| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard critical path analysis question covering routine D1 techniques: forward/backward pass calculations, identifying critical path, drawing a Gantt chart, and basic resource allocation. All parts follow textbook procedures with no novel problem-solving required, making it easier than average but not trivial due to the multi-step nature and potential for arithmetic errors. |
| 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 interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram showing flow network with appropriate functions labeled | M1 A1 | (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| AC IM length 26 | B1 B1' (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Schedule diagram showing \(A(4)\), \(C(19)\), \(I(7)\), \(m(5)\), \(B(6)\), \(D(5)\), \(E(3)\), \(F(15)\), \(G(1)\), \(H(8)\), \(J(8)\), \(K(4)\), \(L(5)\), \(N(4)\) with appropriate timing | M1 A3, 2M, No | (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 5 vertices needed except to 13-14 when C, F, H, J and K must be taking place by only 13-19 when F=H will be kyte place | B2, I, O (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Revised schedule diagram with revised positioning of tasks showing constraints: \(A < \frac{C}{E}\), \(B < \frac{E}{H}\), \(D > E\), \(G < K\), \(\frac{F}{J} > m\), \(\frac{K}{L} \sim H > L\) | M1 A2, I, O | (3) [15] |
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram showing flow network with appropriate functions labeled | M1 A1 | (4) |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| AC IM length 26 | B1 B1' (1) | |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Schedule diagram showing $A(4)$, $C(19)$, $I(7)$, $m(5)$, $B(6)$, $D(5)$, $E(3)$, $F(15)$, $G(1)$, $H(8)$, $J(8)$, $K(4)$, $L(5)$, $N(4)$ with appropriate timing | M1 A3, 2M, No | (4) |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 5 vertices needed except to 13-14 when C, F, H, J and K must be taking place by only 13-19 when F=H will be kyte place | B2, I, O (2) | |
## Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Revised schedule diagram with revised positioning of tasks showing constraints: $A < \frac{C}{E}$, $B < \frac{E}{H}$, $D > E$, $G < K$, $\frac{F}{J} > m$, $\frac{K}{L} \sim H > L$ | M1 A2, I, O | (3) [15] |\includegraphics{figure_5}
The network in Figure 5 shows the activities involved in a process. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, taken to complete the activity.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and late time for each event, showing them on the diagram in the answer book. [4]
\item Determine the critical activities and the length of the critical path. [2]
\item On the grid in the answer book, draw a cascade (Gantt) chart for the process. [4]
\end{enumerate}
Each activity requires only one worker, and workers may not share an activity.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Use your cascade chart to determine the minimum numbers of workers required to complete the process in the minimum time. Explain your reasoning clearly. [2]
\item Schedule the activities, using the number of workers you found in part $(d)$, so that the process is completed in the shortest time. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2006 Q5 [15]}}