| Exam Board | OCR |
|---|---|
| Module | Further Discrete (Further Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.3 This is a comprehensive critical path analysis question covering standard techniques (forward/backward pass, float calculations, cascade charts, and resource scheduling). While it has multiple parts and requires careful bookkeeping, all components are routine textbook procedures with no novel problem-solving or insight required. The resource scheduling with constraints is slightly more demanding than basic CPA but still follows standard algorithms taught in Decision Maths. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | 2 2 C(5) 7 7 |
| Answer | Marks |
|---|---|
| Minimum project completion time = 9 hours | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Forward pass unambiguously placed at vertices (ignore ends) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | 2 2 C(5) 7 7 |
| Answer | Marks |
|---|---|
| Float (hours) 0 2 0 2 2 0 3 | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Backward pass unambiguously placed at vertices (ignore ends) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (c) | Independent floatij = max(EETj – LETi - Dij, 0) |
| Answer | Marks |
|---|---|
| Interfering float (hours) 2 2 2 2 | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 2.2a | At least 3 correct or ft their early event times and late event times |
| Answer | Marks | Guidance |
|---|---|---|
| Activity | A | B |
| Float (hours) | 0 | 2 |
| Activity | B | D |
| Independent float (hours) | 0 | 0 |
| Interfering float (hours) | 2 | 2 |
| 4 | (d) | G |
| Answer | Marks |
|---|---|
| 0 1 2 3 4 5 6 7 8 9 hours | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Critical activities A, C, F labelled and correct early event times and |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (e) | e.g. |
| Answer | Marks |
|---|---|
| Worker 2 B B B B D D D E G | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 2.2a | A, B, C, D and E positioned appropriately, with correct durations |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (f) | e.g. |
| Answer | Marks |
|---|---|
| Worker 2 B B B B E D D D G | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 2.2a | D starts at time 5 (i.e. 5-6) |
| Answer | Marks | Guidance |
|---|---|---|
| A | C | F |
| Worker 1 | A | A |
| Worker 2 | B | B |
| Worker 1 | A | A |
| Worker 2 | B | B |
| 4 | 13 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | 2 | 7 |
| 9 | 7 | 7 |
Question 4:
4 | (a) | 2 2 C(5) 7 7
A(2) F(2)
0 0 D(3) 9 9
B(4) G(1)
4 6 E(1) 5 7
Minimum project completion time = 9 hours | B1
B1
[2] | 1.1
1.1 | Forward pass unambiguously placed at vertices (ignore ends)
2 7
4 5
9 cao
4 | (b) | 2 2 C(5) 7 7
A(2) F(2)
0 0 D(3) 9 9
B(4) G(1)
4 6 E(1) 5 7
Floatij = LETj – EETi – Dij
Activity A B C D E F G
Float (hours) 0 2 0 2 2 0 3 | B1
B1
M1
A1
[4] | 1.1
1.1
1.1
1.1 | Backward pass unambiguously placed at vertices (ignore ends)
2 7
6 7
Float 0 for A, C and F
Float correct for any two of B, D, E, G
Or from their EET and LET
Float correct for B, D, E and G
4 | (c) | Independent floatij = max(EETj – LETi - Dij, 0)
Interfering float = float – independent float
Activity B D E G
Independent float (hours) 0 0 0 1
Interfering float (hours) 2 2 2 2 | M1
M1
A1
[3] | 1.1
1.1
2.2a | At least 3 correct or ft their early event times and late event times
At least 3 correct or ft their float and independent float times
All correct cao
Ignore critical activities if given (with both types of float = 0)
Activity | A | B | C | D | E | F | G
Float (hours) | 0 | 2 | 0 | 2 | 2 | 0 | 3
Activity | B | D | E | G
Independent float (hours) | 0 | 0 | 0 | 1
Interfering float (hours) | 2 | 2 | 2 | 2
4 | (d) | G
E
D
B
A C F
0 1 2 3 4 5 6 7 8 9 hours | B1
M1
A1
[3] | 1.1
1.1
1.1 | Critical activities A, C, F labelled and correct early event times and
durations (on a single row or accept them on separate rows)
May use other representations
Non-critical activities B, D, E, G labelled and correct early event
times and durations (i.e. the solid line boxes), may use other
representations
Float correct, lasting until late event times (i.e. dashed boxes), may
use other representations
4 | (e) | e.g.
Worker 1 A A C C C C C F F
Worker 2 B B B B D D D E G | M1
A1
[2] | 1.1
2.2a | A, B, C, D and E positioned appropriately, with correct durations
and precedences
F, G positioned appropriately, with correct durations and
precedences (F must follow the completion of both D and E)
and project is completed in 10 hours (ends at 9-10)
4 | (f) | e.g.
Worker 1 A A C C C C C F F
Worker 2 B B B B E D D D G | M1
A1
[2] | 3.1b
2.2a | D starts at time 5 (i.e. 5-6)
All positioned appropriately, with correct durations and
precedences, project is completed in 10 hours (ends at 9-10)
G
E
D
B
A | C | F
Worker 1 | A | A | C | C | C | C | C | F | F
Worker 2 | B | B | B | B | D | D | D | E | G
Worker 1 | A | A | C | C | C | C | C | F | F
Worker 2 | B | B | B | B | E | D | D | D | G
4 | 13
21 13
4 | 2 | 7 | 5 | 13
9 | 7 | 7 | 5 | 134 A project is represented by the activity network below. The activity durations are given in hours.\\
\includegraphics[max width=\textwidth, alt={}, center]{f20391b2-e3c1-4021-9a87-47fd4ea7c490-5_346_1033_351_244}
\begin{enumerate}[label=(\alph*)]
\item By carrying out a forward pass, determine the minimum project completion time.
\item By carrying out a backward pass, determine the (total) float for each activity.
\item For each non-critical activity, determine the independent float and the interfering float.
\item Construct a cascade chart showing all the critical activities on one row and each non-critical activity on a separate row, starting at its earliest start time, and using dashed lines to indicate (total) float. You may not need to use all the grid.
Each activity requires exactly one worker.
\item Construct a schedule to show how exactly two workers can complete the project as quickly as possible. You may not need to use all the grid.
Issues with deliveries delay the earliest possible start of activity D by 3 hours.
\item Construct a schedule to show how exactly two workers can complete the project with this delay as quickly as possible. You may not need to use all the grid.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete 2024 Q4 [16]}}