| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a routine Decision Mathematics question testing standard procedures: completing a precedence table, identifying minimax values (likely from a given matrix), and drawing an activity network from precedence information. These are algorithmic tasks requiring careful execution but minimal problem-solving insight, making it easier than average A-level questions. |
| 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 |
|---|---|---|
| Answer | Marks | Guidance |
| Substantially correct network drawn | M1 | A substantially correct network. Condone arrows missing or wrong way round, no end and/or extra dummies. Do NOT allow activity on node formulation |
| Correct network with arrows on at least dummy activities, no extra dummies, single end point | A1 | A correct network, with arrows on at least the dummy activities, with no extra dummies and a single end point |
| A dummy is needed after \(C\) because \(D\) follows both \(B\) and \(C\) | B1 | A valid explanation |
| A dummy is needed after \(D\) because \(F\) and \(G\) both follow \(D\) | B1 | A valid explanation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Substantially correct forward pass | M1 | A substantially correct forward pass |
| Early event times correct (ft their network) | A1 | Early event times correct (ft their network if possible) |
| Substantially correct backwards pass | M1 | A substantially correct backwards pass |
| Late event times correct (ft their network) | A1 | Late event times correct (ft their network if possible) |
| Minimum completion time = 14 days | B1 | For 14 cao. Must be stated, not implied from diagram |
| Critical activities are \(A, C, D, F\) | B1 | For these four activities and no others cao. Must be stated, not implied from diagram |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Reasonable attempt at resource histogram using number of workers for different activities; scales and labels required; some days with 4 workers | M1 | For a reasonable attempt at using the number of workers for the different activities. Scales and labels required and some days with 4 workers |
| Reasonable attempt with no overhanging blocks | M1 dep | For a reasonable attempt with no overhanging blocks |
| Entirely correct histogram | A1 | For an entirely correct histogram |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(E\) cannot happen until after \(C\) has finished so must overlap with \(F\) | B1 | Earliest finish for \(E >\) latest start for \(F\) |
| Start \(E\) immediately after \(C\) but delay the start of \(F\) for 1 day (until after \(E\) has finished) | B1 | For delaying the start of \(F\) (by 1 day) |
# Question 3:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Substantially correct network drawn | M1 | A substantially correct network. Condone arrows missing or wrong way round, no end and/or extra dummies. Do NOT allow activity on node formulation |
| Correct network with arrows on at least dummy activities, no extra dummies, single end point | A1 | A correct network, with arrows on at least the dummy activities, with no extra dummies and a single end point |
| A dummy is needed after $C$ because $D$ follows both $B$ and $C$ | B1 | A valid explanation |
| A dummy is needed after $D$ because $F$ and $G$ both follow $D$ | B1 | A valid explanation |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Substantially correct forward pass | M1 | A substantially correct forward pass |
| Early event times correct (ft their network) | A1 | Early event times correct (ft their network if possible) |
| Substantially correct backwards pass | M1 | A substantially correct backwards pass |
| Late event times correct (ft their network) | A1 | Late event times correct (ft their network if possible) |
| Minimum completion time = 14 days | B1 | For 14 cao. Must be stated, not implied from diagram |
| Critical activities are $A, C, D, F$ | B1 | For these four activities and no others cao. Must be stated, not implied from diagram |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Reasonable attempt at resource histogram using number of workers for different activities; scales and labels required; some days with 4 workers | M1 | For a reasonable attempt at using the number of workers for the different activities. Scales and labels required and some days with 4 workers |
| Reasonable attempt with no overhanging blocks | M1 dep | For a reasonable attempt with no overhanging blocks |
| Entirely correct histogram | A1 | For an entirely correct histogram |
## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $E$ cannot happen until after $C$ has finished so must overlap with $F$ | B1 | Earliest finish for $E >$ latest start for $F$ |
| Start $E$ immediately after $C$ but delay the start of $F$ for 1 day (until after $E$ has finished) | B1 | For delaying the start of $F$ (by 1 day) |
---3 The table shows the activities involved in a project, their durations and precedences, and the number of workers needed for each activity.
(i) On the insert, complete the last two columns of the table.\\
(ii) State the minimax value and write down the minimax route.\\
(iii) Complete the diagram on the insert to show the network that is represented by the table.
\hfill \mbox{\textit{OCR D2 2007 Q3 [15]}}