There are four jobs to be completed. Each job must go through machines

There are four jobs to be completed. Each job must go through machines M1, M2, M3 in the order M1 – M2 – M3. Processing time in hours is given below. Determine the optimal sequence and idle time for Machine M1.JobsABCDM15873M26725M378109

Answer»

The given problem is of n jobs and three machines. We change the problem in of n jobs and two machines.

For this either Min M₁ ≤ M₃× M₂ or min M₃ ≤ max M₂

Here min M₃= 7 = M₁× M₂

Hence we write M₁+ M₂ = G and M₂ + M₃= H the problem will be as follows

Jobs	A	B	C	D
G = M₁+M₂	11	15	9	8
H = M₂+M₃	13	15	12	14

The sequence as follows

Now

job	M₁		M₂		M₃
	Time in	Time out	Time in	Time out	Time in	Time out
D	0	3	3	8	8	17
C	3	10	10	12	17	27
A	10	15	15	21	27	34
B	15	23	23	30	34	42

The minimum elapsed time = 42 hrs. Ideal time for M₁ = 42 – 23 = 19 hrs.

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There are four jobs to be completed. Each job must go through machines M1, M2, M3 in the order M1 – M2 – M3. Processing time in hours is given below. Determine the optimal sequence and idle time for Machine M1.JobsABCDM15873M26725M378109

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