Question

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

Job	I	II	III	IV	V
Lathe	4	1	5	2	5
Surface grinder	3	2	4	3	6

Answer 1

Job	I	II	III	IV	V
Lathe	4	1	5	2	5
Surface grinder	3	2	4	3	6

Observe that Min (lathe, grinder) = 1, corresponds to job II on lathe.

∴ Job II is placed first in sequence.

II

Then the problem reduces to

Job	I	III	IV	V
Lathe	4	5	2	5
Surface grinder	3	4	3	6

Now, Min (lathe, grinder) = 2, corresponds to job IV on lathe.

∴ Job IV is placed after II in sequence.

II

IV

Then the problem reduces to

Job	I	III	V
Lathe	4	5	5
Surface grinder	3	4	6

Now, Min (lathe, grinder) = 3, corresponds to job I on grinder.

∴ Job I is placed last in sequence.

II

IV

I

Then the problem reduces to

Job	III	V
Lathe	5	5
Surface grinder	4	6

Now, Min (lathe, grinder) = 4, corresponds to job III on grinder.

∴ Job III is placed before I and V on remaining in sequence.

∴ Optimal sequence is

II

IV

V

III

I

Total elapsed time

Job	Lath		Surface Grinder
	In	Out	In	Out
II (1, 2)	0	1	1	3
IV (2, 3)	1	3	3	6
V (5, 6)	3	8	8	14
III (5, 4)	8	13	14	18
I (4, 3)	13	17	18	21

∴ Total elapsed time = 21 hrs

Idle time for lathe = 21 – 17 = 4 hrs

Idle time for surface grinder = 1 + 2 = 3 hrs.