| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Complete precedence table from network |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: reading a network diagram to identify precedences, calculating early/late times, finding the critical path, and basic resource allocation. While multi-part with several marks, each component uses well-practiced algorithms without requiring novel insight or complex problem-solving beyond textbook methods. |
| 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 |
| A | Rig foresail |
| B | Lower sprayhood |
| C | Start engine |
| D | Pump out bilges |
| E | Rig mainsail |
| F | Cast off mooring ropes |
| G | Motor out of harbour |
| H | Raise foresail |
| I | Raise mainsail |
| J | Stop engine and start sailing |
| Answer | Marks |
|---|---|
| Activity | Immediate predecessors |
| A | — |
| B | — |
| C | — |
| D | C |
| E | A, B |
| F | C |
| G | C, D |
| H | A |
| I | E, F |
| J | H, I, G |
| B3 | B1 each for correct row, up to 3 marks; accept minor variations consistent with network |
| Answer | Marks | Guidance |
|---|---|---|
| Critical activities: C, G, J | M1 for forward pass | A1 for all correct early times |
| Answer | Marks |
|---|---|
| During activity G (duration 10), Colin can perform activities that do not need to precede G and are available: B and D (or activities with float that fall within G's timeframe) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Schedule: Colin does activities sequentially, one at a time (except G), choosing critical path plus remaining activities in feasible order | M1 for valid approach | A1 for minimum time |
| Answer | Marks | Guidance |
|---|---|---|
| With two workers, minimum time reduced. Schedule allocating activities to Colin and crew member to minimise overall time, showing parallel working | M1 for considering parallel activities | A1 for correct minimum time |
# Question 4:
## Part (i)
| Activity | Immediate predecessors |
|---|---|
| A | — |
| B | — |
| C | — |
| D | C |
| E | A, B |
| F | C |
| G | C, D |
| H | A |
| I | E, F |
| J | H, I, G |
| B3 | B1 each for correct row, up to 3 marks; accept minor variations consistent with network
## Part (ii)
Early times: 0, 0, 0, 3, 3, 3, 7, 3, 4, 14
Late times: calculated from project duration = 14
Critical activities: C, G, J | M1 for forward pass | A1 for all correct early times | M1 for backward pass | A1 for all correct late times | A1 for project duration = 14 | A1 for correct critical activities (C, G, J)
## Part (iii)
During activity G (duration 10), Colin can perform activities that do not need to precede G and are available: **B and D** (or activities with float that fall within G's timeframe) | B1
## Part (iv)
Minimum time = 17 (or consistent with network).
Schedule: Colin does activities sequentially, one at a time (except G), choosing critical path plus remaining activities in feasible order | M1 for valid approach | A1 for minimum time | A1 for valid schedule
## Part (v)
With two workers, minimum time reduced. Schedule allocating activities to Colin and crew member to minimise overall time, showing parallel working | M1 for considering parallel activities | A1 for correct minimum time | A2 for complete valid schedule
---4 Colin is setting off for a day's sailing. The table and the activity network show the major activities that are involved, their durations and their precedences.
\begin{center}
\begin{tabular}{ | c | l | }
\hline
A & Rig foresail \\
\hline
B & Lower sprayhood \\
\hline
C & Start engine \\
\hline
D & Pump out bilges \\
\hline
E & Rig mainsail \\
\hline
F & Cast off mooring ropes \\
\hline
G & Motor out of harbour \\
\hline
H & Raise foresail \\
\hline
I & Raise mainsail \\
\hline
J & Stop engine and start sailing \\
\hline
\end{tabular}
\end{center}
\includegraphics[max width=\textwidth, alt={}, center]{21ab732d-435e-4f0b-bc88-21ddc2a398c9-3_480_912_555_925}\\
(i) Complete the table in your answer book showing the immediate predecessors for each activity.\\
(ii) Find the early time and the late time for each event. Give the project duration and list the critical activities.
When he sails on his own Colin can only do one thing at a time with the exception of activity G, motoring out of the harbour.\\
(iii) Use the activity network to determine which activities Colin can perform whilst motoring out of the harbour.\\
(iv) Find the minimum time to complete the activities when Colin sails on his own, and give a schedule for him to achieve this.\\
(v) Find the minimum time to complete the activities when Colin sails with one other crew member, and give a schedule for them to achieve this.
\hfill \mbox{\textit{OCR MEI D1 2007 Q4 [16]}}