	2	3
C	7	9	5	6	10

Determine the optimum sequence for the five jobs and the minimum elapsed time. 

Answer 1

Min M_A = 3,  Max M_B = 5  and Min M_c = 5 

∵ Min M_c  ≥ Max M_B 

∴ Let G = A + B ; H = B + C

The problem is

Jobs	1	2	3	4	5
G	7	13	8	7	7
H	11	14	6	8	13

the optimal sequence is 

4   1    5     2   3 

Job	Machine A		Machine B		Machine C
	In	Out	In	Out	In	Out
4	0	5	5	7	7	13
1	5	8	8	12	13	20
5	8	12	12	15	20	30
2	12	20	20	25	30	39
3	20	27	27	28	39	44

∴ Minimum elapsed time = 44 hrs