Moderate -0.8 This is a straightforward application of critical path analysis concepts. Part (a) is routine network drawing with standard dummy placement rules. Part (b) requires only basic logical reasoning: if all critical paths include H, then any activity that cannot be on the same path as H (due to precedence constraints) cannot be critical. This is simpler than typical CPA questions that require calculating earliest/latest times or finding float values.
Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies.
Given that all critical paths for the network include activity H ,
Seven activities (labelled on arc), one start and at least two dummies placed
M1
(5)
Activities A, B, C, 1st two dummies (including correct arrows on these two dummies), D and E dealt with correctly. The first two dummies are those at the end of activities A and C
A1
A dummy linking D, F and G into an event node and a dummy linking D, F, G, I and E into an event node and F, G and I dealt with correctly. The dummies must have arrows
A1
Activities H, J, K and L dealt with correctly
A1
CSO - all arrows correctly placed for each activity with one finish and at most four dummies. Note that this is not a unique solution due to for example the 3rd and 4th dummies so please check these carefully. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned
A1
Activities E, I, J and L cannot be critical
M1 A1
(2)
Notes for Question 5:
Condone lack of, or incorrect, numbered events throughout. 'Dealt with correctly' means that the activity starts from the correct event but need not necessarily finishes at the correct event. The table below is very useful in checking this point. Activity on node is M0
If an arc is not labelled, for example, if the arc for activity E is not labelled (but the arc is present) then this will lose the first A mark and the final (CSO) A mark – they can still earn the second A mark on the body. If two or more arcs are not labelled then mark according to the scheme. Assume that a solid line is an activity which has not been labelled rather than a dummy (even if in the correct place for where a dummy should be)
Ignore incorrect or lack of arrows on the activities for the first four marks only
- a1M1: Seven activities (labelled on arc), one start and at least two dummies placed
- a1A1: Activities A, B, C, 1st two dummies (including correct arrows on these two dummies), D and E dealt with correctly. The first two dummies are those at the end of activities A and C
- a2A1: A dummy linking D, F and G into an event node and a dummy linking D, F, G, I and E into an event node and F, G and I dealt with correctly. The dummies must have arrows
- a3A1: Activities H, J, K and L dealt with correctly
- a4A1: CSO - all arrows correctly placed for each activity with one finish and at most four dummies. Note that this is not a unique solution due to for example the 3rd and 4th dummies so please check these carefully. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned
- b1M1: At least two correct activities with no more than 5 activities stated
- b1A1: All four activities (E, I, J and L) and no others
Answer
Marks
Guidance
A
B
C
–
–
–
[Network diagram with activities A through L]
| Seven activities (labelled on arc), one start and at least two dummies placed | M1 | (5) |
|---|---|---|
| Activities A, B, C, 1st two dummies (including correct arrows on these two dummies), D and E dealt with correctly. The first two dummies are those at the end of activities A and C | A1 | |
| A dummy linking D, F and G into an event node and a dummy linking D, F, G, I and E into an event node and F, G and I dealt with correctly. The dummies must have arrows | A1 | |
| Activities H, J, K and L dealt with correctly | A1 | |
| CSO - all arrows correctly placed for each activity with one finish and at most four dummies. Note that this is not a unique solution due to for example the 3rd and 4th dummies so please check these carefully. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned | A1 | |
| Activities E, I, J and L cannot be critical | M1 A1 | (2) |
**Notes for Question 5:**
Condone lack of, or incorrect, numbered events throughout. 'Dealt with correctly' means that the activity starts from the correct event but need not necessarily finishes at the correct event. The table below is very useful in checking this point. Activity on node is M0
If an arc is not labelled, for example, if the arc for activity E is not labelled (but the arc is present) then this will lose the first A mark and the final (CSO) A mark – they can still earn the second A mark on the body. If two or more arcs are not labelled then mark according to the scheme. Assume that a solid line is an activity which has not been labelled rather than a dummy (even if in the correct place for where a dummy should be)
Ignore incorrect or lack of arrows on the activities for the first four marks only
- **a1M1:** Seven activities (labelled on arc), one start and at least two dummies placed
- **a1A1:** Activities A, B, C, 1st two dummies (including correct arrows on these two dummies), D and E dealt with correctly. The first two dummies are those at the end of activities A and C
- **a2A1:** A dummy linking D, F and G into an event node and a dummy linking D, F, G, I and E into an event node and F, G and I dealt with correctly. The dummies must have arrows
- **a3A1:** Activities H, J, K and L dealt with correctly
- **a4A1:** CSO - all arrows correctly placed for each activity with one finish and at most four dummies. Note that this is not a unique solution due to for example the 3rd and 4th dummies so please check these carefully. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned
- **b1M1:** At least two correct activities with no more than 5 activities stated
- **b1A1:** All four activities (E, I, J and L) and no others
| A | B | C | D | E | F | G | H | I | J | K | L |
|---|---|---|---|---|---|---|---|---|---|---|---|
| – | – | – | A | C | A, B, C | A, B, C | D, F, G | A, B, C | D, F, G | H | D, E, F, G, I |
---
5.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & A \\
\hline
E & C \\
\hline
F & A, B, C \\
\hline
G & A, B, C \\
\hline
H & D, F, G \\
\hline
I & A, B, C \\
\hline
J & D, F, G \\
\hline
K & H \\
\hline
L & D, E, F, G, I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies.
Given that all critical paths for the network include activity H ,
\item state which activities cannot be critical.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2020 Q5 [7]}}