Question

Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hours.

Jobs	I	II	III	IV	V	VI	VII
Machine A	6	7	5	11	6	7	12
Machine B	4	3	2	5	1	5	3
Machine C	3	8	7	4	9	8	7

Find the appropriate regression equation and use it to estimate the blood pressure of a woman with age 47 years. Find the optimal sequence that minimizes total time required to complete the following jobs in order A-B-C. The processing times are given in hrs.

Job	I	II	III	IV	V	VI	VII
Machine A	6	7	5	11	6	7	12
Machine B	4	3	2	5	1	5	3
Machine C	3	8	7	4	9	8	7

Answer 1

Job	I	II	III	IV	V	VI	VII
Machine A	6	7	5	11	6	7	12
Machine B	4	3	2	5	1	5	3
Machine C	3	8	7	4	9	8	7

Here min A = 5, max B = 5, min C = 3

Since min A ≥ max B is satisfied, the problem can be converted into a two machine problem.

Let G and H be two fictitious machines such that G = A + B and H = B + C

Then the problem can be written as

Job	I	II	III	IV	V	VI	VII
Machine G	10	10	7	16	7	12	15
Machine H	7	11	9	9	10	13	10

Observe that Min (G, H) = 7, corresponds to job I on machine H, job III on machine G and job V on machine G.

∴ Job I is placed last in sequence, Job III and V are placed either first or second in sequence.

V

III

I

OR

III

V

I

Then the problem reduces to

Job	II	IV	VI	VII
Machine G	10	16	12	15
Machine H	11	9	13	10

Now, Min (G, H) = 9, corresponds to Job IV on machine H.

∴ Job IV is placed second last in the sequence.

V

III

IV

I

OR

III

V

IV

I

Then the problem reduces to

Job	II	VI	VII
Machine G	10	12	15
Machine H	11	13	10

Now, Min (G, H) = 10, corresponds to Job II on machine G and Job VII on machine H.

∴  Job II is placed third in the sequence, Job VII is placed third last in the sequence and remaining Job VI is placed fourth in the sequence.

V

III

II

VI

VII

IV

I

OR

III

V

II

VI

VII

IV

I

∴ We consider the optimal sequence as V – III – II – VI – VII – IV – I

Total elapsed time

Job	Machine A		Machine B		Machine C
	In	Out	In	Out	In	Out
V (6, 1, 9)	0	6	6	7	7	16
III (5, 2, 7)	6	11	11	13	16	23
II (7, 3, 8)	11	18	18	21	23	31
VI (7, 5, 8)	18	25	25	30	31	39
VII (12, 3, 7)	25	37	37	40	40	47
IV (11, 5, 4)	37	48	48	53	53	57
I (6, 4, 3)	48	54	54	58	58	61

Total elapsed time = 61 hrs

Idle time for Machine A = 61 –  54 = 7 hrs

Idle time for Machine B = (61 – 58) + 6 + 4 + 5 + 4 + 7 + 8 + 1 = 38 hrs

Idle time for Machine C = 7 + 1 + 6 + 1 = 15 hrs.