D1 January 2012 Q7

EdexcelOld spec16 marksCritical Path Analysis

Figure 7: activity network on events 1 to 8: A (6) 1–2, B (5) 1–4, C (7) 1–3, D (5) 2–6, E (6) 2–4, F (8) 3–4, G (4) 3–7, H (5) 3–5, dummy 4–6, dummy 5–7, I (6) 4–8, K (3) 6–8, J (4) 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 required, in hours, to complete the activity. The numbers in circles are the event numbers. Each activity requires one worker.

(a) Explain the significance of the dummy activity

(i) from event 4 to event 6,

(ii) from event 5 to event 7

(3)

(b) Calculate the early time and the late time for each event. Write these in the boxes in the answer book. (4)

(c) Calculate the total float on each of activities D and G. You must make the numbers you use in your calculations clear. (3)

(d) Calculate a lower bound for the minimum number of workers required to complete the project in the minimum time. (2)

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

Mark scheme (a)

Scheme	Marks
(i) I depends on B, E and F only, K depends on B, E, F and D	B1 DB1
(ii) This is so that G and H will not share the same start and end events. So that G and H can be uniquely described in terms of their end events.	B1
	(3)

Notes

ai1B1: K, I, D and at least one of B, E, F referred to. Correct statement but maybe incomplete give bod here.

ai2DB1: Clear correct statement. No bod.

aii3B1: correct statement referring to either events or activities. (‘unique’ alone not enough)

Event times (early/late): 1: 0/0; 2: 6/9; 3: 7/7; 4: 15/15; 5: 12/17; 6: 15/18; 7: 12/17; 8: 21/21 — Mark scheme (b)

Scheme	Marks
	M1 A1 M1 A1
	(4)

Mark scheme (c)

Scheme	Marks
Total float on D = 18 – 5 – 6 = 7 Total float on G = 17 – 4 – 7 = 6	M1 A1ft B1
	(3)

Notes

c1M1: Correct calculation seen once, all three numbers correct (ft).

c1A1ft: one float ( \(\geqslant\) 0) correct.

c1B1: Both floats correct (independent of working)

Cascade chart: critical C 0–7, F 7–15, I 15–21; A 0–6 with float; B 0–5 with float; D 6–11 with float; E 6–12 with float; G 7–11 with float; H 7–12 with float; J 12–16 with float; K 15–18 with float — Mark scheme (e)

Scheme	Marks
Lower bound = \(\dfrac{59}{21} = 3\) workers	M1 A1cso
	(2)