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Instructions and data for calculating the total float for various activities in a project using a precedence table and activity network. Students will learn how to identify critical activities and determine the critical path, as well as calculate the float for non-critical activities.
What you will learn
Typology: Study Guides, Projects, Research
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An engineering project is modelled by the activity network shown in the figure above. 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.
(a) Calculate the early time and late time for each event. Write these in the boxes in the diagram below.
(4)
(b) State the critical activities. (1)
(c) Find the total float on activities D and F. You must show your working. (3)
(d) On the below, draw a cascade (Gantt) chart for this project.
Figure 1
A project is modelled by the activity network shown in Figure 1. 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 possible time.
(a) Complete Figure 2 below to show the early and late event times.
Figure 2 (4)
(b) State the critical activities. (1)
(c) On the grid below, draw a cascade (Gantt) chart for this project.
(4)
(d) Use your cascade chart to determine a lower bound for the number of workers needed. You must justify your answer. (2) (Total 11 marks)
The diagram above is the activity network relating to a building project. The number in brackets on each arc gives the time taken, in days, to complete the activity.
(a) Explain the significance of the dotted line from event to event. (2)
(4)
(d) Determine the critical activities and the length of the critical path. (2)
(e) On the grid below, draw a cascade (Gantt) chart for the project.
(4) (Total 15 marks)
4.
Figure 1
A construction project is modelled by the activity network shown in Figure 1. 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 possible time.
(a) Complete Figure 2 below, showing the early and late event times.
(d) On the grid below, draw a cascade (Gantt) chart for this project.
(4)
An inspector visits the project at 1pm on days 16 and 31 to check the progress of the work.
(e) Given that the project is on schedule, which activities must be happening on each of these days? (3) (Total 15 marks)
Figure 1
The network in Figure 1 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.
(a) Calculate the early time and the late time for each event, showing them on Figure 2.
(4)
Given that each task requires just one worker,
(e) use your cascade chart to determine the minimum number of workers required to complete the process in the minimum time. Explain your reasoning clearly. (2) (Total 16 marks)
The network above shows the activities that need to be undertaken to complete a building project. Each activity is represented by an arc. The number in brackets is the duration of the activity in days. The early and late event times are shown at each vertex.
(a) Find the values of v , w , x , y and z. (3)
(b) List the critical activities. (1)
(c) Calculate the total float on each of activities H and J. (2)
(d) Draw a cascade (Gantt) chart for the project.
A project is modelled by the activity network shown in the diagram above. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the activity. Some of the early and late times for each event are shown.
(a) Calculate the missing early and late times and hence complete the diagram above. (4)
(b) Calculate the total float on activities D, G and I. You must make your calculations clear. (4)
(c) List the critical activities. (1)
Each activity requires one worker
(d) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. (2) (Total 11 marks)
8. (a) Draw the activity network described in this precedence table, using activity on arc and exactly two dummies.
Activity Immediately preceding activities A โ
B โ C A D B
E B, C F B, C (4)
(b) Explain why each of the two dummies is necessary. (3) (Total 7 marks)
The network above shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc. The number in brackets is the duration of the activity in days.
Early event time
Late event time
10. Figure 1
A project is modelled by the activity network shown in Figure 1. 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 are the event numbers. Each activity requires one worker.
(a) Explain the purpose of the dotted line from event 6 to event 8. (1)
(b) Calculate the early time and late time for each event. Write these in the boxes in Figure 2 below.
Figure 2
(4)
Early event time Late event time
(c) Calculate the total float on activities D , E and F. (3)
(d) Determine the critical activities. (2)
(e) Given that the sum of all the times of the activities is 95 hours, calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working. (2)
(f) Given that workers may not share an activity, schedule the activities so that the process is completed in the shortest time using the minimum number of workers.
(4) (Total 16 marks)
11.
An engineering project is modelled by the activity network shown in the figure above. 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.
(a) Calculate the early time and late time for each event. Write these in the boxes in the diagram below.
