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Questions
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 |
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Solution
| 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.
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