| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 11 |
| 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 Critical Path Analysis question requiring routine application of forward/backward scan algorithms and basic critical path reasoning. While it involves multiple parts and some interpretation (penalty costs), these are textbook techniques in D2 with no novel problem-solving required, making it slightly easier than average. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| lower figures give forward scan minimum time is 48 days | M1 A1, A1 | |
| (b) upper figures give backward scan critical path is \(BCEHKO\) | M1 A1, A1 | |
| (c) \(E\) on critical path \(\therefore £150,000\) penalty if reduce \(K\) by more than 1 day it is no longer on critical path \(\therefore\) only reduces penalty by £50,000 at cost of £90,000 | B2 | |
| (d) \(B\), \(C\) and \(O\): reducing any of these by 2 days reduces minimum time by 2 days this reduces penalty by £100,000 at cost of £80,000 \(\therefore\) profitable | B3 | (11) |
**(a)**
![Network diagram with forward and backward scan values]
lower figures give forward scan minimum time is 48 days | M1 A1, A1 |
**(b)** upper figures give backward scan critical path is $BCEHKO$ | M1 A1, A1 |
**(c)** $E$ on critical path $\therefore £150,000$ penalty if reduce $K$ by more than 1 day it is no longer on critical path $\therefore$ only reduces penalty by £50,000 at cost of £90,000 | B2 |
**(d)** $B$, $C$ and $O$: reducing any of these by 2 days reduces minimum time by 2 days this reduces penalty by £100,000 at cost of £80,000 $\therefore$ profitable | B3 | **(11)** |
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$\square$\\
$\square$
Fig. 2\\
Construct an activity network to model the work involved in laying the foundations and putting in services for an industrial complex.
\begin{enumerate}[label=(\alph*)]
\item Execute a forward scan to find the minimum time in which the project can be completed.
\item Execute a backward scan to determine which activities lie on the critical path.
The contractor is committed to completing the project in this minimum time and faces a penalty of $\pounds 50000$ for each day that the project is late. Unfortunately, before any work has begun, flooding means that activity $E$ will take 3 days longer than the 7 days allocated.
\item Activity $K$ could be completed in 1 day at an extra cost of $\pounds 90000$. Explain why doing this is not economical.\\
(2 marks)
\item If the time taken to complete any one activity, other than $E$, could be reduced by 2 days at an extra cost of $\pounds 80000$, for which activities on their own would this be profitable. Explain your reasoning.\\
(3 marks)\\
11 marks
\end{enumerate}
\hfill \mbox{\textit{OCR D2 Q4 [11]}}