AS June 2018 Q3

EdexcelAS paperCurrent spec10 marksCritical Path Analysis

Activity	Time taken (days)	Immediately preceding activities
A	5	–
B	8	–
C	4	–
D	14	A
E	10	A
F	3	B, C, E
G	7	C
H	5	D, F, G
I	7	H
J	9	H

The table above shows the activities required for the completion of a building project. For each activity, the table shows the time it takes, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time.

Figure 2: partially completed activity network with A(5), B(8) and C(4) from the start, and F(3), H(5) and I(7) in a chain after B — Figure 2

Figure 2 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the number in brackets on each arc is the time taken, in days, to complete the corresponding activity.

(a) Add the missing activities and necessary dummies to Diagram 1 in the answer book. (3)

(b) Complete Diagram 1 in the answer book to show the early event times and the late event times. (3)

Diagram 1: the network of Figure 2 with an empty box at each event for the early event time (top) and late event time (bottom) — Diagram 1

At the beginning of the project it is decided that activity G is no longer required.

(d) Explain what effect, if any, this will have on

(i) the shortest completion time of the project if activity G is no longer required,

(ii) the timing of the remaining activities. (3)

completed activity network with early/late event times: start 0/0; end of A 5/5; end of B 15/16; end of C 4/12; end of F 19/19; end of H 24/24; end of J 33/33; finish 33/33; E from the end of A to the end of B, dummy from the end of C to the end of B, D from the end of A and G from the end of C both to the end of F, and a dummy from the end of J to the finish — Mark scheme (a)

Scheme	Marks	AO
	M1 A1 A1	1.1b 1.1b 1.1b
	(3)

Scheme	Marks	AO
	M1 M1 A1	1.1b 1.1b 1.1b
	(3)

Scheme	Marks	AO
The critical activities are A, D, H and J	B1	1.1b
	(1)

Mark scheme (d)

Scheme	Marks	AO
(i) No effect (as G is not one of the critical activities)	B1	2.4
(ii) Activity C is the only affected activity and it can now start 4 days later at time 12 (rather than at time 8) or finish as late as time 16	M1 A1	3.4 1.1b
	(3)
	(10 marks)

Notes

(d)(i) B1: Explanation that there is no effect on the completion time (as G is not critical)

(d)(ii) M1: Use their model to deduce that C is the (only) activity that is affected

A1: Correct answer that activity C (only – maybe implicit) can e.g. finish at time 16 or start at time 12 – for this mark the explanation must give a relevant time