Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the total elapsed time :JobsIIIIIIIVVLathe41525Surface grinder32436

Answer: Optimal sequence II → IV → V → III → I; total elapsed time 21 hours.

Johnson's rule (lathe = M₁, grinder = M₂):

• Smallest time 1 (job II on lathe): place II first.
• Next smallest 2 (job IV on lathe): place IV in the next position from the start.
• Next smallest 3 (job I on grinder): place I last.
• Next smallest 4 (job III on grinder): place III just before I.
• Remaining job V takes the middle position.

Optimal sequence: II, IV, V, III, I.

Total elapsed time \(T = 21\) hours.

Idle time on lathe \(= 21 - 17 = 4\) hours; idle time on grinder \(= 1 + 2 = 3\) hours.