| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D2 techniques: drawing activity networks, finding earliest/latest times, identifying critical paths, and drawing resource histograms. While part (e) requires some problem-solving for resource levelling, the overall question follows textbook procedures with no novel insights required. The multi-part structure and moderate computational demands place it slightly below average difficulty for A-level. |
| 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 |
| Activity | Immediate predecessors | Duration (days) | Number of workers required |
| A | - | 3 | 5 |
| B | A | 8 | 2 |
| C | A | 7 | 3 |
| \(D\) | \(B , C\) | 8 | 4 |
| E | C | 10 | 2 |
| \(F\) | C | 3 | 3 |
| \(G\) | D, E | 3 | 4 |
| H | \(F\) | 6 | 1 |
| I | \(G , H\) | 2 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 2 | 3 |
| 1 | H | T |
| I | T | 6 |
Question 1:
1 | 2 | 3 | 5 | 0 | 0 | 0 | 0
1 | H | T | 5
I | T | 61 [Figures 1 and 2, printed on the insert, are provided for use in this question.]\\
A group of workers is involved in a building project. The table shows the activities involved. Each worker can perform any of the given activities.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Immediate predecessors & Duration (days) & Number of workers required \\
\hline
A & - & 3 & 5 \\
\hline
B & A & 8 & 2 \\
\hline
C & A & 7 & 3 \\
\hline
$D$ & $B , C$ & 8 & 4 \\
\hline
E & C & 10 & 2 \\
\hline
$F$ & C & 3 & 3 \\
\hline
$G$ & D, E & 3 & 4 \\
\hline
H & $F$ & 6 & 1 \\
\hline
I & $G , H$ & 2 & 3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Complete the activity network for the project on Figure 1.
\item Find the earliest start time and the latest finish time for each activity, inserting their values on Figure 1.
\item Find the critical path and state the minimum time for completion.
\item The number of workers required for each activity is given in the table above. Given that each activity starts as early as possible and assuming there is no limit to the number of workers available, draw a resource histogram for the project on Figure 2, indicating clearly which activities take place at any given time.
\item It is later discovered that there are only 7 workers available at any time. Use resource levelling to explain why the project will overrun and indicate which activities need to be delayed so that the project can be completed with the minimum extra time. State the minimum extra time required.
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2008 Q1 [15]}}