| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.3 This is a standard multi-part critical path analysis question covering routine D2 techniques (activity network, critical path, Gantt chart, resource histograms). While lengthy with multiple parts, each component follows textbook procedures with no novel problem-solving required. The precedence relationships are straightforward, making it slightly easier than average for A-level standard. |
| 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 float |
| Activity | Duration (hours) | Immediate Predecessor(s) | No. of Workers |
| A | 3 | - | 9 |
| B | 2 | A | 5 |
| C | 5 | \(A\) | 6 |
| D | 3 | C | 5 |
| E | 6 | \(B , D\) | 2 |
| \(F\) | 13 | D | 5 |
| \(G\) | 4 | E | 6 |
| \(H\) | 12 | E | 4 |
| I | 3 | \(F\) | 4 |
| J | 5 | H, I | 3 |
| K | 7 | \(G , J\) | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| Content | Marks | Guidance |
| (a) Network diagram showing: A (3); B (2) with edges 0-3, 0-3; C (5) with edges 3-8, 3-8; D (3) with edges 8-11, 8-11; E (6) with edges 11-17, 11-17; F (13) with edges 13-26, 11-24; G (4) with edges 30-34, 17-21; H (12) with edges 17-29, 17-29; I (3) with edges 26-29, 24-27; J (5) with edges 29-34, 29-34; K (7) with edges 34-41, 34-41 | M1 A2 | |
| (b) lower figures give forward scan; upper figures give backward scan; critical path is ACDEHJK; minimum time is 41 hours | M1 M1 A1 A1 | |
| (c) Gantt chart showing activities A, C, D, E positioned 0-10; B (shaded) 3-5; F (shaded) 10-24; G (shaded) 17-34; I (shaded) 24-27; H positioned 11-23; J positioned 24-29; K positioned 34-41 | B3 | |
| (d) Resource histogram (number of workers vs time) showing: A requires 6 workers 0-5; B requires 9 workers 3-5; C requires 3 workers 5-8; D requires 4 workers 8-10; E requires 2 workers 10-11; F requires 8 workers 11-19; G requires 14 workers 17-30; H requires 6 workers 11-23; I requires 7 workers 24-27; J requires 3 workers 24-29; K requires 4 workers 34-41; maximum of 15 workers required | M1 A2 | |
| (e) Resource histogram (number of workers vs time) showing: A requires 6 workers 0-10; B requires 8 workers 3-5; C requires 3 workers 5-8; D requires 4 workers 8-12; E requires 2 workers 12-17; F requires 6 workers 10-20; H requires 6 workers 11-20; G requires 10 workers 20-34; I requires 5 workers 20-27; J requires 3 workers 27-31; K requires 4 workers 31-41 | M1 A1 | (15) |
| Content | Marks | Guidance |
|---------|-------|----------|
| (a) Network diagram showing: A (3); B (2) with edges 0-3, 0-3; C (5) with edges 3-8, 3-8; D (3) with edges 8-11, 8-11; E (6) with edges 11-17, 11-17; F (13) with edges 13-26, 11-24; G (4) with edges 30-34, 17-21; H (12) with edges 17-29, 17-29; I (3) with edges 26-29, 24-27; J (5) with edges 29-34, 29-34; K (7) with edges 34-41, 34-41 | M1 A2 | |
| (b) lower figures give forward scan; upper figures give backward scan; critical path is ACDEHJK; minimum time is 41 hours | M1 M1 A1 A1 | |
| (c) Gantt chart showing activities A, C, D, E positioned 0-10; B (shaded) 3-5; F (shaded) 10-24; G (shaded) 17-34; I (shaded) 24-27; H positioned 11-23; J positioned 24-29; K positioned 34-41 | B3 | |
| (d) Resource histogram (number of workers vs time) showing: A requires 6 workers 0-5; B requires 9 workers 3-5; C requires 3 workers 5-8; D requires 4 workers 8-10; E requires 2 workers 10-11; F requires 8 workers 11-19; G requires 14 workers 17-30; H requires 6 workers 11-23; I requires 7 workers 24-27; J requires 3 workers 24-29; K requires 4 workers 34-41; maximum of 15 workers required | M1 A2 | |
| (e) Resource histogram (number of workers vs time) showing: A requires 6 workers 0-10; B requires 8 workers 3-5; C requires 3 workers 5-8; D requires 4 workers 8-12; E requires 2 workers 12-17; F requires 6 workers 10-20; H requires 6 workers 11-20; G requires 10 workers 20-34; I requires 5 workers 20-27; J requires 3 workers 27-31; K requires 4 workers 31-41 | M1 A1 | (15) |
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**Total (60)**\begin{enumerate}
\item A project consists of the activities listed in the table below. For each activity the table shows how long it will take, which other activites must be completed before it can be done and the number of workers needed to complete it.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration (hours) & Immediate Predecessor(s) & No. of Workers \\
\hline
A & 3 & - & 9 \\
\hline
B & 2 & A & 5 \\
\hline
C & 5 & $A$ & 6 \\
\hline
D & 3 & C & 5 \\
\hline
E & 6 & $B , D$ & 2 \\
\hline
$F$ & 13 & D & 5 \\
\hline
$G$ & 4 & E & 6 \\
\hline
$H$ & 12 & E & 4 \\
\hline
I & 3 & $F$ & 4 \\
\hline
J & 5 & H, I & 3 \\
\hline
K & 7 & $G , J$ & 8 \\
\hline
\end{tabular}
\end{center}
(a) Draw an activity network for the project.\\
(b) Find the critical path and the minimum time in which the project can be completed.\\
(c) Represent all of the activities on a Gantt diagram.\\
(d) By drawing a resource histogram, find out the maximum number of workers required at any one time if each activity is begun as soon as possible.\\
(e) Draw another resource histogram to show how the project can be completed in the minimum time possible using a maximum of 10 workers at any one time.
Sheet for answering question 4
\section*{Please hand this sheet in for marking}
\includegraphics[max width=\textwidth, alt={}, center]{b8eb80d5-5af5-4a8b-8335-6fae95f3aa73-6_729_1227_482_338}\\
\includegraphics[max width=\textwidth, alt={}, center]{b8eb80d5-5af5-4a8b-8335-6fae95f3aa73-6_723_1223_1466_338}
\hfill \mbox{\textit{OCR D2 Q6 [15]}}