Question

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 total elapsed time:

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

Answer 1

Jobs	Time (in hours)
	Lathe (A)	Surface grinder (B)
I	4	3
II	1	2
III	5	4
IV	2	3
V	5	6

Here, min(A, B) = 1, which corresponds to A. 

Therefore, job II is processed first.

II

The problem now reduces to jobs I, III, IV, and V.

Here, Min.(A, B) = 2, which corresponds to A.

Therefore, job IV is processed next to job II.

II

IV

The problem now reduces to jobs I, III, and V.

Here, Min. (A, B) = 3, which corresponds to B

Therefore, job I is processed at the last.

II

IV

I

The problem now reduces to jobs III and V.

Here, Min. (A, B) = 4, which corresponds to B.

Therefore, job III is processed at the last, next to job I

II

IV

III

I

Now, job V is processed next to job IV, and we get the optional sequence of jobs as follows:

II

IV

V

III

I

Total elapsed time is obtained as follows:

Jobs Sequence	Lathe (A)		Surface grinder (B)
	Time in	Time out	Time in	Time out
II	0	1	1	3
IV	1	3	3	6
V	3	8	8	14
III	8	13	14	18
I	13	17	18	21

Total elapsed time T = 21 hours.