Question 26 of 32
Q.
Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both the machines.
| Job | I | II | III | IV | V | VI | VII |
|---|---|---|---|---|---|---|---|
| Machine A | 7 | 16 | 19 | 10 | 14 | 15 | 5 |
| Machine B | 12 | 14 | 14 | 10 | 16 | 5 | 7 |
Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2025Subjective· 4mImportance★★★★★
81% · 26/32 Questions
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Start your 14-day free trial to unlock the full solution →Johnson's rule gives the sequence VII–I–IV–V–II–III–VI. Total elapsed time ; machine A idle ; machine B idle .
Step 1 — Johnson's rule (order A then B). Repeatedly find the smallest time in the table: if it is under machine A, place that job as early as possible; if under machine B, place it as late as possible.
- Smallest : at A(VII) VII first; at B(VI) VI last.
- Next at A(I) I next.
- Next at IV (both A and B) IV next.
- Next at A(V) V next; then B ties place II, III before VI.
Sequence: .
Step 2 — Elapsed and idle time table. Times (A, B): VII, I, IV, V, II, III, VI.
| Job | A-in | A-out | B-in | B-out |
|---|---|---|---|---|
| VII | 0 | 5 | 5 | 12 |
| I | 5 | 12 | 12 | 24 |
| IV | 12 | 22 | 24 | 34 |
| V | 22 | 36 | 36 | 52 |
| II | 36 | 52 | 52 | 66 |
| III | 52 | 71 | 71 | 85 |
| VI | 71 | 86 | 86 | 91 |
| … |
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