7.05a Critical path analysis: activity on arc networks

Robert, a project manager, and his team of builders are working on a small building project. Robert has divided the project into ten activities labelled \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), \(H\), \(I\) and \(J\) as shown in the precedence table below:

Activity	Immediate Predecessor(s)	Duration (Days)
\(A\)	None	1
\(B\)	None	1
\(C\)	\(A\)	10
\(D\)	\(A\)	2
\(E\)	\(B, D\)	5
\(F\)	\(E\)	6
\(G\)	\(E\)	1
\(H\)	\(F\)	1
\(I\)	\(F\)	2
\(J\)	\(C, G, H, I\)	4

1. On the opposite page, construct an activity network for the project and fill in the earliest start time and latest finish time for each activity. [4 marks]
2. Robert claims that the project can be completed in 20 days. Comment on the validity of Robert's claim. [2 marks]

Bill Durrh Ltd undertake a construction project. The activity network for the project is shown below. The duration of each activity is given in weeks. \includegraphics{figure_7}

1. 1. Find the earliest start time and the latest finish time for each activity and show these values on the activity network above. [3 marks]
   2. Identify all of the critical activities. [1 mark]
2. The manager of Bill Durrh Ltd recruits some additional temporary workers in order to reduce the duration of one activity by 2 weeks. The manager wants to reduce the minimum completion time of the project by the largest amount. State, with a reason, which activity the manager should choose. [2 marks]

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies. [5]

Every activity shown in the precedence table has the same duration.

1. Explain why activity B cannot be critical. [1]
2. State which other activities are not critical. [1]

The activities involved in a project, their durations, immediate predecessors and the number of workers required for each activity are shown in the table.

Activity	Duration (hours)	Immediate predecessors	Number of workers
A	6	-	2
B	4	-	1
C	4	-	1
D	2	A	2
E	3	A, B	1
F	4	C	1
G	3	D	1
H	3	E, F	2

1. Model the project using an activity network.
2. Draw a cascade chart for the project, showing each activity starting at its earliest possible start time. [3]
3. Construct a schedule to show how three workers can complete the project in the minimum possible time. [4]

Kirstie has bought a house that she is planning to renovate. She has broken the project into a list of activities and constructed an activity network, using activity on arc. \includegraphics{figure_1}

1. Construct a cascade chart for the project, showing the float for each non-critical activity. [7]
2. Calculate the float for remodelling the internal layout stating how much of this is independent float and how much is interfering float. [3]

Kirstie needs to supervise the project. This means that she cannot allow more than three activities to happen on any day.

1. Describe how Kirstie should organise the activities so that the project is completed in the minimum project completion time and no more than three activities happen on any day. [3]