| Exam Board | OCR |
|---|---|
| Module | Further Discrete (Further Discrete) |
| Year | 2018 |
| Session | March |
| Marks | 15 |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Standard +0.3 This is a standard critical path analysis question covering routine Further Maths techniques: activity networks, float calculations, and resource scheduling. While it requires multiple steps and careful bookkeeping across three parts, all methods are algorithmic applications of textbook procedures without requiring novel insight or problem-solving beyond following established algorithms. |
| 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 interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Activity | Duration (hours) | Immediate predecessors | Number of workers |
| A | 6 | - | 2 |
| B | 4 | - | 1 |
| C | 4 | - | 1 |
| D | 2 | A | 2 |
| E | 3 | A, B | 1 |
| F | 4 | C | 1 |
| G | 3 | D | 1 |
| H | 3 | E, F | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Activity network diagram with Activity-on-arc showing all activities A through H with correct durations and exactly one dummy activity used | M1, A1 | Activity network; All correct with exactly one dummy used |
| Forward pass and backward pass calculations with all values correct, cao | M1 ft, M ft, A1 | Forward pass; Backward pass; All correct (cao) |
| Critical activities: A, E, H; Independent float at B: 2 hours; Interfering float at C, D, F, G: 1 hour each | B1, B1, B1 | Critical activities A, E, H; 2 hours independent float at B; 1 hour interfering float at C, D, F, G |
| Answer | Marks | Guidance |
|---|---|---|
| Gantt chart showing non-critical activities with correct start and duration | M1, A1 | Non-critical activities; All correct and floats |
| Critical activities shown correctly, may be on separate rows | B1 | Critical activities correct |
| Answer | Marks | Guidance |
|---|---|---|
| Resource histogram or table showing worker allocation by time period with correct durations and precedences for activities A, B, D, E; C, F; G, H and total time = 15 hours. A, D, H have two workers (simultaneously) | M1, M1, M1, A1 | Durations and precedences for A, B, D, E; Durations and precedences for C, F; Durations and precedences for G, H; A, D, H have two workers (simultaneously) and total time = 15 |
## (i)
| Activity network diagram with Activity-on-arc showing all activities A through H with correct durations and exactly one dummy activity used | M1, A1 | Activity network; All correct with exactly one dummy used |
| Forward pass and backward pass calculations with all values correct, cao | M1 ft, M ft, A1 | Forward pass; Backward pass; All correct (cao) |
| Critical activities: A, E, H; Independent float at B: 2 hours; Interfering float at C, D, F, G: 1 hour each | B1, B1, B1 | Critical activities A, E, H; 2 hours independent float at B; 1 hour interfering float at C, D, F, G |
## (ii)
| Gantt chart showing non-critical activities with correct start and duration | M1, A1 | Non-critical activities; All correct and floats |
| Critical activities shown correctly, may be on separate rows | B1 | Critical activities correct |
## (iii)
| Resource histogram or table showing worker allocation by time period with correct durations and precedences for activities A, B, D, E; C, F; G, H and total time = 15 hours. A, D, H have two workers (simultaneously) | M1, M1, M1, A1 | Durations and precedences for A, B, D, E; Durations and precedences for C, F; Durations and precedences for G, H; A, D, H have two workers (simultaneously) and total time = 15 |
---The activities involved in a project, their durations, immediate predecessors and the number of workers required for each activity are shown in the table.
\begin{tabular}{|c|c|c|c|}
\hline
Activity & Duration (hours) & Immediate predecessors & Number of workers \\
\hline
A & 6 & - & 2 \\
\hline
B & 4 & - & 1 \\
\hline
C & 4 & - & 1 \\
\hline
D & 2 & A & 2 \\
\hline
E & 3 & A, B & 1 \\
\hline
F & 4 & C & 1 \\
\hline
G & 3 & D & 1 \\
\hline
H & 3 & E, F & 2 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Model the project using an activity network.
\begin{itemize}
\item Calculate the early and late event times.
\item Calculate the independent and interfering float for each activity. [8]
\end{itemize}
\item Draw a cascade chart for the project, showing each activity starting at its earliest possible start time. [3]
\item Construct a schedule to show how three workers can complete the project in the minimum possible time. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete 2018 Q6 [15]}}