| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard textbook critical path analysis question requiring routine application of well-defined algorithms (drawing network, forward/backward pass, finding float). The precedence table is straightforward with no ambiguities, and parts (i)-(iii) are mechanical procedures taught in D1. Part (iv) scheduling adds minor complexity but follows standard methods. Easier than average A-level as it's purely algorithmic with no problem-solving insight required. |
| Spec | 7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float |
| Activity | Duration (mins) | Immediate predecessor(s) | |
| A | shampoo | 5 | - |
| B | prepare perm lotion | 2 | - |
| C | make coffee for customer | 3 | - |
| D | trim | 5 | A |
| E | clean sink | 3 | A |
| F | put rollers in | 15 | D |
| G | clean implements | 3 | D |
| H | apply perm lotion | 5 | B, F |
| I | leave to set | 20 | C,H |
| J | clean lotion pot and spreaders | 3 | H |
| K | neutralise and rinse | 10 | I, E |
| L | dry | 10 | K |
| M | wash up and clean up | 15 | K |
| N | style | 4 | G, L |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Network drawn with single start/end node | M1 | |
| I and J correctly placed | A1 | |
| Activities A D F H K L N correct | A1 | |
| Activities B C E G M correct | A1 | |
| Forward pass correct | M1 A1 | |
| Backward pass correct | M1 A1 | |
| Results correct | B1 B1 | |
| Critical path: A, D, F, H, I, K, M; duration = 75 minutes | B1 B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total float for G = 58 | B1\(\checkmark\) | Follow through |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gantt chart with stylist row correct | M1 A1 | |
| Gantt chart with trainee row correct | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| C — make coffee | B1 |
# Question 4:
## Parts (i) & (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Network drawn with single start/end node | M1 | |
| I and J correctly placed | A1 | |
| Activities A D F H K L N correct | A1 | |
| Activities B C E G M correct | A1 | |
| Forward pass correct | M1 A1 | |
| Backward pass correct | M1 A1 | |
| Results correct | B1 B1 | |
| Critical path: A, D, F, H, I, K, M; duration = 75 minutes | B1 B1 | |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total float for G = 58 | B1$\checkmark$ | Follow through |
## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gantt chart with stylist row correct | M1 A1 | |
| Gantt chart with trainee row correct | A1 | |
## Part (v)
| Answer | Marks | Guidance |
|--------|-------|----------|
| C — make coffee | B1 | |
---4 Answer this question on the insert provided.
The table shows activities involved in a "perm" in a hair salon, their durations and immediate predecessors.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Activity & Duration (mins) & Immediate predecessor(s) \\
\hline
A & shampoo & 5 & - \\
\hline
B & prepare perm lotion & 2 & - \\
\hline
C & make coffee for customer & 3 & - \\
\hline
D & trim & 5 & A \\
\hline
E & clean sink & 3 & A \\
\hline
F & put rollers in & 15 & D \\
\hline
G & clean implements & 3 & D \\
\hline
H & apply perm lotion & 5 & B, F \\
\hline
I & leave to set & 20 & C,H \\
\hline
J & clean lotion pot and spreaders & 3 & H \\
\hline
K & neutralise and rinse & 10 & I, E \\
\hline
L & dry & 10 & K \\
\hline
M & wash up and clean up & 15 & K \\
\hline
N & style & 4 & G, L \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 4}
\end{center}
\end{table}
(i) Complete the activity-on-arc network in the insert to represent the precedences.\\
(ii) Perform a forward pass and a backward pass to find early and late event times. Give the critical activities and the time needed to complete the perm.\\
(iii) Give the total float time for the activity $G$.
Activities $\mathrm { D } , \mathrm { F } , \mathrm { H } , \mathrm { K }$ and N require a stylist.\\
Activities $\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { E } , \mathrm { G } , \mathrm { J }$ and M are done by a trainee.\\
Activities $I$ and $L$ require no-one in attendance.\\
A stylist and a trainee are to give a perm to a customer.\\
(iv) Use the chart in the insert to show a schedule for the activities, assuming that all activities are started as early as possible.\\
(v) Which activity would be better started at its latest start time?
\hfill \mbox{\textit{OCR MEI D1 2005 Q4 [16]}}