7.05d Latest start and earliest finish: independent and interfering float

\includegraphics{figure_5} A project is modelled by the activity network shown in Fig. 5. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the activity. The numbers in circles give the event numbers. Each activity requires one worker.

1. Explain the purpose of the dotted line from event 4 to event 5. [1]
2. Calculate the early time and the late time for each event. Write these in the boxes in the answer book. [4]
3. Determine the critical activities. [1]
4. Obtain the total float for each of the non-critical activities. [3]
5. On the grid in the answer book, draw a cascade (Gantt) chart, showing the answers to parts (c) and (d). [4]
6. Determine the minimum number of workers needed to complete the project in the minimum time. Make your reasoning clear. [2]

\includegraphics{figure_4} An engineering project is modelled by the activity network shown in Figure 4. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest time.

1. Calculate the early time and late time for each event. Write these in boxes in Diagram 1 in the answer book. [4]
2. State the critical activities. [1]
3. Find the total float on activities D and F. You must show your working. [3]
4. On the grid in the answer book, draw a cascade (Gantt) chart for this project. [4]

The chief engineer visits the project on day 15 and day 25 to check the progress of the work. Given that the project is on schedule,

1. which activities must be happening on each of these two days? [3]

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}

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]