I am having a tough time trying to solve the question given below

I am supposed to find the critical path but not able to draw the network diagram. Any help would be appreciated.


  • This is ADM (activity on arrow) notation. With only 4 nodes, it should be simple, but the combination of activity 3-4 and activity 4-3 introduces a loop that makes it unsolvable. Typo in your homework assignment? – Tom Boyle Mar 18 '18 at 16:28
  • @TomBoyle Actually, this was asked in our end semester examination. When we asked the professor about it, he said that there is no mistake in the question. Thanks for the reply! – Dexter Mar 18 '18 at 16:29

Why Test Questions and Homework Questions Like This Are Bad

In general, the only "correct" answer is the one that your teacher (or the test designer) says is correct. Your question is a great example of why: the activity-on-node diagram that results is not an acyclic digraph, and is therefore ambiguous.

If the "correct" answer for the question was not provided in your class materials or lectures, one has to make the assumption that Activity 3 is actually the terminal node to avoid a loop. This may or may not be correct, but ringing an answer with assumptions is often part of the project management process.

A Reasonable Solution

Given your data, you should come up with the following diagram:

Activity-on-Node Diagram

Because more activities point to "3" than "4", we're going to assume that's the terminal node and that the loop at the end resolves as 4 -> 3 rather than continuing to cycle. If you want to make other assumptions, go right ahead; just recalculate your path accordingly.

Given the assumptions stated, the longest path from 1..3 is 1 -> 2 -> 3 -> 4 -> 3, which yields a total duration of 46. No path (other than a continuous loop) that leads to 4 as the terminal activity is longer, so this is as reasonable an answer as any.

It's the answer a professional like me would give if the ambiguity couldn't be resolved beforehand. However, as noted above, its "correctness" for test purposes will be entirely at the whim of your professor.

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