| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.8 This is a straightforward D1 critical path analysis question with standard procedures: drawing an activity network, calculating early/late times, identifying critical path, and drawing a resource histogram. The network is small (5 activities), calculations are simple, and part (iv) requires only basic scheduling logic with one worker constraint. All techniques are routine textbook exercises. |
| 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 (hours) | Immediate predecessors | |
| A | Agree date | 1 | - |
| B | Construct agenda | 0.5 | - |
| C | Book venue | 0.25 | A |
| D | Order refreshments | 0.25 | C |
| E | Inform participants | 0.5 | B, C |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Network diagram with nodes and activities as shown | M1 A1 A1 A1 B1 B1 B1 | sca activity-on-arc; A, B, C labels; D label; E label; forward pass (1.25 at end of B/dummy); backward pass (1.25 at start of dummy/D) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Resource histogram showing: 1 person on B and D; A, A, C, E, E activities with 0.5 hours duration | M1 A1 M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 2 hours (resource smoothing on A/B, but extra time needed for D/E) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| P: — | B1 | |
| Q: — | B1 | |
| R: — | B1 | |
| S: Q, R | B1 | |
| T: Q, R | B1 | |
| U: R | B1 | |
| V: S, T, U | B1 | |
| W: U | B1 |
**Parts (i) & (ii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Network diagram with nodes and activities as shown | M1 A1 A1 A1 B1 B1 B1 | sca activity-on-arc; A, B, C labels; D label; E label; forward pass (1.25 at end of B/dummy); backward pass (1.25 at start of dummy/D) |
Critical activities: A, C, E
**Part (iii)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resource histogram showing: 1 person on B and D; A, A, C, E, E activities with 0.5 hours duration | M1 A1 M1 A1 | |
**Part (iv)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| 2 hours (resource smoothing on A/B, but extra time needed for D/E) | | |
**Part (v)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| P: — | B1 | |
| Q: — | B1 | |
| R: — | B1 | |
| S: Q, R | B1 | |
| T: Q, R | B1 | |
| U: R | B1 | |
| V: S, T, U | B1 | |
| W: U | B1 | |4 Table 4.1 shows some of the activities involved in preparing for a meeting.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | l | c | c | }
\hline
& Activity & Duration (hours) & Immediate predecessors \\
\hline
A & Agree date & 1 & - \\
\hline
B & Construct agenda & 0.5 & - \\
\hline
C & Book venue & 0.25 & A \\
\hline
D & Order refreshments & 0.25 & C \\
\hline
E & Inform participants & 0.5 & B, C \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 4.1}
\end{center}
\end{table}
(i) Draw an activity-on-arc network to represent the precedences.\\
(ii) Find the early event time and the late event time for each vertex of your network, and list the critical activities.\\
(iii) Assuming that each activity requires one person and that each activity starts at its earliest start time, draw a resource histogram.\\
(iv) In fact although activity A has duration 1 hour, it actually involves only 0.5 hours work, since 0.5 hours involves waiting for replies. Given this information, and the fact that there is only one person available to do the work, what is the shortest time needed to prepare for the meeting?
Fig. 4.2 shows an activity network for the tasks which have to be completed after the meeting.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c429bfed-9241-409a-9cd5-9553bf16c9df-5_533_844_1688_294}
\captionsetup{labelformat=empty}
\caption{Fig. 4.2}
\end{center}
\end{figure}
P: Clean room\\
Q: Prepare draft minutes\\
R: Allocate action tasks\\
S: Circulate draft minutes\\
T: Approve task allocations\\
U: Obtain budgets for tasks\\
V: Post minutes\\
W: Pay refreshments bill\\
(v) Draw a precedence table for these activities.
\hfill \mbox{\textit{OCR MEI D1 2006 Q4 [16]}}