| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question with straightforward precedence relationships and a small number of activities. Part (i) requires drawing a basic activity network (routine skill), part (ii) is standard forward/backward pass calculation, and part (iii) requires identifying critical activities and recalculating - all textbook procedures with no novel insight needed. Slightly easier than average due to the small scale and clear structure. |
| 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 |
| Activity | Immediate predecessors | Duration (days) |
| A | - | 5 |
| B | - | 3 |
| C | A | 3 |
| D | A, B | 4 |
| E | A, B | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) & (ii) Network diagram with critical path A, E identified; Critical activities shown with ES/LS times 0/0, 3/3, 5/5 at B; 5/5, 4/4 at D; 5/5 at E; Project duration 10 days | B1 C OK; B1 D OK; B1 E OK | Early and late times marked |
| (iii) Activities A, E, and D are critical; Project duration 6 days | B1 critical |
**(i) & (ii)** Network diagram with critical path A, E identified; Critical activities shown with ES/LS times 0/0, 3/3, 5/5 at B; 5/5, 4/4 at D; 5/5 at E; Project duration 10 days | B1 C OK; B1 D OK; B1 E OK | Early and late times marked
**(iii)** Activities A, E, and D are critical; Project duration 6 days | B1 critical |
---1 Table 1 shows a precedence table for a project.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Immediate predecessors & Duration (days) \\
\hline
A & - & 5 \\
\hline
B & - & 3 \\
\hline
C & A & 3 \\
\hline
D & A, B & 4 \\
\hline
E & A, B & 5 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}
(i) Draw an activity-on-arc network to represent the precedences.\\
(ii) Find the early event time and late event time for each vertex of your network, and list the critical activities.\\
(iii) Extra resources become available which enable the durations of three activities to be reduced, each by up to two days. Which three activities should have their durations reduced so as to minimise the completion time of the project? What will be the new minimum project completion time?
\hfill \mbox{\textit{OCR MEI D1 2006 Q1 [8]}}