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Draw a critical path network from the above info

Computer Science

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Step-by-step solution

3 steps

To draw a Critical Path Method (CPM) network, we represent activities as nodes or arrows and dependencies as connections between them. The durations are assigned to each activity.

  1. Identify start activities.

    Activities A and B have no predecessors, so they start from a common 'Start' node.

  2. Draw activities and their immediate predecessors.

    • Activity C depends on A.
    • Activity D depends on A and B. This requires a merge point for A and B before D can start.
    • Activity E depends on C.
    • Activity F depends on D.
    • Activity G depends on E and F. This requires a merge point for E and F before G can start.
  3. Assign durations to each activity.

    The durations are: A=4, B=6, C=3, D=5, E=4, F=3, G=2.

    The critical path network diagram is shown below. Each node represents an event, and each arrow represents an activity with its duration.

    Start→A (4)Node 1→C (3)Node 2→E (4)Node 3↘Start→B (6)Node 4↗Node 1↘Node 4→D (5)Node 5→F (3)Node 6↗Node 3 and Node 6 merge→G (2)End\boxed{ \text{Start} \xrightarrow{\text{A (4)}} \text{Node 1} \xrightarrow{\text{C (3)}} \text{Node 2} \xrightarrow{\text{E (4)}} \text{Node 3} \searrow \\ \text{Start} \xrightarrow{\text{B (6)}} \text{Node 4} \nearrow \\ \text{Node 1} \searrow \\ \text{Node 4} \xrightarrow{\text{D (5)}} \text{Node 5} \xrightarrow{\text{F (3)}} \text{Node 6} \nearrow \\ \text{Node 3} \text{ and } \text{Node 6} \text{ merge} \xrightarrow{\text{G (2)}} \text{End} }

    Here is a more visual representation of the network:

    (Start)
       |
       |-- A (4 weeks) --> (Node 1) -- C (3 weeks) --> (Node 2) -- E (4 weeks) --> (Node 3)
       |                                                                               |
       |-- B (6 weeks) --> (Node 4) -- D (5 weeks) --> (Node 5) -- F (3 weeks) --> (Node 6)
                                                                                   |
                                                                                   V
                                                                                 (Node 7) -- G (2 weeks) --> (End)
    

    Note: Node 7 represents the merge point of E and F before G can start.

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