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MathidiaMathematics Academy
Operations research
Lesson 55 of 75
Review

Scheduling

Objective. Model precedence, resources and completion time.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Scheduling models how tasks with durations and precedence constraints are sequenced onto resources to minimise completion time, using tools such as the critical path method (CPM). The critical path is the longest chain of dependent tasks from start to finish, and it determines the minimum project duration since any delay on it delays the whole project; tasks off this path have slack. For example, if task A (3 days) must precede task B (5 days), and task C (4 days) runs independently, the critical path is A→B with length 8 days, longer than C's 4 days. Resource levelling then adjusts timing to avoid overloading any single resource.

Worked example

A scheduling problem has two paths from start to finish: path P1 = task X (2 days) then task Y (6 days), and path P2 = task Z (5 days) then task W (5 days). Find the project's minimum completion time using the critical path.

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Illustrated card showing 1 … 2
  1. 1Compute the duration of path P1: 2 + 6 = 8 days.
  2. 2Compute the duration of path P2: 5 + 5 = 10 days.
  3. 3Compare the two path durations, 8 and 10, to identify the critical (longest) path.
  4. 4Since P2 is longer, the minimum completion time equals the critical path length of 10 days.

Answer: 10 days

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Common mistake. A common mistake is assuming the path with the most tasks is automatically the critical path; the critical path is the one with the longest total duration, which can have fewer, longer tasks than a path with more, shorter ones.

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