A2 October 2021 Q7

EdexcelCurrent spec8 marksCritical Path Analysis

Figure 5: partial activity network: A, B and C leave the start; D, E and F leave the end of A; F ends at the end of B; a dummy runs from there to the end of C; G leaves the end of B and F; H leaves the end of C and the dummy; E, G and H end at the same event; D ends at its own event — Figure 5

Figure 5 shows a partially completed activity network for a project that consists of 14 activities.

(a) Complete the precedence table in the answer book for the 8 activities in Figure 5. (2)

Activity	Immediately preceding activities	Activity	Immediately preceding activities
A		E
B		F
C		G
D		H

The precedence table for the remaining 6 activities is given below.

Activity	Immediately preceding activities
I	D, E, G, H
J	D, E, G, H
K	E, G, H
L	I, J, K
M	J, K
N	J, K

(b) Complete the activity network in the answer book for the project. Your completed activity network must contain only the minimum number of dummies. (4)

[The activity network in the answer book is a copy of Figure 5.]

Given that all 14 activities have the same duration,

Mark scheme (a)

Scheme

Marks

Activity	Immediately preceding activities
A	-
B	-
C	-
D	A
E	A
F	A
G	B, F
H	B, C, F

B1
B1

1.1b
1.1b

(2)

Notes

(a) B1: Either row G or H correct

B1: All rows correct (condone blanks in A, B and C rows)

completion of the network: D ends at an event from which I and J leave; E, G and H end at an event from which K leaves, with a dummy from it up to the end of D; J and K end at the same event, from which N leaves; a dummy runs from there up to a middle event, from which M leaves, and a second dummy from the middle event up to the end of I, from which L leaves; L, M and N end at the finish — Mark scheme (b)

Scheme	Marks	AO
e.g.	M1 A1 A1 A1	2.1 1.1b 1.1b 1.1b
	(4)

Mark scheme (c)

Scheme	Marks	AO
If all activities have the same duration then any critical path must contain 5 activities. All paths that pass-through D have only 4 activities and so therefore D cannot be critical.	B1 B1	2.4 2.4
	(2)
	(8 marks)

Notes

(c) B1: Explains that all critical paths must contain 5 activities (oe method e.g., attempting a forward and backward pass with each activity having the same duration)

B1: cao that D cannot be critical with mention of all paths through D only contain 4 activities (oe method e.g., showing that the total float on activity D is not zero)

SCB1: stating or implying that D has a float of 1 (oe) by considering a forward pass (which may or may not be done mathematically) up to at least activity D