ITPEC IP April 2024 Question 67

Topic: Corporate ActivitiesAlso asked in October 2019, Spring 2021 and April 2026

There are activities A, B, and C that use machines X and Y, and it is required in each activity that the machines are used in the sequence of machine X, machine Y. When the use times of machines X and Y in each activity are as shown in the table below, which of the following is the sequence of the activities where the total time required to complete the three (3) activities becomes minimum? Here, machines X and Y can be used in parallel as shown in the figure below, but two (2) or more tasks cannot be performed simultaneously with any machine and the sequence of activities must be the same for both machines.

Table Use times of machines X and Y in each activity

 Use time of machine XUse time of machine Y
Activity A8 minutes10 minutes
Activity B10 minutes5 minutes
Activity C6 minutes8 minutes
Activity A(8 minutes)Activity B(10 minutes)Activity C(6 minutes)Activity A(10 minutes)Activity B(5 minutes)Activity C(8 minutes)Machine XMachine Y

Figure Schedule of using the machines (Example of when activities are performed in the sequence A → B → C)

Explanation

C → A → B — start with the activity that frees machine X soonest and end with the one that is shortest on machine Y.

Johnson's rule: take the smallest time in the table; if it is on X, schedule that activity first, if on Y, last; repeat with the rest. The smallest is B on Y (5 minutes), so B goes last; of A and C the smallest is C on X (6 minutes), so C goes first. Tracing each order (Y starts an activity when X has finished it and Y is free):

OrderMachine Y finishes at
A → B → C32 minutes (Y idles 8, then waits 1 for C)
A → C → B31 minutes (Y idles 8 at the start)
C → A → B29 minutes
C → B → A34 minutes (Y waits 2 for B and 3 for A)

For C → A → B: X runs C 0–6, A 6–14, B 14–24; Y runs C 6–14, A 14–24, B 24–29. Y never waits after starting: 6 + 23 = 29 minutes.

Answer (c)

Why not others:

  • •(a) A → B → C — the example in the figure; Y waits 8 minutes for A to start and again between B and C, finishing at 32
  • •(b) A → C → B — no gaps once Y starts, but starting with A's 8 minutes on X instead of C's 6 delays Y by 2 minutes, finishing at 31
  • •(d) C → B → A — Y waits for B and then for A, and A's 10 minutes on Y come last, finishing at 34

Key rule: In two-machine scheduling, keep the second machine busy: the first job should be short on the first machine, and the last job short on the second machine.

Corporate Activities · AI-written, may contain errors

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