Consider a job scheduling problem with 4 jobs J1, J2, J3, J4 and with…
2007
Consider a job scheduling problem with 4 jobs J1, J2, J3, J4 and with corresponding deadlines: ( d1, d2, d3, d4) = (4, 2, 4, 2). Which of the following is not a feasible schedule without violating any job's deadline?
Answer: B. J4, J1, J2, J3 — In job sequencing with unit processing time on a single processor, a schedule is a permutation (ordering) of the jobs; the job placed at position k…
- A.
J2, J4, J1, J3
- B.
J4, J1, J2, J3
- C.
J4, J2, J1, J3
- D.
J4, J2, J3, J1
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Correct answer: B
In job sequencing with unit processing time on a single processor, a schedule is a permutation (ordering) of the jobs; the job placed at position k (1-indexed, counting from the start) finishes at time k. A schedule is feasible only when every job's completion time is less than or equal to its own deadline — a single job finishing even one time unit late makes the whole schedule infeasible.
J4 is scheduled first, so it finishes at time 1; its deadline is 2, so 1 ≤ 2 holds.
J1 is scheduled second, so it finishes at time 2; its deadline is 4, so 2 ≤ 4 holds.
J2 is scheduled third, so it finishes at time 3; its deadline is 2, so 3 ≤ 2 fails — J2 misses its deadline by one time unit.
Because J2 already violates its deadline, the schedule (J4, J1, J2, J3) is infeasible regardless of when J3 finishes.
Cross-check against the other three orders: in each of them, the two deadline-2 jobs (J2 and J4) occupy positions 1 and 2 in some order, so both finish by time 2; the two deadline-4 jobs (J1 and J3) then occupy positions 3 and 4, comfortably finishing by time 4. Only the order that pushes a deadline-2 job to position 3 — as this schedule does with J2 — breaks feasibility, confirming that (J4, J1, J2, J3) is the one infeasible schedule among the four.
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