| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard textbook critical path analysis question requiring routine application of well-defined algorithms (drawing activity network with dummy, forward/backward pass, resource histogram). While multi-part with several marks, each step follows a mechanical procedure taught explicitly in D2 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 interpretation7.05d Latest start and earliest finish: independent and interfering float |
| Activity | Duration (minutes) | Immediate predecessors | Number of workers |
| A Cover furniture with dust sheets | 20 | - | 1 |
| B Repair any cracks in the plaster | 100 | A | 1 |
| C Hang wallpaper | 60 | B | 1 |
| D Paint feature wall | 90 | B | 1 |
| \(E\) Paint woodwork | 120 | C, D | 1 |
| \(F\) Put up shelves | 30 | C | 2 |
| G Paint ceiling | 60 | A | 1 |
| \(H\) Clean paintbrushes | 10 | \(E , G\) | 1 |
| I Tidy room | 20 | \(F , H\) | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | 0 | 0 |
| A1 | 0 | 3 |
Question 2:
M1 | 0 | 0 | 15 | 15
A1 | 0 | 3 | 32 The table lists the durations (in minutes), immediate predecessors and number of workers required for each activity in a project to decorate a room.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration (minutes) & Immediate predecessors & Number of workers \\
\hline
A Cover furniture with dust sheets & 20 & - & 1 \\
\hline
B Repair any cracks in the plaster & 100 & A & 1 \\
\hline
C Hang wallpaper & 60 & B & 1 \\
\hline
D Paint feature wall & 90 & B & 1 \\
\hline
$E$ Paint woodwork & 120 & C, D & 1 \\
\hline
$F$ Put up shelves & 30 & C & 2 \\
\hline
G Paint ceiling & 60 & A & 1 \\
\hline
$H$ Clean paintbrushes & 10 & $E , G$ & 1 \\
\hline
I Tidy room & 20 & $F , H$ & 2 \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity network, using activity on arc, to represent the project. Your network will require a dummy activity.\\
(ii) Carry out a forward pass and a backward pass through the activity network, showing the early event time and the late event time at each vertex of your network.
State the minimum project completion time and list the critical activities.\\
(iii) Draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time.
Suppose that there is only one worker available at the start of the project, but another two workers are available later.\\
(iv) Find the latest possible time for the other workers to start and still have the project completed on time. Which activities could happen at the same time as painting the ceiling if the other two workers arrive at this latest possible time?\\[0pt]
[Do not change your resource histogram from part (iii).]
\hfill \mbox{\textit{OCR D2 2012 Q2 [11]}}