Scheduling and Sequencing Questions and Answers

Answer: B

The minimum total completion time is 33 hours.

Two machines in a fixed order is the case solved by Johnson's rule: parts whose milling time is less than their polishing time go first, in increasing order of milling time; the rest go last, in decreasing order of polishing time.

• Milling less than polishing: P3 (3, 4), P4 (4, 6), P5 (5, 7), in that order.
• The rest, by decreasing polishing time: P1 (6), P6 (4), P2 (2), P7 (1).

Sequence P3, P4, P5, P1, P6, P2, P7. Milling ends at 3, 7, 12, 20, 26, 29, 31 hours. Each polishing job starts at the later of its milling end and the previous polishing end:

The last part finishes polishing at 33 hours. 31 is only the total milling time, which ignores the final part's polishing; no sequence can finish in 30 or 32, since Johnson's rule gives the minimum.

Answer: A

The jobs with critical ratio below one are Job N and Job O.

Critical ratio = (time remaining until due date) / (work remaining). On day 20:

\[ \begin{aligned} M &: (26 - 20)/5 = 1.2 \\ N &: (24 - 20)/10 = 0.4 \\ O &: (28 - 20)/10 = 0.8 \\ P &: (31 - 20)/5 = 2.2 \end{aligned} \]

A ratio below 1 means the job is behind schedule. Only N and O qualify. M and P are ahead of schedule, so the options containing them are wrong.