D1 June 2011 Q7

EdexcelOld spec16 marksCritical Path Analysis

Figure 7: activity network on events 1 to 8: A (4) 1–2, B (7) 1–3, dummy 3–2, E (2) 2–5, C (4) 2–4, D (5) 3–4, F (5) 3–6, G (4) 3–7, dummy 4–5, H (4) 4–6, I (3) 5–6, J (10) 5–8, K (5) 6–8, dummy 6–7, L (6) 7–8 — Figure 7

A project is modelled by the activity network shown in Figure 7. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest possible time.

(a) Complete the precedence table in the answer book. (3)

(b) Complete Diagram 1 in the answer book, to show the early event times and late event times. (4)

(d) On the grid in your answer book, draw a cascade (Gantt) chart for this project. (4)

(e) By considering the activities that must take place between time 7 and time 16, explain why it is not possible to complete this project with just 3 workers in the minimum time. (3)

Mark scheme (a)

Scheme

Marks

Activity	Proceeded by	Activity	Proceeded by	Activity	Proceeded by
(A)	(-)	E	A B	I	C D E
(B)	(-)	(F)	(B)	J	C D E
C	A B	(G)	(B)	K	F H I
(D)	(B)	H	C D	L	F G H I

B3,2,1,0

(3)

Notes

(a)1B1 Any two rows correct

2B1 Any four rows correct

3B1 All seven rows correct

Event times (early/late): 1: 0/0; 2: 7/8; 3: 7/7; 4: 12/12; 5: 12/12; 6: 16/16; 7: 16/16; 8: 22/22 — Mark scheme (b)

Scheme	Marks
	M1 A1 M1 A1
	(4)

Scheme	Marks
Critical activities are B D J H L	M1 A1
	(2)

Cascade chart: critical B 0–7, D 7–12, H 12–16, L 16–22, J 12–22; A 0–4 float to 8; C 7–11 float to 12; E 7–9 float to 12; F 7–12 float to 16; G 7–11 float to 16; I 12–15 float to 16; K 16–21 float to 22 — Mark scheme (d)

Scheme	Marks
	M1 A1 M1 A1
	(4)

Mark scheme (e)

Scheme	Marks
E.g. Between time 7 and 16, 3 workers could do 3 x 9 = 27 days work. Activities C, D, E, F, G, H, I and 4 days of J need to be done This totals 31 days work. So it is not possible to complete the project with three workers.	B3,2,1,0
OR If three workers are used three activities H, J and I need to happen at time 13.5, this reduces the float on F and G, meaning that at 10.5 D, C, F and G need to be happening. Our initial assumption is incorrect hence four workers are needed.
	(3)
	(16 marks)

Notes

(e)1B1 Attempt at explanation – one correct idea.

2B1 Good explanation, some imprecise or vague statements – give bod

3B1 Fully correct explanation. No bod needed