| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms: drawing an activity network from a precedence table, finding early/late times, calculating lower bound for workers, and scheduling. While multi-part with 13 marks, each component follows textbook procedures with no novel problem-solving required, making it easier than average A-level maths questions. |
| 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 interpretation7.05e Cascade charts: scheduling and effect of delays |
| Activity | Time taken (days) | Immediately preceding activities |
| A | 5 | - |
| B | 7 | - |
| C | 8 | - |
| D | 5 | A |
| E | 7 | A |
| F | 10 | B, C |
| G | 4 | B, C |
| H | 9 | C |
| I | 8 | G, H |
| J | 12 | G, H |
| K | 7 | D |
| L | 10 | E, F, I, J |
7.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Time taken (days) & Immediately preceding activities \\
\hline
A & 5 & - \\
\hline
B & 7 & - \\
\hline
C & 8 & - \\
\hline
D & 5 & A \\
\hline
E & 7 & A \\
\hline
F & 10 & B, C \\
\hline
G & 4 & B, C \\
\hline
H & 9 & C \\
\hline
I & 8 & G, H \\
\hline
J & 12 & G, H \\
\hline
K & 7 & D \\
\hline
L & 10 & E, F, I, J \\
\hline
\end{tabular}
\end{center}
The table shows the activities required for the completion of a building project. For each activity the table shows the time taken, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ba22b22e-c0d5-438d-821b-88619eacdb5d-8_768_1162_1238_431}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
Figure 6 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the numbers in brackets on the arcs are the times taken, in days, to complete each activity.
\begin{enumerate}[label=(\alph*)]
\item Add activities, E, F and I, and exactly one dummy to Diagram 1 in the answer book.
\item Complete Diagram 1 in the answer book to show the early event times and late event times.
\item Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.\\
(2)
\item Schedule the activities, using the minimum number of workers, so that the project is completed in the minimum time.\\
(Total 13 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2015 Q7 [13]}}