Skip to main content

CAT DILR

CAT DILR: scheduling puzzles practice

Scheduling puzzles give you tasks, durations and dependencies and ask about minimum time, delays or which task is critical. They look intimidating but follow a simple routine: a forward pass to find the earliest finish of every task, then a backward pass to find the latest finish that does not delay the project. The difference between the two is the slack.

Key ideas

  • Forward pass: earliest finish = latest earliest finish among prerequisites + duration.
  • The project time is the largest earliest finish.
  • Backward pass: latest finish of a task = earliest latest start among the tasks that depend on it.
  • Slack = latest finish - earliest finish. Tasks with zero slack form the critical path.
  • A delay on a critical task delays the whole project by the same amount.

Common traps

  • Adding all durations instead of following dependencies.
  • Forgetting that a task can start only when all prerequisites are complete.
  • Assuming only one critical path when two can tie.

Practice set: A small project

A project has five tasks. A task can start only when all of its prerequisite tasks are complete, and there are enough workers to do any tasks in parallel.

TaskDuration (hours)Must be completed first
A3None
B2None
C4A
D2B
E3C and D

Practice questions with solutions

Try each question first, then open the solution.

  1. What is the minimum time needed to complete the project?

    • A 10 hours
    • B 7 hours
    • C 9 hours
    • D 14 hours
    Show answer and solution

    Answer: A. 10 hours

    Earliest finish: A 3, B 2, C 7, D 4, E 10. The project ends at hour 10.

  2. Which tasks lie on the critical path?

    • A A, C and E
    • B B, D and E
    • C A, D and E
    • D A, C and D
    Show answer and solution

    Answer: A. A, C and E

    A + C + E = 3 + 4 + 3 = 10 hours, equal to the project time. B + D + E is only 7 hours.

  3. How many hours of slack does task D have?

    Type in the answer (no options).

    Show answer and solution

    Answer: 3

    D finishes at hour 4 at the earliest. E starts at hour 7, so D can finish as late as hour 7. Slack = 7 - 4 = 3 hours.

  4. If task C takes 6 hours instead of 4, what is the minimum time, in hours, to complete the project?

    Type in the answer (no options).

    Show answer and solution

    Answer: 12

    The chain A, C, E now takes 3 + 6 + 3 = 12 hours.

Keep practising