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GATE 2023 PI – Question 40

Operations Research and Operations Management · Production Control · 2 marks · Multiple choice

Six jobs require drilling followed by reaming. Processing times (drilling, reaming), in minutes, are 1:(30,45), 2:(30,15), 3:(60,40), 4:(20,25), 5:(35,28), 6:(45,70). Find their sequence under Johnson’s rule.

  1. 4–1–6–3–5–2
  2. 4–6–1–5–3–2
  3. 2–1–6–3–5–4
  4. 2–1–3–6–5–4

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Correct answer: (A) 4–1–6–3–5–2

Explanation

Select the smallest remaining time, placing its job at the earliest free position for drilling or latest free position for reaming. Job 2 (15, reaming) goes last; job 4 (20, drilling) first; job 5 (28, reaming) next-to-last; job 1 (30, drilling) next; job 3 (40, reaming) into the last remaining rear slot; job 6 fills the gap. **4–1–6–3–5–2, A**.

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