| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.8 This is a routine Decision Mathematics question testing standard CPA procedures: reading a precedence diagram, identifying critical path (straightforward from given graph), drawing a resource histogram (mechanical plotting from given schedule), and basic resource leveling with simple constraints. All techniques are textbook exercises requiring careful execution but no problem-solving insight or novel reasoning. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Duration (hours) | Immediate predecessors | Number of workers |
| \(A\) | 3 | - | 3 |
| \(B\) | 5 | \(A\) | 2 |
| C | 3 | A | 2 |
| \(D\) | 3 | B | 1 |
| E | 3 | C | 3 |
| \(F\) | 5 | D, E | 2 |
| \(G\) | 3 | \(B , E\) | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | 16 hours; A, B, D, F | B1 |
| B1 | All four critical activities and no others | |
| (ii) | Workers histogram showing appropriate resource allocation | M1 |
| A1 | An entirely correct graph with scales and labels | |
| [2] | ||
| (iii) | Start C at time 3 | B1 |
| Start E at time 8 | B1 | 'E' and '8' or 'after B' or 'with D' |
| Start G at time 16 | B1 | 'G' and '16' or 'after F' |
| Complete in 19 hours | B1 | 19 |
| [4] |
(i) | 16 hours; A, B, D, F | B1 | 16 with units |
| | B1 | All four critical activities and no others |
(ii) | Workers histogram showing appropriate resource allocation | M1 | A reasonable attempt at a resource histogram |
| | | A1 | An entirely correct graph with scales and labels |
| | | [2] | |
(iii) | Start C at time 3 | B1 | 'C' and '3' or 'after A' or 'with B' |
| | Start E at time 8 | B1 | 'E' and '8' or 'after B' or 'with D' |
| | Start G at time 16 | B1 | 'G' and '16' or 'after F' |
| | Complete in 19 hours | B1 | 19 |
| | | [4] | |
---2 The table shows the activities involved in a project, their durations, precedences and the number of workers needed for each activity. The graph gives a schedule with each activity starting at its earliest possible time.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration (hours) & Immediate predecessors & Number of workers \\
\hline
$A$ & 3 & - & 3 \\
\hline
$B$ & 5 & $A$ & 2 \\
\hline
C & 3 & A & 2 \\
\hline
$D$ & 3 & B & 1 \\
\hline
E & 3 & C & 3 \\
\hline
$F$ & 5 & D, E & 2 \\
\hline
$G$ & 3 & $B , E$ & 3 \\
\hline
\end{tabular}
\end{center}
\includegraphics[max width=\textwidth, alt={}, center]{3d8f3593-7923-40f7-b5c0-ac5c3bc21292-03_473_1591_964_278}\\
(i) Using the graph, find the minimum completion time for the project and state which activities are critical.\\
(ii) Draw a resource histogram, using graph paper, assuming that there are no delays and that every activity starts at its earliest possible time.
Assume that only four workers are available but that they are equally skilled at all tasks. Assume also that once an activity has been started it continues until it is finished.\\
(iii) The critical activities are to start at their earliest possible times. List the start times for the non-critical activities for completion of the project in the minimum possible time. What is this minimum completion time?
\hfill \mbox{\textit{OCR D2 2007 Q2 [8]}}