| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - create schedule/chart |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question with routine steps: drawing an activity network, finding critical path (straightforward with 7 activities), and creating a simple 2-worker schedule. Part (iv) requires recalculation after a duration change, which is mechanical. The small network size and standard question structure make this slightly easier than average A-level, though the multi-part nature and scheduling component keep it close to typical difficulty. |
| 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 (hours) | Immediate predecessor(s) | |
| A | measure | 0.5 | - |
| B | manufacture frame and door | 5 | A |
| C | cut hole in wall | 2 | A |
| D | fit lintel and marble step | 1.5 | C |
| E | fit frame | 1 | B, C |
| F | fit door | 1 | E |
| G | repair plaster around door | 1 | E |
| Answer | Marks | Guidance |
|---|---|---|
| (i) & (ii) Activity on arc diagram with proper notation showing: 0–0–0.5 → A → 0.5–0.5; B → 5.5–5.5; E → 1 → 6.5–6.5; F → 1 → 7.5–7.5; C → 2 → 2.5–5.5; D → 1.5 → 7.5–7.5; G → 1 (with dashed line to 7.5–7.5) | M1, A1, A1, A1, M1 A1∨, M1 A1∨ | Activity on arc; Single start and end; A, B, C, D (precedences); E (precedences); F and G (all correct); forward pass; backward pass |
| minimum completion time = 7.5 hours; critical activities – A, B, E, F, G (or ABEG + ABEF) | B1, B1 | time (cao); critical activities (cao) |
| (iii) e.g. [diagram showing network with boxes labeled and positioned with times as indicated] | B1, B1 | not ft; must be labelled or to scale (e.g. on the squares provided) Can be written out instead. |
| (iv) 8.0 hours or delay 0.5 hours A, C, D; 8.5 hours or delay of 1 hour | B1, B1, B1 | cao ISW if needed; cao; cao ISW if needed |
**(i) & (ii)** Activity on arc diagram with proper notation showing: 0–0–0.5 → A → 0.5–0.5; B → 5.5–5.5; E → 1 → 6.5–6.5; F → 1 → 7.5–7.5; C → 2 → 2.5–5.5; D → 1.5 → 7.5–7.5; G → 1 (with dashed line to 7.5–7.5) | M1, A1, A1, A1, M1 A1∨, M1 A1∨ | Activity on arc; Single start and end; A, B, C, D (precedences); E (precedences); F and G (all correct); forward pass; backward pass
| | | minimum completion time = 7.5 hours; critical activities – A, B, E, F, G (or ABEG + ABEF) | B1, B1 | time (cao); critical activities (cao)
**(iii)** e.g. [diagram showing network with boxes labeled and positioned with times as indicated] | B1, B1 | not ft; must be labelled or to scale (e.g. on the squares provided) Can be written out instead.
**(iv)** 8.0 hours or delay 0.5 hours A, C, D; 8.5 hours or delay of 1 hour | B1, B1, B1 | cao ISW if needed; cao; cao ISW if needed4 The table lists tasks which are involved in adding a back door to a garage. The table also lists the duration and immediate predecessor(s) for each task. Each task is undertaken by one person.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{Task} & Duration (hours) & Immediate predecessor(s) \\
\hline
A & measure & 0.5 & - \\
\hline
B & manufacture frame and door & 5 & A \\
\hline
C & cut hole in wall & 2 & A \\
\hline
D & fit lintel and marble step & 1.5 & C \\
\hline
E & fit frame & 1 & B, C \\
\hline
F & fit door & 1 & E \\
\hline
G & repair plaster around door & 1 & E \\
\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.\\
(iii) Produce a schedule to show how two people can complete the project in the minimum time.
Soon after starting activity D , the marble step breaks. Getting a replacement step adds 4 hours to the duration of activity D.\\
(iv) How does this delay affect the minimum completion time, the critical activities and the minimum time needed for two people to complete the project?
\section*{Question 5 begins on page 6}
\hfill \mbox{\textit{OCR MEI D1 2014 Q4 [16]}}