| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question requiring drawing an activity network, finding early/late times, and identifying the critical path. Part (iii) adds resource allocation but follows routine scheduling algorithms. The precedence table is straightforward with no tricky dependencies, making this slightly easier than average for A-level. |
| 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 |
| Task | Duration (minutes) | Immediate predecessor(s) | |
| A | measure windows | 5 | - |
| B | calculate material required | 5 | A |
| C | choose material | 15 | - |
| D | buy material | 15 | B, C |
| E | cut material | 5 | D |
| F | stitch sides of wide curtain | 30 | E |
| G | stitch top of wide curtain | 30 | F |
| H | stitch sides of narrow curtain | 30 | E |
| I | stitch top of narrow curtain | 15 | H |
| J | hang curtains and pin hems | 20 | G, I |
| K | hem wide curtain | 30 | J |
| L | hem narrow curtain | 15 | J |
| M | fit curtains | 10 | K, L |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Activity on arc network drawn | M1 | activity on arc |
| Single start and end nodes | A1 | single start and end |
| A, B, C correct | A1 | A, B, C OK |
| J, K, L correct | A1 | J, K, L OK |
| Rest correct | A1 | rest OK |
| Forward pass with at least one join correct | M1 A1 | forward pass |
| Backward pass with at least one burst correct | M1 A1 | backward pass |
| Minimum completion time = 155 minutes | B1 | cao |
| Critical activities: C, D, E, F, G, J, K and M | B1 | cao |
| [6] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Schedule shown with ABCD correct | B1 | ABCD |
| Remaining schedule correct (watch for M's after K's and L's) | B1 | rest |
| 215 minutes (3 hours and 35 minutes) | B1 | cao |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Two more people needed, so H's and I's could be done at same time as F's and G's, and two L's could be done at same time as two K's | B1 B1 | cao; reasoning |
| [2] |
# Question 4:
## Parts (i) & (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity on arc network drawn | M1 | activity on arc |
| Single start and end nodes | A1 | single start and end |
| A, B, C correct | A1 | A, B, C OK |
| J, K, L correct | A1 | J, K, L OK |
| Rest correct | A1 | rest OK |
| Forward pass with at least one join correct | M1 A1 | forward pass |
| Backward pass with at least one burst correct | M1 A1 | backward pass |
| Minimum completion time = 155 minutes | B1 | cao |
| Critical activities: C, D, E, F, G, J, K and M | B1 | cao |
| **[6]** | | |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Schedule shown with ABCD correct | B1 | ABCD |
| Remaining schedule correct (watch for M's after K's and L's) | B1 | rest |
| 215 minutes (3 hours and 35 minutes) | B1 | cao |
| **[3]** | | |
## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Two more people needed, so H's and I's could be done at same time as F's and G's, and two L's could be done at same time as two K's | B1 B1 | cao; reasoning |
| **[2]** | | |
---4 A room has two windows which have the same height but different widths. Each window is to have one curtain. The table lists the tasks involved in making the two curtains, their durations, and their immediate predecessors. The durations assume that only one person is working on the activity.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{Task} & Duration (minutes) & Immediate predecessor(s) \\
\hline
A & measure windows & 5 & - \\
\hline
B & calculate material required & 5 & A \\
\hline
C & choose material & 15 & - \\
\hline
D & buy material & 15 & B, C \\
\hline
E & cut material & 5 & D \\
\hline
F & stitch sides of wide curtain & 30 & E \\
\hline
G & stitch top of wide curtain & 30 & F \\
\hline
H & stitch sides of narrow curtain & 30 & E \\
\hline
I & stitch top of narrow curtain & 15 & H \\
\hline
J & hang curtains and pin hems & 20 & G, I \\
\hline
K & hem wide curtain & 30 & J \\
\hline
L & hem narrow curtain & 15 & J \\
\hline
M & fit curtains & 10 & K, L \\
\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.
Kate and Pete have two rooms to curtain, each identical to that above. Tasks A, B, C and D only need to be completed once each. All other tasks will have two versions, one for room 1 and one for room 2, eg E1 and E2. Kate and Pete share the tasks between them so that each task is completed by only one person.\\
(iii) Complete the diagram to show how the tasks can be shared between them, and scheduled, so that the project can be completed in the least possible time. Give that least possible time.\\
(iv) How much extra help would be needed to curtain both rooms in the minimum completion time from part (ii)? Explain your answer.
\hfill \mbox{\textit{OCR MEI D1 2013 Q4 [16]}}