Decision Mathematics 1 Unit Test 5: Critical path analysis

Decision Mathematics 1 Unit Test 5: Critical path analysis

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1 The precedence table for activities in a small project is shown below.

Activity Preceding activities

A -

B -

C -

D A

E A,B

F C

G E,F

H C

I H

J H

a Draw an activity network, using the minimum amount of dummies, to model this project. (3 marks)

b Explain why each of the dummy activities is needed. (2 marks)



2 This diagram shows an activity network for a project.

The figures in brackets show the durations of the activities in days.

Complete the table below to show the precedences for these activities. (3 marks)

Activity Preceding activities

A

B

C

D

E

F

G

H

I

J



3 This diagram shows part of an activity network, including the early and late event times, given in days.

Activities C and D are critical.

Find the value of x. Explain why activity E is not critical even though it connects two critical events. (2 marks)



4 This diagram shows an activity network for a project.

The numbers in brackets show the durations of the activities in days.

a Use the boxes on the diagram to carry out a forward pass and a backward pass. (4 marks) b Find the project duration and list the critical activities. (2 marks) c Calculate the lower bound for the number of workers required to complete the

project. (2 marks)



5 A construction project is modelled by the activity network shown below.

The activities are represented by the arcs.

The numbers in brackets on each arc gives the times, in days, to complete the activity.

a Calculate the total floats for activities D and H. You must make the numbers you use in your calculations clear. (3 marks) b Using the grid on the next page, draw a cascade (Gantt) chart for this project. (3 marks)



c Which activities must be taking place on day 22? (1 mark) d Activity I is delayed by one day. Explain how this affects the project. (2 marks)





The number in brackets on each arc gives the times, in days, to complete the activity.

The number of workers required for each activity is shown in the table.

The project is to be completed in the shortest possible time.

Activity A B C D E F G H I J

Number of workers 2 1 4 2 3 2 2 1 2 3



a On the grid below, draw a resource histogram to show the number of workers required each day when each activity begins at its earliest time. (3 marks)

b Use the grid below to show that the project can be completed in 20 days using six workers. (4 marks)





The number in brackets on each arc gives the times, in days, to complete the activity.

One worker is required for each activity.

a Using the grid below, draw up a schedule for the project, using the minimum number of workers. (3 marks)

b The start of activity D is delayed until day 10. Explain the effect this has on the duration of the project. (2 marks)



8 A project is modelled by the activity network shown below.

a Use the grid below to schedule the project, allocating one worker per activity and using the minimum number of workers. (3 marks)

b On the grid below, draw a resource histogram to show the number of workers required each day when each activity begins at its earliest time. (2 marks)



Question 8 continued

Two workers are available for the project.

Worker 1 can do any activity.

Worker 2 cannot help with activities C, D and H, but can do activities G, I and J alone.

If the workers share an activity then its duration is reduced by one day.

c Explain how the two workers can share the work so that activity F can start on the fifth day of the project. (2 marks)

d Explain how the project can be completed in fewer than 20 days with these two workers. (4 marks)

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Decision Mathematics 1 Unit Test 5: Critical path analysis