Question

There are five jobs, each of which must go through two machines in the order XY. Processing times (in hours) are given below. Determine the sequence for the jobs that will minimize the total elapsed time. Also find the total elapsed time and idle time for each machine.

Job	A	B	C	D	E
Machine X	10	2	18	6	20
Machine Y	4	12	14	16	8

Answer 1

Job	A	B	C	D	E
Machine X	10	2	18	6	20
Machine Y	4	12	14	16	8

Observe that Min(X, Y) = 2, corresponding to job B on machine X.

∴ Job B is placed first in the sequence.

B

Then the problem reduces to

Job	A	C	D	E
Machine X	10	18	6	20
Machine Y	4	14	16	8

Now, Min(X, Y) = 4, corresponds to job A on machine Y.

∴ Job A is placed last in the sequence.

B

A

Then the problem reduces to

Job	C	D	E
Machine X	18	6	20
Machine Y	14	16	8

Now, Min(X, Y) = 6, corresponds to job D on machine X.

∴ Job D is placed second in sequence.

B

D

A

Then the problem reduces to

Job	C	E
Machine X	18	20
Machine Y	14	8

Now, Min(X, Y) = 8, corresponds to job E on machine Y.

∴ Job E is placed fourth and job C on remaining in sequence.

∴ The optimal sequence is

B

D

C

E

A

Total elapsed time,

Job	Machine X		Machine Y
	In	Out	In	Out
B (2, 12)	0	2	2	14
D (6, 16)	2	8	14	30
C (18, 14)	8	26	30	44
E (20, 8)	26	46	46	54
A (10, 4)	46	56	56	60

∴ Total elapsed time = 60 hrs.

Idle time for machine X = 60 – 56 = 4 hrs

Idle time for machine Y = 2 + 2 + 2 = 6 hrs.