Chapter: Assignment Problem and Sequencing· Mathematics & Statistics (Commerce) Part 2

If jobs I, II, III have processing times as 8, 6, 5 on machine M1 and 8, 3, 4 on machine M2 in the order M1-M2. Then the optimal sequence is ____.

Q.4 (A)(iv) If jobs I, II, III have processing times as 8, 6, 5 on machine M₁ and 8, 3, 4 on machine M₂ in the order M₁-M₂. Then the optimal sequence is ____.

A. I II III

B. I III II

C. II I III

D. III II I

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Answer: (b) I III II

By Johnson's rule: the smallest time is 3 (job II on M₂), so job II is placed last. Next smallest is 4 (job III on M₂), so job III is placed in the last available position, just before II. Job I takes the remaining first position. Optimal sequence: I → III → II.

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If jobs I, II, III have processing times as 8, 6, 5 on machine M1 and 8, 3, 4 on machine M2 in the order M1-M2. Then the optimal sequence is ____.

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