7.05b Forward and backward pass: earliest/latest times, critical activities

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]

A company undertakes a project which consists of 12 activities, \(A\), \(B\), \(C\), \(\ldots\), \(L\) Each activity requires one worker. The resource histogram below shows the duration of each activity. Each activity begins at its earliest start time. The path \(ADGJL\) is critical. \includegraphics{figure_1} The company only has two workers available to work on the project. Which of the following could be a correctly levelled histogram? Tick \((\checkmark)\) one box. [1 mark] \includegraphics{figure_2} \includegraphics{figure_3} \includegraphics{figure_4} \includegraphics{figure_5}

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]

A project is undertaken by Higton Engineering Ltd. The project is broken down into 11 separate activities \(A\), \(B\), \(\ldots\), \(K\) Figure 3 below shows a completed activity network for the project, along with the earliest start time, duration, latest finish time and the number of workers required for each activity. All times and durations are given in days. \includegraphics{figure_3}

1. Write down the critical path. [1 mark]
2. Using Figure 4 below, draw a resource histogram for the project to show how the project can be completed in the minimum possible time. Assume that each activity is to start as early as possible. [3 marks] \includegraphics{figure_4}
3. Higton Engineering Ltd only has four workers available to work on the project. Find the minimum completion time for the project. Use Figure 5 below in your answer. [3 marks] \includegraphics{figure_5} Minimum completion time _____________________________________

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]