| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Crashing/reducing activity durations |
| Difficulty | Standard +0.3 This is a standard critical path analysis question with routine crashing calculations. While it requires multiple steps (drawing network, finding critical path, then systematically reducing durations), all techniques are textbook procedures from D1 with no novel problem-solving required. The crashing optimization is straightforward greedy selection of cheapest options on the critical path. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Task | Duration (months) | Immediate predecessors |
| A | 4 | - |
| B | 2 | - |
| C | 7 | - |
| D | 12 | A |
| E | 5 | A |
| F | 7 | A, B |
| G | 6 | D, J |
| H | 3 | C |
| I | 12 | E, F, H |
| J | 7 | E, F, H |
| K | 12 | C |
| Tasks which can be completed more quickly by employing extra resources | Number of months which can be saved | Cost per month of employing extra resources (£m) |
| A | 2 | 3 |
| D | 1 | 1 |
| C | 3 | 3 |
| F | 2 | 2 |
| G | 2 | 4 |
6 The table shows the tasks that have to be completed in building a stadium for a sporting event, their durations and their precedences. The stadium has to be ready within two years.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Task & Duration (months) & Immediate predecessors \\
\hline
A & 4 & - \\
\hline
B & 2 & - \\
\hline
C & 7 & - \\
\hline
D & 12 & A \\
\hline
E & 5 & A \\
\hline
F & 7 & A, B \\
\hline
G & 6 & D, J \\
\hline
H & 3 & C \\
\hline
I & 12 & E, F, H \\
\hline
J & 7 & E, F, H \\
\hline
K & 12 & C \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity on arc network for these activities.\\
(ii) Mark on your diagram the early time and the late time for each event. Give the project duration and the critical activities.
In the later stages of planning the project it is discovered that task J will actually take 9 months to complete. However, other tasks can have their durations shortened by employing extra resources. The costs of "crashing" tasks (i.e. the costs of employing extra resources to complete them more quickly) are given in the table.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Tasks which can be completed more quickly by employing extra resources & Number of months which can be saved & Cost per month of employing extra resources (£m) \\
\hline
A & 2 & 3 \\
\hline
D & 1 & 1 \\
\hline
C & 3 & 3 \\
\hline
F & 2 & 2 \\
\hline
G & 2 & 4 \\
\hline
\end{tabular}
\end{center}
(iii) Find the cheapest way of completing the project within two years.\\
(iv) If the delay in completing task J is not discovered until it is started, how can the project be completed in time, and how much extra will it cost?
\hfill \mbox{\textit{OCR MEI D1 2010 Q6 [16]}}