D1 June 2013 (R) Q3
3.

A project is modelled by the activity network shown in Figure 3. 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.
Diagram 2 in the answer book shows a partly completed scheduling diagram for this project.
| Scheme | Marks |
|---|---|
![]() | M1 A1 M1 A1 |
| (4) |
Notes
a1M1 All top boxes complete, values generally increasing left to right, condone one rogue.
a1A1 CAO.
a2M1 Bottom boxes complete, values generally decreasing right to left, condone one rogue. Condone missing 0 or 37 for the M mark only.
a2A1 CAO
| Scheme | Marks |
|---|---|
| Total float on H = 20 – 9 – 5 = 6 | M1 A1 |
| (2) |
Notes
b1M1 Correct calculation seen. All three numbers correct (ft).
b1A1 Float correct (no follow through on this mark)
| Scheme | Marks |
|---|---|
| 93/37 = 2.5135 so 3 (workers) | M1 A1 |
| (2) |
Notes
c1M1 Attempt to find lower bound. [82 – 104 / their finish time] accept awrt 2.5
c1A1 CAO – correct calculation seen or awrt 2.5, then 3. (Beware 37/13 gives 3 also, so 3 with no working gets M0A0.)
| Scheme | Marks |
|---|---|
![]() | M1 A1 M1 A1 |
| (4) | |
| (12 marks) |
Notes
d1M1 Not a cascade chart. 4 workers used at most. At least 8 new (10 in total) activities placed.
d1A1 The critical activities (F I K M) and B correct. F – 8; I – 9; K – 5; M – 6; B – 7. B completed by 9 (its late finish time).
Now check the last 6 activities – the last two marks are for D, E, G, H, J and L only
First check that there are only three workers and that all 11 new (13 in total) activities are present (just once).
Then check precedences (see table below) – each row of the table could give rise to 1 error only in precedences
Finally check the length of each activity (see number in brackets in the activity column in the table below)
| Activity | I.P.A | Activity | I.P.A |
|---|---|---|---|
| A (8) | - | H (5) | C |
| B (7) | - | I (9) | E F |
| C (9) | - | J (11) | G H |
| D (9) | A | K (5) | D I |
| E (5) | A | L (4) | D I |
| F (8) | B C | M (6) | E F J K |
| G (7) | B C |
d2M1 3 workers. All 11 new (13 in total) activities present (just once). Condone one error either precedence, or activity length, on activities D, E, G, H, J and L.
d2A1 3 workers. All 11 new (13 in total) activities present (just once). No errors on activities D, E, G, H, J and L.

