| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question covering routine D1 techniques: calculating early/late times, identifying critical path, finding float, and drawing a Gantt chart. All steps follow algorithmic procedures taught directly in the syllabus with no novel problem-solving required, making it easier than average but not trivial due to the multi-part nature and potential for arithmetic errors. |
| 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/Scheme | Marks | Guidance |
| (a) 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) | M1 | (4) |
| (a) CAO for the top boxes | A1 | |
| (a) 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 43 for the M only | a2M1 | |
| (a) CAO for the bottom boxes | a2A1 | |
| (b) Critical activities: B, G, L and N | B1 | (2) |
| (b) Length of the critical path: 43 (days) | DB2B1ft | |
| (c) Total float on D = 27 – 10 – 11 = 6 (days) | M1 A1 | (2) |
| (d) Gantt chart showing: critical activities on separate lines or several activities on same line as long as their length and floats are clear and do not overlap; at least 10 activities including at least 5 floats; A scheduling diagram scores M0 | M1 | (4) |
| (d) The critical activities dealt with correctly and appearing just once (B, G, L and N) and three non-critical activities dealt with correctly | A1 | |
| (d) Any 6 non-critical activities correct (this mark is not dependent on the previous A mark) | d2A1 | |
| (d) CSO – completely correct Gantt chart (exactly 15 activities appearing just once) | d3A1 | |
| (e) Lower bound is 5 workers e.g. activities G, D, E, F and H together with 17 < time < 19 | M1 A1 | (2) |
| 14 marks |
| Answer/Scheme | Marks | Guidance |
|---|---|---|
| (a) 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) | M1 | (4) |
| (a) CAO for the top boxes | A1 | |
| (a) 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 43 for the M only | a2M1 | |
| (a) CAO for the bottom boxes | a2A1 | |
| (b) Critical activities: B, G, L and N | B1 | (2) |
| (b) Length of the critical path: 43 (days) | DB2B1ft | |
| (c) Total float on D = 27 – 10 – 11 = 6 (days) | M1 A1 | (2) |
| (d) Gantt chart showing: critical activities on separate lines or several activities on same line as long as their length and floats are clear and do not overlap; at least 10 activities including at least 5 floats; A scheduling diagram scores M0 | M1 | (4) |
| (d) The critical activities dealt with correctly and appearing just once (B, G, L and N) and three non-critical activities dealt with correctly | A1 | |
| (d) Any 6 non-critical activities correct (this mark is not dependent on the previous A mark) | d2A1 | |
| (d) CSO – completely correct Gantt chart (exactly 15 activities appearing just once) | d3A1 | |
| (e) Lower bound is 5 workers e.g. activities G, D, E, F and H together with 17 < time < 19 | M1 A1 | (2) |
| | **14 marks** | |
**Notes for Question 4:**
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 43 for the M only
a2A1: CAO for the bottom boxes
b1B1: CAO – critical activities (B, G, L and N)
Db2B1ft: follow through from their (a) – dependent on scoring the first M mark in (a)
c1M1: Correct calculation for their activity D seen – correct for their three numbers. Final value must be non-negative
c1A1: CAO (no ft on this mark). Answer of 6 with no working scores no marks in this part
Note that it is acceptable for the critical activities to appear on separate lines or for several activities to appear on the same line as long as their length and floats are clear and do not overlap
d1M1: At least 10 activities including at least 5 floats. A scheduling diagram scores M0
d1A1: The critical activities dealt with correctly and appearing just once (B, G, L and N) and three non-critical activities dealt with correctly
d2A1: Any 6 non-critical activities correct (this mark is not dependent on the previous A mark)
d3A1: CSO – completely correct Gantt chart (exactly 15 activities appearing just once)
e1M1: A statement with the correct number of workers (5) and the correct activities (G, D, E, F and H) and any time stated
e1A1: A completely correct statement with details of both time and activities. Candidates only need to give a time within the correct interval. Please note the strict inequalities for the time interval. Allow for example, 'on day 18' as equivalent to interval 17 < time < 18 – but for this mark it must absolutely clear that they are considering a time in the required interval (and not at time 17 and/or 19)
---4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{39bbf9e2-efa7-4f3e-a22d-227f83184abd-05_739_1490_239_276}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
A project is modelled by the activity network shown in Figure 3. 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 exactly 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 late event times.
\item Determine the critical activities and the length of the critical path.
\item Calculate the total float for activity D. You must make the numbers you use in your calculation clear.
\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 times and activities.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2017 Q4 [14]}}