| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find range for variable duration |
| Difficulty | Standard +0.3 This is a standard Critical Path Analysis question requiring network drawing, critical path identification, and float calculation. Part (c) asks for total float of activity F, which is a routine application of CPA techniques taught in D2. The network is straightforward with no complex dependencies or tricky logic. |
| 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 float |
| Activity | Depends on | Duration (hours) |
| A | - | 5 |
| B | A | 4 |
| C | A | 2 |
| D | B, C | 11 |
| E | C | 4 |
| \(F\) | D | 3 |
| G | D | 8 |
| \(H\) | D, E | 2 |
| I | \(F\) | 1 |
| J | \(F , G , H\) | 7 |
| \(K\) | \(I , J\) | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Completed activity network with all values (forward and backward scan) | M2 A2 | Must show all early/late event times correctly |
| Answer | Marks |
|---|---|
| Lower figures give forward scan | M1 |
| Upper figures give backward scan | M1 A1 |
| Critical path is \(ABDGJK\) | A1 |
| Minimum time is 37 hours | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(28 - 20 = 8\) hours | B1 | (10 marks total) |
# Question 3:
## Part (a)
| Completed activity network with all values (forward and backward scan) | M2 A2 | Must show all early/late event times correctly |
## Part (b)
| Lower figures give forward scan | M1 | |
| Upper figures give backward scan | M1 A1 | |
| Critical path is $ABDGJK$ | A1 | |
| Minimum time is 37 hours | A1 | |
## Part (c)
| $28 - 20 = 8$ hours | B1 | **(10 marks total)** |
---3. A project consists of 11 activities, some of which are dependent on others having been completed. The following precedence table summarises the relevant information.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Depends on & Duration (hours) \\
\hline
A & - & 5 \\
\hline
B & A & 4 \\
\hline
C & A & 2 \\
\hline
D & B, C & 11 \\
\hline
E & C & 4 \\
\hline
$F$ & D & 3 \\
\hline
G & D & 8 \\
\hline
$H$ & D, E & 2 \\
\hline
I & $F$ & 1 \\
\hline
J & $F , G , H$ & 7 \\
\hline
$K$ & $I , J$ & 2 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw an activity network for the project.
\item Find the critical path and the minimum time in which the project can be completed.
Activity $F$ can be carried out more cheaply if it is allocated more time.
\item Find the maximum time that can be allocated to activity $F$ without increasing the minimum time in which the project can be completed.
\end{enumerate}
\hfill \mbox{\textit{OCR D2 Q3 [10]}}