| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2019 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms: forward/backward pass for event times, identifying critical path, and drawing a cascade chart. While multi-part with several marks, each step follows a mechanical procedure taught explicitly in the specification with no novel problem-solving or insight required. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| [Activity network diagram with nodes and values shown] | M1 | |
| A1 | ||
| M1 | ||
| A1 | (4) | |
| Critical activities: E, F and K | B1 | (1) |
| [Gantt chart showing activities and time intervals] | M1 | |
| A1 | ||
| A1 | ||
| A1 | (4) | |
| Minimum workers is 4 activities K, I, J and L together with \(18 < t < 22\) | M1 | |
| A1 | (2) | |
| 11 marks |
| Answer/Working | Marks | Guidance |
|---|---|---|
| [Activity network diagram with nodes and values shown] | M1 | |
| | A1 | |
| | M1 | |
| | A1 | (4) |
| **Critical activities**: E, F and K | B1 | (1) |
| [Gantt chart showing activities and time intervals] | M1 | |
| | A1 | |
| | A1 | |
| | A1 | (4) |
| **Minimum workers is 4 activities** K, I, J and L together with $18 < t < 22$ | M1 | |
| | A1 | (2) |
| | **11 marks** | |
**Notes for Question 3:**
- **a1M1**: All top boxes complete, values in the top boxes generally increasing in the direction of the arrows ('left to right'), condone one 'rogue' value (if values do not increase in the direction of the arrows then if one value is ignored and then the values do increase in the direction of the arrows then this is considered to be only one rogue value)
- **a1A1**: CAO for the top boxes
- **a2M1**: All bottom boxes complete, values generally decreasing in the opposite direction of the arrows ('right to left'), condone one rogue. Condone missing 0 and/or 33 for the M only
- **a2A1**: CAO for the bottom boxes
- **b1B1**: CAO (E, F and K only)
- **c1M1**: At least ten activities including at least six floats. A scheduling diagram scores M0.
- **c1A1**: The correct critical activities dealt with correctly and appearing just once (E, F and K) and three non-critical activities dealt with correctly
- **c2A1**: Any seven non-critical activities correct (this mark is not dependent on the previous A mark)
- **c3A1**: CSO – completely correct Gantt chart (exactly thirteen activities appearing just once)
- **d1M1**: Either a statement with the correct number of workers (4) and the correct activities (K, I, J and L) with any numerical time stated or the correct number of workers (4) and a correct time in the interval $18 < t < 22$ (note strict inequalities) or the correct activities and a correct time in the interval $18 < t < 22$
- **d1A1**: A completely correct statement with details of both time and activities. Candidates only need to give a time within the correct interval of $18 < t < 22$. Please note the strict inequalities for the time interval (e.g. implying a time of 18 is incorrect). Answers given as an interval of time are acceptable provided the time interval stated is correct for all its possible values (e.g. time $18 – 19$ is A0). Allow for example, 'on day 19' as equivalent to $18 < t < 19$.
**Alternative solution for (d)**: M1 for 4 workers, correct activities of E, A, G and H, and a mention of a time in the interval $4 < t < 6$. A1 for the above + explicit reference to G having to take place in either the time interval $4 < t < 5$ or the time interval $5 < t < 6$ (so must infer that if G doesn't happen in one time interval then it must happen in the other – mentioning just one of these intervals is A0)
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-04_848_1394_210_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 days, to complete the corresponding activity. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
\item State the critical activities.
\item Draw a cascade (Gantt) chart for this project on Grid 1 in the answer book.
\item Use your cascade chart to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2019 Q3 [11]}}