| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 16 |
| Paper | 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: drawing an activity network, calculating early/late times, identifying the critical path, and performing straightforward crashing analysis. While multi-part with several calculations, each step follows textbook procedures without requiring novel insight or complex problem-solving. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Duration (weeks) | Immediate Predecessors | |
| A | Survey sites | 8 | - |
| B | Purchase land | 22 | A |
| C | Supply materials | 10 | - |
| D | Supply machinery | 4 | - |
| E | Excavate foundations | 9 | B, D |
| F | Lay drains | 11 | B, C, D |
| G | Build walls | 9 | E, F |
| H | Lay floor | 10 | E, F |
| I | Install roof | 3 | G |
| J | Install electrics | 5 | G |
| Task | E | F | H | J | ||
| 3 | 3 | 1 | 3 | ||
| 30 | 15 | 6 | 20 |
5 The table shows some of the activities involved in building a block of flats. The table gives their durations and their immediate predecessors.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|l|}{Activity} & Duration (weeks) & Immediate Predecessors \\
\hline
A & Survey sites & 8 & - \\
\hline
B & Purchase land & 22 & A \\
\hline
C & Supply materials & 10 & - \\
\hline
D & Supply machinery & 4 & - \\
\hline
E & Excavate foundations & 9 & B, D \\
\hline
F & Lay drains & 11 & B, C, D \\
\hline
G & Build walls & 9 & E, F \\
\hline
H & Lay floor & 10 & E, F \\
\hline
I & Install roof & 3 & G \\
\hline
J & Install electrics & 5 & G \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity on arc network for these activities.\\
(ii) Mark on your diagram the early and late times for each event. Give the minimum completion time and the critical activities.
Each of the tasks E, F, H and J can be speeded up at extra cost. The maximum number of weeks by which each task can be shortened, and the extra cost for each week that is saved, are shown in the table below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Task & E & F & H & J \\
\hline
\begin{tabular}{ l }
Maximum number of weeks by \\
which task may be shortened \\
\end{tabular} & 3 & 3 & 1 & 3 \\
\hline
\begin{tabular}{ l }
Cost per week of shortening task \\
(in thousands of pounds) \\
\end{tabular} & 30 & 15 & 6 & 20 \\
\hline
\end{tabular}
\end{center}
(iii) Find the new shortest time for the flats to be completed.\\
(iv) List the activities which will need to be speeded up to achieve the shortest time found in part (iii), and the times by which each must be shortened.\\
(v) Find the total extra cost needed to achieve the new shortest time.
\hfill \mbox{\textit{OCR MEI D1 2008 Q5 [16]}}