| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question requiring routine application of forward and backward passes to find early/late times, identification of critical path, and basic optimization of task durations. The network is small (8 activities), the precedence relationships are straightforward, and part (iii) only requires comparing a few combinations to reduce completion time by 10 minutes—all mechanical procedures covered in D1 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 | Duration (mins) | Immediate Predecessors |
| A Refuel | 30 | - |
| B Clean cabin | 25 | - |
| C Pre-flight technical check | 15 | A |
| D Load luggage | 20 | - |
| E Load passengers | 25 | A, B |
| F Safety demonstration | 5 | E |
| G Obtain air traffic clearance | 10 | C |
| H Taxi to runway | 5 | G, D |
| Task | A | B | D | E |
| New time (mins) | 20 | 20 | 15 | 15 |
| Extra cost | 250 | 50 | 50 | 100 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Activity on arc network drawn | M1 | sca (activity on arc) |
| Single start and end node | A1 | single start & end |
| Dummy activity included correctly | A1 | dummy |
| Remaining activities correct | A1 | rest |
| Correct forward pass | M1 | forward pass |
| Forward pass values correct | A1 | |
| Correct backward pass | M1 | backward pass |
| Backward pass values correct | A1 | |
| Time = 60 minutes | B1 | \(\checkmark\) |
| Critical path: \(A; C; E; F; G; H\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| A and B both needed at £300 each | B1 | 2 out of A, B, E |
| Activity A identified | B1 | A |
| Activity B identified | B1 | B |
| Cost = £300 from A and B | B1 | 300 from A and B |
| Schedule: \(A; C; G; H\) and \(B; E; F\) | B1 | |
| Both sequences correct | B1 |
# Question 5:
## Parts (i) & (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Activity on arc network drawn | M1 | sca (activity on arc) |
| Single start and end node | A1 | single start & end |
| Dummy activity included correctly | A1 | dummy |
| Remaining activities correct | A1 | rest |
| Correct forward pass | M1 | forward pass |
| Forward pass values correct | A1 | |
| Correct backward pass | M1 | backward pass |
| Backward pass values correct | A1 | |
| Time = 60 minutes | B1 | $\checkmark$ |
| Critical path: $A; C; E; F; G; H$ | B1 | cao |
## Part (iii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| A and B both needed at £300 each | B1 | 2 out of A, B, E |
| Activity A identified | B1 | A |
| Activity B identified | B1 | B |
| Cost = £300 from A and B | B1 | 300 from A and B |
| Schedule: $A; C; G; H$ and $B; E; F$ | B1 | |
| Both sequences correct | B1 | |
---5 The tasks involved in turning around an "AirGB" aircraft for its return flight are listed in the table. The table gives the durations of the tasks and their immediate predecessors.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Duration (mins) & Immediate Predecessors \\
\hline
A Refuel & 30 & - \\
\hline
B Clean cabin & 25 & - \\
\hline
C Pre-flight technical check & 15 & A \\
\hline
D Load luggage & 20 & - \\
\hline
E Load passengers & 25 & A, B \\
\hline
F Safety demonstration & 5 & E \\
\hline
G Obtain air traffic clearance & 10 & C \\
\hline
H Taxi to runway & 5 & G, D \\
\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 minimum completion time and the critical activities.
Because of delays on the outbound flight the aircraft has to be turned around within 50 minutes, so as not to lose its air traffic slot for the return journey. There are four tasks on which time can be saved. These, together with associated costs, are listed below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Task & A & B & D & E \\
\hline
New time (mins) & 20 & 20 & 15 & 15 \\
\hline
Extra cost & 250 & 50 & 50 & 100 \\
\hline
\end{tabular}
\end{center}
(iii) List the activities which need to be speeded up in order to turn the aircraft around within 50 minutes at minimum extra cost. Give the extra cost and the new set of critical activities.
\hfill \mbox{\textit{OCR MEI D1 2009 Q5 [16]}}