| Exam Board | Edexcel |
|---|---|
| Module | FD1 (Further Decision 1) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - create schedule/chart |
| Difficulty | Standard +0.8 This is a multi-part critical path analysis question requiring precedence network calculations, lower bound determination using sum of activity times divided by project duration, and construction of a resource-constrained schedule. While the techniques are standard for Further Decision 1, the combination of tasks and the need to optimize worker allocation while respecting precedence constraints requires careful systematic work and is more demanding than typical single-concept 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 interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| All top boxes completed, numbers generally increasing L to R | M1 | Condone one "rogue" |
| Top boxes correct (including zero at source node) | A1 | cao |
| All bottom boxes completed, numbers generally decreasing R to L | M1 | Condone one "rogue" |
| Bottom boxes correct (including zero at sink node) | A1 | cao |
| (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{71}{22} = \ldots\) | M1 | |
| \(\ldots = 3.22\ldots\) therefore 4 workers | A1 | |
| (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Cascade/Gantt chart with correct structure and time axis 0–26 | M1 | |
| Tasks A, B, C, D, E, F, G, H, I, J, K, L correctly placed | A1 | |
| Task M correctly placed | A1 | |
| (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempt to find lower bound \((71 \pm 10)\) / their completion time | M1 | A value of 3.2... seen with no working can imply this mark |
| cso - correct calculation seen or 3.2 followed by 4 | A1 | An answer of 4 with no working scores M0A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Not a cascade chart, 4 'workers' used at most and at least 9 different activities placed | M1 | — |
| 4 workers. All 13 activities present (just once). Condone at most two errors. | A1 | If an activity appears for two different workers simultaneously this is A0. An activity can give rise to at most three errors: one on duration, one on time interval, one on IPA |
| 4 workers. All 13 activities present (just once). No errors | A1 | — |
| Answer | Marks | Guidance |
|---|---|---|
| Activity | Duration | Time Interval |
| A | 4 | \(0-4\) |
| B | 6 | \(0-8\) |
| C | 10 | \(0-15\) |
| D | 2 | \(4-9\) |
| E | 4 | \(4-8\) |
| F | 5 | \(8-15\) |
| G | 6 | \(8-15\) |
| H | 7 | \(8-15\) |
| I | 2 | \(8-16\) |
| J | 7 | \(15-22\) |
| K | 6 | \(13-22\) |
| L | 7 | \(13-22\) |
| M | 5 | \(13-22\) |
# Question 2:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| All top boxes completed, numbers generally increasing L to R | M1 | Condone one "rogue" |
| Top boxes correct (including zero at source node) | A1 | cao |
| All bottom boxes completed, numbers generally decreasing R to L | M1 | Condone one "rogue" |
| Bottom boxes correct (including zero at sink node) | A1 | cao |
| | **(4)** | |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{71}{22} = \ldots$ | M1 | |
| $\ldots = 3.22\ldots$ therefore 4 workers | A1 | |
| | **(2)** | |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Cascade/Gantt chart with correct structure and time axis 0–26 | M1 | |
| Tasks A, B, C, D, E, F, G, H, I, J, K, L correctly placed | A1 | |
| Task M correctly placed | A1 | |
| | **(3)** | |
# Question (b) [Scheduling/Cascade Chart]:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt to find lower bound $(71 \pm 10)$ / their completion time | M1 | A value of 3.2... seen with no working can imply this mark |
| cso - correct calculation seen or 3.2 followed by 4 | A1 | An answer of 4 with no working scores **M0A0** |
# Question (c) [Cascade Chart]:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Not a cascade chart, 4 'workers' used at most and at least 9 different activities placed | M1 | — |
| 4 workers. All 13 activities present (just once). Condone at most two errors. | A1 | If an activity appears for two different workers simultaneously this is A0. An activity can give rise to at most three errors: one on duration, one on time interval, one on IPA |
| 4 workers. All 13 activities present (just once). No errors | A1 | — |
Schedule table (correct answer):
| Activity | Duration | Time Interval | IPA |
|---|---|---|---|
| A | 4 | $0-4$ | - |
| B | 6 | $0-8$ | - |
| C | 10 | $0-15$ | - |
| D | 2 | $4-9$ | A |
| E | 4 | $4-8$ | A |
| F | 5 | $8-15$ | B, E |
| G | 6 | $8-15$ | B, D, E |
| H | 7 | $8-15$ | B, E |
| I | 2 | $8-16$ | B, E |
| J | 7 | $15-22$ | G, H |
| K | 6 | $13-22$ | C, F, I |
| L | 7 | $13-22$ | C, F |
| M | 5 | $13-22$ | C, F |
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{43bc1e60-d8b2-4ea5-9652-4603a26c2f78-03_700_1412_258_331}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
A project is modelled by the activity network shown in Figure 2. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity.
\begin{enumerate}[label=(\alph*)]
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
Each activity requires one worker and the project must be completed in the shortest possible time using as few workers as possible.
\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.
\item Schedule the activities using Grid 1 in the answer book.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 2021 Q2 [9]}}