| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: forward/backward pass, identifying critical path, and calculating float. Part (v)-(vi) require redrawing the network with a new activity, which adds mild complexity but remains algorithmic. The dummy activity explanation is textbook knowledge. Overall slightly easier than average A-level due to being purely procedural with no novel problem-solving 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 |
| Activity | Description | Duration (days) |
| A | Architect produces plans | 10 |
| Pl | Obtain planning permission | 14 |
| Demo | Demolish existing structure | 3 |
| Fo | Excavate foundations | 4 |
| W | Build walls | 3 |
| Pb | Install plumbing | 2 |
| R | Construct roof | 3 |
| Fl | Lay floor | 2 |
| E | Fit electrics | 2 |
| WD | Install windows and doors | 1 |
| Deco | Decorate | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| (i) | Table showing activities and immediate predecessors: A (–), Pl (A), Demo (–), Fo (Pl; Demo), W (Fo), Pb (Fo), R (W), Fl (Pb; W), E (R; Fl), WD (W), Deco (WD; E) | M1, A1 |
| (ii) | Network diagram with at least one correct nontrivial join in forward pass; At least one correct nontrivial burst in backward pass (excluding start node) | M1, A1, M1, A1 |
| (iii) | Critical activities: A; Pl; Fo; W; R; E; Deco; Project duration = 41 days | B1, B1 |
| Float table for activities: A (0), Pl (0), Dm (21), Fo (0), W (0), Pb (2), R (0), Fl (1), E (0), WD (4), Dc (0) | B1, B1 | A, Pl, Dm, Fo, W cao; rest cao—most see zeros, dashes or empty spaces won't do |
| (iv) | Fl has both W and Pb as immediate predecessors. R and WD have only W as immediate predecessor. | B1, B1 |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|-----------|------------|
| (i) | Table showing activities and immediate predecessors: A (–), Pl (A), Demo (–), Fo (Pl; Demo), W (Fo), Pb (Fo), R (W), Fl (Pb; W), E (R; Fl), WD (W), Deco (WD; E) | M1, A1 | Fl correct; rest |
| (ii) | Network diagram with at least one correct nontrivial join in forward pass; At least one correct nontrivial burst in backward pass (excluding start node) | M1, A1, M1, A1 | |
| (iii) | Critical activities: A; Pl; Fo; W; R; E; Deco; Project duration = 41 days | B1, B1 | cao; cao |
| | Float table for activities: A (0), Pl (0), Dm (21), Fo (0), W (0), Pb (2), R (0), Fl (1), E (0), WD (4), Dc (0) | B1, B1 | A, Pl, Dm, Fo, W cao; rest cao—most see zeros, dashes or empty spaces won't do |
| (iv) | Fl has both W and Pb as immediate predecessors. R and WD have only W as immediate predecessor. | B1, B1 | SC1 for convincing but not specific answer, e.g. "A dummy is needed to cater for both joint and separate precedences". |
---5 The activity network and table together show the tasks involved in constructing a house extension, their durations and precedences.\\
\includegraphics[max width=\textwidth, alt={}, center]{2e03f6fb-69db-438a-a79e-3e04fab0d08a-5_231_985_338_539}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Description & Duration (days) \\
\hline
A & Architect produces plans & 10 \\
\hline
Pl & Obtain planning permission & 14 \\
\hline
Demo & Demolish existing structure & 3 \\
\hline
Fo & Excavate foundations & 4 \\
\hline
W & Build walls & 3 \\
\hline
Pb & Install plumbing & 2 \\
\hline
R & Construct roof & 3 \\
\hline
Fl & Lay floor & 2 \\
\hline
E & Fit electrics & 2 \\
\hline
WD & Install windows and doors & 1 \\
\hline
Deco & Decorate & 5 \\
\hline
\end{tabular}
\end{center}
(i) Show the immediate predecessors for each activity.\\
(ii) Perform a forward pass and a backward pass to find the early time and the late time for each event.\\
(iii) Give the critical activities, the project duration, and the total float for each activity.\\
(iv) The activity network includes one dummy activity. Explain why this dummy activity is needed.
Whilst the foundations are being dug the customer negotiates the installation of a decorative corbel. This will take one day. It must be done after the walls have been built, and before the roof is constructed. The windows and doors cannot be installed until it is completed. It will not have any effect on the construction of the floor.\\
(v) Redraw the activity network incorporating this extra activity.\\
(vi) Find the revised critical activities and the revised project duration.
\hfill \mbox{\textit{OCR MEI D1 2011 Q5 [16]}}