| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2001 |
| Session | January |
| Marks | 13 |
| 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 textbook critical path analysis question requiring routine application of the forward and backward pass algorithms, identification of critical path, and basic scheduling. While multi-part with 13 marks total, each step follows a mechanical procedure taught explicitly in D1 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 interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | B1 | \(e_1 = 0\), \(e_2 = 5\), \(c_3 = 9\) |
| M1 A1 | \(e_4 = 11\), \(e_5 = \max(10, 12, 13) = 13\) | |
| B1 | \(e_6 = \max(16, 17) = 17\), \(e_7 = \max(18, 23) = 23\) | |
| M1 A1(6) | \(\ell_7 = 23\), \(\ell_6 = 17\), \(\ell_5 = 13\), \(\ell_4 = \min(16, 12, 11) = 11\), \(\ell_3 = 10\), \(\ell_2 = \min(6,7,5) = 5\), \(\ell_1 = \min(2,0) = 0\) | |
| (b) | A1(5) | Critical activities: A, D, G, H, K |
| A1(5) | Length of critical path: \(5 + 6 + 2 + 4 + 6 = 23\) | |
| (c) | M1 A1 2−10 | Gantt chart showing activities A through K scheduled on timeline with critical path |
| M1 A2−10 |
(a) | B1 | $e_1 = 0$, $e_2 = 5$, $c_3 = 9$ |
| M1 A1 | $e_4 = 11$, $e_5 = \max(10, 12, 13) = 13$ |
| B1 | $e_6 = \max(16, 17) = 17$, $e_7 = \max(18, 23) = 23$ |
| M1 A1(6) | $\ell_7 = 23$, $\ell_6 = 17$, $\ell_5 = 13$, $\ell_4 = \min(16, 12, 11) = 11$, $\ell_3 = 10$, $\ell_2 = \min(6,7,5) = 5$, $\ell_1 = \min(2,0) = 0$ |
(b) | A1(5) | Critical activities: A, D, G, H, K |
| A1(5) | Length of critical path: $5 + 6 + 2 + 4 + 6 = 23$ |
(c) | M1 A1 2−10 | Gantt chart showing activities A through K scheduled on timeline with critical path |
| M1 A2−10 | |
---This question should be answered on the sheet provided in the answer booklet.
\includegraphics{figure_2}
Figure 2 shows the activity network used to model a small building project. The activities are represented by the edges and the number in brackets on each edge represents the time, in hours, taken to complete that activity.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event. Write your answers in the boxes on the answer sheet. [6 marks]
\item Hence determine the critical activities and the length of the critical path. [2 marks]
\end{enumerate}
Each activity requires one worker. The project is to be completed in the minimum time.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Schedule the activities for the minimum number of workers using the time line on the answer sheet. Ensure that you make clear the order in which each worker undertakes his activities. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2001 Q5 [13]}}