| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question requiring routine application of forward/backward pass algorithms, reading a resource histogram, and calculating float times. While multi-part with several steps, each component uses well-practiced D2 techniques without requiring novel problem-solving insight or complex reasoning beyond textbook methods. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Precedences correct for \(D\) and \(E\): AB, B | B1 | |
| Precedences correct for \(F\) and \(G\): BC, C | B1 | |
| Precedences correct for \(H\), \(I\) and \(J\): DEFG, FG, HI | B1 | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Substantially correct forward pass (at most one independent error) | M1 | |
| Substantially correct backward pass (at most one independent error) | M1 | No follow through, 28 given in question |
| Both passes wholly correct | A1 | |
| Critical activities \(C\ F\ H\ J\) | B1 | \(CFHJ\) and no others (no follow through) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(J\) correct: float = 4 | B1 | |
| \(H\) and \(I\) correct: float = 2, float = 3 | B1 | |
| \(F\) and \(G\) correct: float = 1, float = 1 | B1 | |
| \(D\) and \(E\) correct: float = 3, float = 2 | B1 | |
| \(B\) and \(C\) correct: float = 1, float = 3 | B1 | |
| \(A\) correct: float = 1 | B1 | [6] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Minimum delay 1 day | B1 | 1 |
| Maximum delay 3 days | B1 | 3 |
# Question 2:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Precedences correct for $D$ and $E$: **AB**, **B** | B1 | |
| Precedences correct for $F$ and $G$: **BC**, **C** | B1 | |
| Precedences correct for $H$, $I$ and $J$: **DEFG**, **FG**, **HI** | B1 | [3] |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Substantially correct forward pass (at most one independent error) | M1 | |
| Substantially correct backward pass (at most one independent error) | M1 | No follow through, 28 given in question |
| Both passes wholly correct | A1 | |
| Critical activities $C\ F\ H\ J$ | B1 | $CFHJ$ and no others (no follow through) | [4] |
## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $J$ correct: float = 4 | B1 | |
| $H$ and $I$ correct: float = 2, float = 3 | B1 | |
| $F$ and $G$ correct: float = 1, float = 1 | B1 | |
| $D$ and $E$ correct: float = 3, float = 2 | B1 | |
| $B$ and $C$ correct: float = 1, float = 3 | B1 | |
| $A$ correct: float = 1 | B1 | [6] |
## Part (iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| Minimum delay **1** day | B1 | 1 |
| Maximum delay **3** days | B1 | 3 | [2] |
---2 Answer this question on the insert provided.
The diagram shows an activity network for a project. The figures in brackets show the durations of the activities in days.\\
\includegraphics[max width=\textwidth, alt={}, center]{c5bfbe78-64c4-4254-ad83-0c90f4a54b18-3_497_1230_493_459}\\
(i) Complete the table in the insert to show the precedences for the activities.\\
(ii) Use the boxes on the diagram in the insert to carry out a forward pass and a backward pass. Show that the minimum project completion time is 28 days and list the critical activities.
The resource histogram below shows the number of workers required each day when the activities each begin at their earliest possible start time. Once an activity has been started it runs for its duration without a break.\\
\includegraphics[max width=\textwidth, alt={}, center]{c5bfbe78-64c4-4254-ad83-0c90f4a54b18-3_457_1543_1503_299}\\
(iii) By considering which activities are happening each day, complete the table in the insert to show the number of workers required for each activity. You are advised to start at day 28 and work back through the days towards day 1 .
Only five workers are actually available, but they are all equally skilled at each of the activities. The project can still be completed in 28 days by delaying the start of activity $E$.\\
(iv) Find the minimum possible delay and the maximum possible delay on activity $E$ in this case.
\hfill \mbox{\textit{OCR D2 2009 Q2 [15]}}