Determine the optimal sequence of jobs that minimizes the total elapsed time for the data given below (processing time on machines is given in hours). Also find the total elapsed time and the idle time for three machines.JobsIIIIIIIVVVIVIIMachine A38…

Answer: Optimal sequence I \(\to\) IV \(\to\) VII \(\to\) VI \(\to\) II \(\to\) III \(\to\) V; total elapsed time 59 hrs; idle time A = 13 hrs, B = 37 hrs, C = 7 hrs.

Finding the sequence (Johnson's rule on G and H):

• Smallest time is 6 (job V on H): place V last.
• Next smallest is 7: job I on G (place first) and job III on H (place in the last free position, before V).
• Next is 9: job IV on G, place in the next free position from the start.
• Next is 10: job VII on G goes next from the start; jobs II and VI both have 10 on H, so they fill the remaining positions from the end (II, then VI before it), as given in the paper.

Optimal sequence: I, IV, VII, VI, II, III, V

Completed boxes in the work table: the third job is VII (A 7 hrs, B 3 hrs, C 12 hrs); job II enters machine C at 42 (C is free only when job VI leaves it at 42); the sixth job is III (A 7, B 2, C 5).

Total elapsed time = 59 hrs.

Idle time for machine A = \(59-46=13\) hrs (A finishes its last job at 46).

Idle time for machine B = \(59-\) (total processing time on B) \(=59-(4+3+2+5+1+4+3)=59-22=37\) hrs.

Idle time for machine C = \(59-(6+7+5+11+5+6+12)=59-52=7\) hrs.