| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2011 |
| Session | June |
| Marks | 14 |
| 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 D2 techniques: drawing an activity network, forward/backward pass calculations, and resource scheduling. While multi-part with several marks, each component follows textbook procedures without requiring novel insight or complex problem-solving—slightly easier than average A-level maths due to its algorithmic nature. |
| 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 (hours) | Immediate predecessors | Number of workers |
| \(A\) : Choose summerhouse | 2 | - | 2 |
| \(B\) : Buy slabs for base | 1 | - | 2 |
| \(C\) : Take goods home | 2 | \(A , B\) | 2 |
| \(D\) : Level ground | 3 | - | 1 |
| E: Lay slabs | 2 | \(C , D\) | 2 |
| \(F\) : Treat wood | 3 | C | 1 |
| \(G\) : Install floor, walls and roof | 4 | \(E , F\) | 2 |
| \(H\) : Fit windows and door | 2 | \(G\) | 1 |
| \(I\) : Fit patio rail | 1 | \(G\) | 1 |
| \(J\) : Fit shelving | 1 | \(G\) | 1 |
4 Jamil is building a summerhouse in his garden. The activities involved, the duration, immediate predecessors and number of workers required for each activity are listed in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration (hours) & Immediate predecessors & Number of workers \\
\hline
$A$ : Choose summerhouse & 2 & - & 2 \\
\hline
$B$ : Buy slabs for base & 1 & - & 2 \\
\hline
$C$ : Take goods home & 2 & $A , B$ & 2 \\
\hline
$D$ : Level ground & 3 & - & 1 \\
\hline
E: Lay slabs & 2 & $C , D$ & 2 \\
\hline
$F$ : Treat wood & 3 & C & 1 \\
\hline
$G$ : Install floor, walls and roof & 4 & $E , F$ & 2 \\
\hline
$H$ : Fit windows and door & 2 & $G$ & 1 \\
\hline
$I$ : Fit patio rail & 1 & $G$ & 1 \\
\hline
$J$ : Fit shelving & 1 & $G$ & 1 \\
\hline
\end{tabular}
\end{center}
(i) Represent the project by an activity network, using activity on arc. You should make your diagram quite large so that there is room for working.\\
(ii) Carry out a forward pass and a backward pass through the activity network, showing the early event times and late event times at the vertices 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 each hour when each activity begins at its earliest possible start time.\\
(iv) Describe how it is possible for the project to be completed in the minimum project completion time when only four workers are available.\\
(v) Describe how two workers can complete the project as quickly as possible. Find the minimum time in which two workers can complete the project.
\hfill \mbox{\textit{OCR D2 2011 Q4 [14]}}