| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Standard +0.3 This is a standard critical path analysis question with routine cascade chart construction and resource allocation. While part (iv) requires some scheduling thought with two workers, the network is small, the precedence relationships are straightforward, and the techniques are directly taught in D2 with minimal problem-solving required beyond applying the standard algorithm. |
| 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 (minutes) | Preceded by |
| A: Check weather | 8 | - |
| B: Get maps out | 4 | - |
| C: Make sandwiches | 12 | - |
| D: Check bikes over | 20 | \(A\) |
| E: Plan route | 12 | A, B |
| \(F\) : Pack bike bags | 4 | A, B, \(C\) |
| G: Get bikes out ready | 2 | \(D , E , F\) |
| \(H\) : Change into suitable clothes | 12 | E, F |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct activity network with \(D(20), A(8), B(4), C(12), E(12), F(4), G(2), H(12)\) | M1 | For a correct activity network. Durations not necessary |
| A1 | For directions indicated correctly |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Forward pass correct | M1 | Follow through their network if possible, provided not significantly simpler |
| A1 | For forward pass correct | |
| Backward pass correct | M1 | |
| A1 | For backward pass correct | |
| Minimum completion time \(= 32\) minutes | B1 | For 32 stated, not just on diagram (cao) |
| Critical activities \(A, E, H\) | B1 | For \(A, E, H\) stated, not just on diagram (cao) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Gantt chart with correct structure | M1 | For structure of chart correct; activities may be collected together or on individual rows |
| Non-critical activities correct (floats optional) | A1 | |
| Critical activities correct | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Schedule correct with all activities shown (with \(H\) appearing twice) | M1 | |
| Activities \(A, B, C, D, E, F\) correct: \(A=8\), \(B=4\), \(C=12\), \(D=20\), \(E=12\), \(F=4\); \(D\) after \(A\); \(E\) after \(A,B\); \(F\) after \(A,B,C\); \(C,D,E\) done by \(J\) and \(K\) at same time | A1 | |
| Activities \(G\) and \(H\) correct: \(G=2\) (may see 4), \(H=12\); \(G,H\) after \((D), E, F\) (not alongside \(F\)); \(H\) done by each of \(J\) and \(K\); total time taken \(= 70\) minutes | A1 |
# Question 3:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct activity network with $D(20), A(8), B(4), C(12), E(12), F(4), G(2), H(12)$ | M1 | For a correct activity network. Durations not necessary |
| | A1 | For directions indicated correctly |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Forward pass correct | M1 | Follow through their network if possible, provided not significantly simpler |
| | A1 | For forward pass correct |
| Backward pass correct | M1 | |
| | A1 | For backward pass correct |
| Minimum completion time $= 32$ minutes | B1 | For 32 stated, not just on diagram (cao) |
| Critical activities $A, E, H$ | B1 | For $A, E, H$ stated, not just on diagram (cao) |
## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Gantt chart with correct structure | M1 | For structure of chart correct; activities may be collected together or on individual rows |
| Non-critical activities correct (floats optional) | A1 | |
| Critical activities correct | A1 | |
## Part (iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| Schedule correct with all activities shown (with $H$ appearing twice) | M1 | |
| Activities $A, B, C, D, E, F$ correct: $A=8$, $B=4$, $C=12$, $D=20$, $E=12$, $F=4$; $D$ after $A$; $E$ after $A,B$; $F$ after $A,B,C$; $C,D,E$ done by $J$ and $K$ at same time | A1 | |
| Activities $G$ and $H$ correct: $G=2$ (may see 4), $H=12$; $G,H$ after $(D), E, F$ (not alongside $F$); $H$ done by each of $J$ and $K$; total time taken $= 70$ minutes | A1 | |
---3 The table lists the activities involved in preparing for a cycle ride, their expected durations and their immediate predecessors.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Duration (minutes) & Preceded by \\
\hline
A: Check weather & 8 & - \\
\hline
B: Get maps out & 4 & - \\
\hline
C: Make sandwiches & 12 & - \\
\hline
D: Check bikes over & 20 & $A$ \\
\hline
E: Plan route & 12 & A, B \\
\hline
$F$ : Pack bike bags & 4 & A, B, $C$ \\
\hline
G: Get bikes out ready & 2 & $D , E , F$ \\
\hline
$H$ : Change into suitable clothes & 12 & E, F \\
\hline
\end{tabular}
\end{center}
(i) Draw an activity network to represent the information in the table. Show the activities on the arcs and indicate the direction of each activity and dummy activity. You are advised to make your network quite large.\\
(ii) Carry out a forward pass and a backward pass to determine the minimum completion time for preparing for the ride. List the critical activities.\\
(iii) Construct a cascade chart, showing each activity starting at its earliest possible time.
Two people, John and Kerry, are intending to go on the cycle ride. Activities $A , B , F$ and $G$ will each be done by just one person (either John or Kerry), but both are needed (at the same time) for activities $C , D$ and $E$. Also, each of John and Kerry must carry out activity $H$, although not necessarily at the same time. All timings and precedences in the original table still apply.\\
(iv) Draw up a schedule showing which activities are done by each person at which times in order to complete preparing for the ride in the shortest time possible. The schedule should have three columns, the first showing times in 4-minute intervals, the second showing which activities John does and the third showing which activities Kerry does.
\hfill \mbox{\textit{OCR D2 2005 Q3 [14]}}