| Exam Board | OCR |
|---|---|
| Module | Further Discrete AS (Further Discrete AS) |
| Year | 2020 |
| Session | November |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a straightforward critical path analysis question requiring standard techniques: completing a partially-drawn activity network from a precedence table, finding minimum completion time via forward/backward pass, identifying critical activities, and calculating float. The precedence relationships are clearly stated, and all parts follow textbook procedures with no novel problem-solving required. Slightly easier than average due to the clear structure and partial network already provided. |
| 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 (days) | Notes | |
| A | Archie takes measurements | 1 | |
| B | Archie draws up plans | 3 | Must come after A |
| C | Plans are approved | 21 | Must come after B |
| D | Bob orders materials | 2 | Must come after B |
| E | Materials delivered | 10 | Must come after D |
| F | Work area cleared | 5 | Must come after A |
| G | Plumbing and electrics | 3 | Must come after C, E and F |
| H | Floors, walls and ceilings | 24 | Must come after G |
| I | Staircase | 2 | Must come after H |
| J | Windows | 1 | Must come after H |
| K | Decorating | 6 | Must come after I and J |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | C I |
| Answer | Marks |
|---|---|
| Critical activities: A, B, C, G, H, I, K | M1 |
| Answer | Marks |
|---|---|
| [6] | H, I , J, K added appropriately, apart from possibly not |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | The start of an activity may be delayed (e.g. a delay in the delivery would |
| Answer | Marks |
|---|---|
| the required times | B1 |
| Answer | Marks |
|---|---|
| [2] | A reason why the duration of an activity may be extended |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (c) | F has the longest float = 25 – 1 – 5 = 19 days |
| Answer | Marks |
|---|---|
| (day 1) to day 20 without delaying the project | M1 |
| Answer | Marks |
|---|---|
| [2] | 19 or ft their forward and backward passes |
Question 4:
4 | (a) | C I
A B D E G H K
0 1 4 6 25 28 52 54 60
0 1 4 15 25 28 52 54 60
53
F J 54
Minimum project completion time = 60 days
Critical activities: A, B, C, G, H, I, K | M1
A1
M1
A1
M1
A1
[6] | H, I , J, K added appropriately, apart from possibly not
using a dummy (or using too many dummies) and possibly
not showing arcs as directed.
Durations need not be shown.
Network correct, including the use of exactly one dummy
(before or after I or J) and all arcs directed
Follow through their network, even if only A to G
Forward pass, or implied from minimum time correct
60
Backward pass, or implied from critical activities correct
A, B, C, G, H, I, K (and no others)
4 | (b) | The start of an activity may be delayed (e.g. a delay in the delivery would
hold up the start of G or an activity may take longer than Bob has planned
There may not be enough workers available who can do the activities at
the required times | B1
B1
[2] | A reason why the duration of an activity may be extended
A resourcing issue related to the worker availability
4 | (c) | F has the longest float = 25 – 1 – 5 = 19 days
The clearing of the work area can start at any time from the end of A
(day 1) to day 20 without delaying the project | M1
A1
[2] | 19 or ft their forward and backward passes
Interpretation in context, must refer to ‘clearing work
area’ and start or finish times (or needing 5 days from the
window of 24 days) or reference to opportunity window4 Bob is extending his attic with the help of some friends, including his architect friend Archie.
The activities involved, their durations (in days) and Bob's notes are given below.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|l|}{Activity} & Duration (days) & Notes \\
\hline
A & Archie takes measurements & 1 & \\
\hline
B & Archie draws up plans & 3 & Must come after A \\
\hline
C & Plans are approved & 21 & Must come after B \\
\hline
D & Bob orders materials & 2 & Must come after B \\
\hline
E & Materials delivered & 10 & Must come after D \\
\hline
F & Work area cleared & 5 & Must come after A \\
\hline
G & Plumbing and electrics & 3 & Must come after C, E and F \\
\hline
H & Floors, walls and ceilings & 24 & Must come after G \\
\hline
I & Staircase & 2 & Must come after H \\
\hline
J & Windows & 1 & Must come after H \\
\hline
K & Decorating & 6 & Must come after I and J \\
\hline
\end{tabular}
\end{center}
Archie has started to construct an activity network to represent the project.\\
\includegraphics[max width=\textwidth, alt={}, center]{c2deec7d-0617-4eb0-a47e-5b42ba55b753-5_401_1253_1475_406}
\begin{enumerate}[label=(\alph*)]
\item Complete the activity network in the Printed Answer Booklet and use it to determine
\begin{itemize}
\item the minimum completion time
\item the critical activities\\
for the project.
\item Give two different reasons why the project might take longer than the minimum completion time.
\item For the activity with the longest float
\item calculate this float, in days
\item interpret this float in context.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete AS 2020 Q4 [10]}}