| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2002 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - determine minimum time |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question covering routine D1 algorithms (early/late times, critical path, float, Gantt chart, resource allocation). All parts follow textbook procedures with no novel problem-solving required, making it easier than average but not trivial due to the multi-step nature and potential for arithmetic errors. |
| Spec | 7.05b Forward and backward pass: earliest/latest times, critical activities7.05d Latest start and earliest finish: independent and interfering float |
| Answer | Marks | Guidance |
|---|---|---|
| [Network diagram with float/slack values] | Forwards pass: M1, A1 | Backwards pass: M1, A1, (4) |
| Answer | Marks |
|---|---|
| Activities A, C, F and H, length 21 | B1, B1, (2) |
| Answer | Marks |
|---|---|
| Float for B is 1 (: 10 - 5 - 4); D is 1 (: 12 - 9 - 2); E is 2 (: 21 - 12 - 7); G is 4 (: 21 - 9 - 8) | M1, A1, A1, (3) |
| Answer | Marks |
|---|---|
| [Gantt chart showing activities on timeline 0-30] | M1, A1, A1, (4) |
| Answer | Marks |
|---|---|
| E.g. [Gantt chart with revised schedule] | M1, A1, A1, (4) |
## (a)
[Network diagram with float/slack values] | Forwards pass: M1, A1 | Backwards pass: M1, A1, (4) |
## (b)
Activities A, C, F and H, length 21 | B1, B1, (2) |
## (c)
Float for B is 1 (: 10 - 5 - 4); D is 1 (: 12 - 9 - 2); E is 2 (: 21 - 12 - 7); G is 4 (: 21 - 9 - 8) | M1, A1, A1, (3) |
## (d)
[Gantt chart showing activities on timeline 0-30] | M1, A1, A1, (4) |
## (e)
E.g. [Gantt chart with revised schedule] | M1, A1, A1, (4) |
---\includegraphics{figure_3}
A project is modelled by the activity network shown in Fig 3. The activities are represented by the edges. The number in brackets on each edge gives the time, in days, taken to complete the activity.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event. Write these in the boxes on the answer sheet. [4]
\item Hence determine the critical activities and the length of the critical path. [2]
\item Obtain the total float for each of the non-critical activities. [3]
\item On the first grid on the answer sheet, draw a cascade (Gantt) chart showing the information obtained in parts (b) and (c). [4]
\end{enumerate}
Each activity requires one worker. Only two workers are available.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{4}
\item On the second grid on the answer sheet, draw up a schedule and find the minimum time in which the 2 workers can complete the project. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2002 Q7 [17]}}