| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Standard +0.3 This is a standard Critical Path Analysis question requiring routine application of well-defined algorithms (drawing network, calculating early/late times, identifying critical path, then constructing a cascade chart). While it has multiple parts and requires careful bookkeeping, it involves no novel problem-solving or insight—just methodical application of D1 techniques that students practice extensively. |
| 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 |
| Jobs | Duration (mins) | Immediate predecessors | |
| A | prune bushes | 100 | - |
| B | weed borders | 60 | A |
| C | cut hedges | 150 | - |
| D | hoe vegetable patch | 60 | - |
| E | mow lawns | 40 | B |
| F | edge lawns | 20 | D, E |
| G | clean up cuttings | 30 | B, C |
| H | clean tools | 10 | F, G |
| Answer | Marks |
|---|---|
| (i) & (ii) Network diagram with forward pass showing: A–B: 100–160; A–D: 60–60; D–E: 200–200; B–C: 160–160; E–F: 220–220; C–G: 150–190; G–H: 230–230. Time: 230 minutes. Critical: A; B; E; F; H. | M1 sca (activity on arc), A1 single start & end, A1 dummy, A1 rest, M1 forward pass, A1 backward pass, M1 |
| (iii) Cascade chart showing activities A through H in order with appropriate time intervals. Least time: 240 mins. Note: Minimum project completion times assumes no resource constraints. | B1 cao, M1 cascade, A2, B1, B1, B1 |
**(i) & (ii)** Network diagram with forward pass showing: A–B: 100–160; A–D: 60–60; D–E: 200–200; B–C: 160–160; E–F: 220–220; C–G: 150–190; G–H: 230–230. Time: 230 minutes. Critical: A; B; E; F; H. | M1 sca (activity on arc), A1 single start & end, A1 dummy, A1 rest, M1 forward pass, A1 backward pass, M1 |
**(iii)** Cascade chart showing activities A through H in order with appropriate time intervals. Least time: 240 mins. Note: Minimum project completion times assumes no resource constraints. | B1 cao, M1 cascade, A2, B1, B1, B1 |6 Joan and Keith have to clear and tidy their garden. The table shows the jobs that have to be completed, their durations and their precedences.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{Jobs} & Duration (mins) & Immediate predecessors \\
\hline
A & prune bushes & 100 & - \\
\hline
B & weed borders & 60 & A \\
\hline
C & cut hedges & 150 & - \\
\hline
D & hoe vegetable patch & 60 & - \\
\hline
E & mow lawns & 40 & B \\
\hline
F & edge lawns & 20 & D, E \\
\hline
G & clean up cuttings & 30 & B, C \\
\hline
H & clean tools & 10 & F, G \\
\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) Each job is to be done by one person only. Joan and Keith are equally able to do all jobs. Draw a cascade chart indicating how to organise the jobs so that Joan and Keith can complete the project in the least time. Give that least time and explain why the minimum project completion time is shorter.
\hfill \mbox{\textit{OCR MEI D1 2009 Q6 [16]}}