D1 January 2013 Q7

EdexcelOld spec16 marksCritical Path Analysis

Figure 7: activity network with events 1 to 9 and activities A to M — Figure 7

Figure 7 is the activity network relating to a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time to complete the activity. Each activity requires one worker.

The project must be completed in the shortest possible time.

(a) Explain the reason for the dotted line from event 4 to event 6 as shown in Figure 7. (2)

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

(d) Calculate the total float for activity G. You must make the numbers you use in your calculation clear. (2)

(e) Draw a Gantt chart for this project on the grid provided in the answer book. (4)

(f) State the activities that must be happening at time 5.5 (1)

(g) Use your Gantt chart to determine the minimum number of workers needed to complete the project in the minimum time. You must justify your answer. (2)

Mark scheme (a)

Scheme	Marks
Activity K depends on activities E, F and B, but activity I depends on F and B only.	B2, 1, 0
	(2)

Notes

a1B1 K, I, E and at least one of B or F referred to. Correct statement but may be incomplete give bod here.

a2B1 Clear correct statement no bod (at least one of only B or F referred to can score this mark).

Activity network with early and late event times: 1 0/0, 2 9/9, 3 6/9, 4 16/16, 5 12/15, 6 16/17, 7 19/19, 8 14/18, 9 21/21 — Mark scheme (b)

Scheme	Marks
	M1 A1 M1 A1
	(4)

Scheme	Marks
Critical activities are: A, F, I, L	B1
	(1)

Scheme	Marks
Total float on G = 15 – 6 – 6 = 3	M1 A1
	(2)

Gantt chart: critical activities A, F, I, L on one row; non-critical activities B, C, D, E, G, H, J, K, M with floats shaded — Mark scheme (e)

Scheme	Marks
	M1 A1 A1 A1
	(4)

Scheme	Marks
Activities A, C and D must be happening at time 5.5	B1
	(1)

Mark scheme (g)

Scheme	Marks
E.g. Activities F, B, C and G together with \(9 \lt \text{time} \lt 10\) stated	M1
So 4 workers are needed	A1
	(2)
	(16 marks)

Notes

g1M1 A statement with the correct number of workers and details of either time or activities correct. If no part of their statement is correct then allow M mark (only) on the ft with time and activities from their 13 activity, 9 float diagram. Scheduling the activities only or a lower bound calculation argument scores M0.

g1A1 A correct, complete full statement details of time and activities (The two options are F, B, C and G with \(9 \lt \text{time} \lt 10\) or F, C, G and H with \(10 \lt \text{time} \lt 11\)). Please note strict inequalities for the time. Allow e.g. on ‘day 10’ as equivalent to \(9 \lt \text{time} \lt 10\).