| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question requiring routine application of learned procedures: calculating event times using given float information, drawing a cascade chart, and resource scheduling. While multi-part with several marks, it involves methodical application of algorithms rather than problem-solving or insight, making it slightly easier than average. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(w=11,\ x=21,\ y=17,\ z=4\) | B3, 2, 1, 0 | a1B1: any two values correct; a2B1: any three correct; a3B1: all four correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cascade/Gantt chart with at least 10 activities including 6 floats | M1 | Scheduling diagram scores M0 |
| Critical activities correct and five other non-critical activities correct | A1 | |
| Exactly 14 activities (each once) including all 10 floats on correct non-critical activities | M1 | Independent of previous A mark |
| CAO | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| At time 12.5, activities H, D, G, I and J must all be happening, so 5 workers needed | M1 A1 | M1: correct number (5) and correct activities with any mention of time; A1: complete statement with \(12 < \text{time} < 13\); allow 'on day 13' or 'during day 13' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Schedule using 3 workers (not a cascade chart), at most 4 workers used, at least 12 activities placed, completion time \(\leq 36\) | M1 | |
| 3 workers, all 14 activities present (once), condone two errors (precedence or duration), completion time \(\leq 36\) | A1 | One activity can give rise to at most two errors |
| 3 workers, all 14 activities present (once), no errors, completion time \(= 36\) | A1 |
# Question 7:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $w=11,\ x=21,\ y=17,\ z=4$ | B3, 2, 1, 0 | a1B1: any two values correct; a2B1: any three correct; a3B1: all four correct |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cascade/Gantt chart with at least 10 activities including 6 floats | M1 | Scheduling diagram scores M0 |
| Critical activities correct and five other non-critical activities correct | A1 | |
| Exactly 14 activities (each once) including all 10 floats on correct non-critical activities | M1 | Independent of previous A mark |
| CAO | A1 | |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| At time 12.5, activities H, D, G, I and J must all be happening, so 5 workers needed | M1 A1 | M1: correct number (5) and correct activities with any mention of time; A1: complete statement with $12 < \text{time} < 13$; allow 'on day 13' or 'during day 13' |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Schedule using 3 workers (not a cascade chart), at most 4 workers used, at least 12 activities placed, completion time $\leq 36$ | M1 | |
| 3 workers, all 14 activities present (once), condone two errors (precedence or duration), completion time $\leq 36$ | A1 | One activity can give rise to at most two errors |
| 3 workers, all 14 activities present (once), no errors, completion time $= 36$ | A1 | |
---7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{22ff916a-4ba8-4e0c-9c53-e82b0aff0b98-08_860_1383_239_342}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
The network in Figure 6 shows the activities that need to be undertaken by a company to complete a project. Each activity is represented by an arc and the duration, in days, is shown in brackets. Each activity requires exactly one worker. The early event times and late event times are shown at each vertex.
Given that the total float on activity D is 1 day,
\begin{enumerate}[label=(\alph*)]
\item find the values of $\boldsymbol { w } , \boldsymbol { x } , \boldsymbol { y }$ and $\boldsymbol { z }$.
\item On Diagram 1 in the answer book, draw a cascade (Gantt) chart for the project.
\item Use your cascade chart to determine a lower bound for the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to times and activities.
It is decided that the company may use up to 36 days to complete the project.
\item On Diagram 2 in the answer book, construct a scheduling diagram to show how the project can be completed within 36 days using as few workers as possible.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2016 Q7 [12]}}