OCR D2 2016 June — Question 5 16 marks

Exam BoardOCR
ModuleD2 (Decision Mathematics 2)
Year2016
SessionJune
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeIdentify guaranteed critical activities
DifficultyStandard +0.3 This is a standard critical path analysis question covering routine D2 techniques: identifying critical activities from network structure, forward/backward pass calculations, resource scheduling, and activity crashing. While multi-part with several marks, each component follows textbook procedures without requiring novel insight or complex problem-solving—slightly easier than average A-level maths.
Spec7.05a 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
5 The network below represents a project using activity on arc. The durations of the activities are not yet shown. \includegraphics[max width=\textwidth, alt={}, center]{490ff276-6639-40a1-bffb-dc6967f3ab21-6_597_1257_340_386}
  1. If \(C\) were to turn out to be a critical activity, which two other activities would be forced to be critical?
  2. Complete the table, in the Answer Book, to show the immediate predecessor(s) for each activity. In fact, \(C\) is not a critical activity. Table 1 lists the activities and their durations, in minutes. \begin{table}[h]
    Activity\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)\(I\)\(J\)
    Duration10151051551015515
    \captionsetup{labelformat=empty} \caption{Table 1}
    \end{table}
  3. Carry out a forward pass and a backward pass through the activity network, showing the early event time and late event time at each vertex of the network. State the minimum project completion time and list the critical activities. Each activity requires one person.
  4. Draw a schedule to show how three people can complete the project in the minimum time, with each activity starting at its earliest possible time. Each box in the Answer Book represents 5 minutes. For each person, write the letter of the activity they are doing in each box, or leave the box blank if the person is resting for those 5 minutes.
  5. Show how two people can complete the project in the minimum time. It is required to reduce the project completion time by 10 minutes. Table 2 lists those activities for which the duration could be reduced by 5 minutes, and the cost of making each reduction. \begin{table}[h]
    Activity\(A\)\(B\)\(C\)\(E\)\(G\)\(H\)\(J\)
    Cost \(( \pounds )\)200400100600100500500
    New duration51051051010
    \captionsetup{labelformat=empty} \caption{Table 2}
    \end{table}
  6. Explain why the cost of saving 5 minutes by reducing activity \(A\) is more than \(\pounds 200\). Find the cheapest way to complete the project in a time that is 10 minutes less than the original minimum project completion time. State which activities are reduced and the total cost of doing this.
5 The network below represents a project using activity on arc. The durations of the activities are not yet shown.\\
\includegraphics[max width=\textwidth, alt={}, center]{490ff276-6639-40a1-bffb-dc6967f3ab21-6_597_1257_340_386}\\
(i) If $C$ were to turn out to be a critical activity, which two other activities would be forced to be critical?\\
(ii) Complete the table, in the Answer Book, to show the immediate predecessor(s) for each activity.

In fact, $C$ is not a critical activity. Table 1 lists the activities and their durations, in minutes.

\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Activity & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Duration & 10 & 15 & 10 & 5 & 15 & 5 & 10 & 15 & 5 & 15 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}

(iii) Carry out a forward pass and a backward pass through the activity network, showing the early event time and late event time at each vertex of the network. State the minimum project completion time and list the critical activities.

Each activity requires one person.\\
(iv) Draw a schedule to show how three people can complete the project in the minimum time, with each activity starting at its earliest possible time. Each box in the Answer Book represents 5 minutes. For each person, write the letter of the activity they are doing in each box, or leave the box blank if the person is resting for those 5 minutes.\\
(v) Show how two people can complete the project in the minimum time.

It is required to reduce the project completion time by 10 minutes. Table 2 lists those activities for which the duration could be reduced by 5 minutes, and the cost of making each reduction.

\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Activity & $A$ & $B$ & $C$ & $E$ & $G$ & $H$ & $J$ \\
\hline
Cost $( \pounds )$ & 200 & 400 & 100 & 600 & 100 & 500 & 500 \\
\hline
New duration & 5 & 10 & 5 & 10 & 5 & 10 & 10 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{center}
\end{table}

(vi) Explain why the cost of saving 5 minutes by reducing activity $A$ is more than $\pounds 200$. Find the cheapest way to complete the project in a time that is 10 minutes less than the original minimum project completion time. State which activities are reduced and the total cost of doing this.

\hfill \mbox{\textit{OCR D2 2016 Q5 [16]}}
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