| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find range for variable duration |
| Difficulty | Moderate -0.5 This is a standard D1 critical path analysis question requiring routine application of learned techniques: identifying precedence differences, calculating project durations for different parameter values, drawing an activity network, and finding early/late times. While multi-part with several steps, it involves no novel problem-solving or insight beyond textbook methods, 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 activities |
| Activity | A | B | C | D | E |
| Duration | 2 | 1 | \(x\) | 3 | 2 |
| Activity | Duration | Immediate predecessors |
| R | 2 | - |
| S | 1 | - |
| T | 5 | - |
| w | 3 | R, S |
| X | 2 | R, S, T |
| Y | 3 | R |
| Z | 1 | W, Y |
| Answer | Marks |
|---|---|
| Activity D depends on A and B in project 1, but on A, B and C in project 2. | M1 A1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Project 1: Duration is 5 for \(x<3\), thence \(x+2\). Project 2: Duration is 5 for \(x<2\), thence \(x+3\) | B1 B1 B1 | "5" beyond 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Network diagram showing: Activity-on-arc with single start and single end; precedences shown; arcs AF, FB, BD, DE, EC; Project duration = 7; Critical activities = T, X | M1 A1 A2 M1 A1 M1 A1 B1 B1 | activity-on-arc; single start and single end; precedences (\(-1\) each error); forward pass; backward pass |
**(a)(i)**
| Activity D depends on A and B in project 1, but on A, B and C in project 2. | M1 A1 A1 | |
**(a)(ii)**
| Project 1: Duration is 5 for $x<3$, thence $x+2$. Project 2: Duration is 5 for $x<2$, thence $x+3$ | B1 B1 B1 | "5" beyond 5 |
**(b)(i) & (ii)**
| Network diagram showing: Activity-on-arc with single start and single end; precedences shown; arcs AF, FB, BD, DE, EC; Project duration = 7; Critical activities = T, X | M1 A1 A2 M1 A1 M1 A1 B1 B1 | activity-on-arc; single start and single end; precedences ($-1$ each error); forward pass; backward pass |5
\begin{enumerate}[label=(\alph*)]
\item The graphs below illustrate the precedences involved in running two projects, each consisting of the same activities $\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }$ and E .
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Project 1}
\includegraphics[alt={},max width=\textwidth]{8eba759f-38bc-4d14-ac65-9a0ee6c79741-6_280_385_429_495}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Project 2}
\includegraphics[alt={},max width=\textwidth]{8eba759f-38bc-4d14-ac65-9a0ee6c79741-6_255_392_429_1187}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item For one activity the precedences in the two projects are different. State which activity and describe the difference.
\item The table below shows the durations of the five activities.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Activity & A & B & C & D & E \\
\hline
Duration & 2 & 1 & $x$ & 3 & 2 \\
\hline
\end{tabular}
\end{center}
Give the total time for project 1 for all possible values of $x$.\\
Give the total time for project 2 for all possible values of $x$.
\end{enumerate}\item The durations and precedences for the activities in a project are shown in the table.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Duration & Immediate predecessors \\
\hline
R & 2 & - \\
\hline
S & 1 & - \\
\hline
T & 5 & - \\
\hline
w & 3 & R, S \\
\hline
X & 2 & R, S, T \\
\hline
Y & 3 & R \\
\hline
Z & 1 & W, Y \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Draw an activity on arc network to represent this information.
\item Find the early time and the late time for each event. Give the project duration and list the critical activities.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI D1 2008 Q5 [16]}}