Critical path analysis

A project is modelled by the activity network shown in Figure 6. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the corresponding activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.

Complete Diagram 1 in the answer book to show the early event times and the late event times.

Draw a Gantt chart for the project on the grid provided in the answer book.

State the activities that must be happening at time 18.5

An additional activity, P, is now included in the activity network shown in Figure 6. Activity P is immediately preceded only by activity D. No activity is dependent on the completion of activity P. Each activity still requires exactly one worker and the revised project is to be completed in the shortest possible time.

Explain, briefly, whether or not the revised project can be completed in the same time as the original project if the duration of activity P is

10 days

17 days

Draw the activity network described in the precedence table below, using activity on arc and exactly three dummies.

The network in Figure 6 shows the activities that need to be undertaken by a company to complete a project. Each activity is represented by an arc and the duration, in days, is shown in brackets. Each activity requires exactly one worker. The early event times and late event times are shown at each vertex. Given that the total float on activity D is 1 day,

find the values of w, x, y and z.

On Diagram 1 in the answer book, draw a cascade (Gantt) chart for the project.

Use your cascade chart to determine a lower bound for the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to times and activities.

It is decided that the company may use up to 36 days to complete the project.

On Diagram 2 in the answer book, construct a scheduling diagram to show how the project can be completed within 36 days using as few workers as possible.

The table shows the activities required for the completion of a building project. For each activity the table shows the time taken, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time.

Figure 6 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the numbers in brackets on the arcs are the times taken, in days, to complete each activity.

Add activities, E, F and I, and exactly one dummy to Diagram 1 in the answer book.

Complete Diagram 1 in the answer book to show the early event times and late event times.

Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.

Schedule the activities, using the minimum number of workers, so that the project is completed in the minimum time.

A project is modelled by the activity network shown in Figure 3. 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.

Complete Diagram 1 in the answer book to show the early event times and late event times.

Calculate the total float for activity H. You must make the numbers you use in your calculation clear.

Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. Show your calculation.

Diagram 2 in the answer book shows a partly completed scheduling diagram for this project.

Complete the scheduling diagram, using the minimum number of workers, so that the project is completed in the minimum time.

Draw the activity network described in the precedence table, using activity on arc and exactly two dummies.

Explain why each of the two dummies is necessary.

[ The sum of the duration of all activities is 172 days ] A project is modelled by the activity network shown in Figure 5. 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.

Complete Diagram 1 in the answer book to show the early event times and late event times.

Calculate the total float for activity M. You must make the numbers you use in your calculation clear.

For each of the situations below, explain the effect that the delay would have on the project completion date.

A 2 day delay on the early start of activity P.

A 2 day delay on the early start of activity Q.

Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time.

Diagram 2 in the answer book shows a partly completed cascade chart for this project.

Complete the cascade chart.

Use your cascade chart to determine a second lower bound on the number of workers needed to complete the project in the shortest possible time. You must make specific reference to times and activities.

State which of the two lower bounds found in (d) and (f) is better. Give a reason for your answer.

Figure 7 is the activity network relating to a building project. The activities are represented by the arcs. The number in brackets on each arc gives the time to complete the activity. Each activity requires one worker. The project must be completed in the shortest possible time.

Explain the reason for the dotted line from event 4 to event 6 as shown in Figure 7.

Complete Diagram 1 in the answer book to show the early event times and the late event times.

State the critical activities.

Calculate the total float for activity G. You must make the numbers you use in your calculation clear.

Draw a Gantt chart for this project on the grid provided in the answer book.

State the activities that must be happening at time 5.5

Use your Gantt chart to determine the minimum number of workers needed to complete the project in the minimum time. You must justify your answer.

Figure 5 is the activity network relating to a development project. 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.

Complete the precedence table in the answer book.

Complete Diagram 1 in the answer book to show the early event times and late event times.

Calculate the total float for activity E. You must make the numbers you use in your calculation clear.

Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.

Schedule the activities using the minimum number of workers so that the project is completed in the minimum time.

A project is modelled by the activity network shown in Figure 7. 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.

Complete the precedence table in the answer book.

Complete Diagram 1 in the answer book, to show the early event times and late event times.

State the critical activities.

On the grid in your answer book, draw a cascade (Gantt) chart for this project.

By considering the activities that must take place between time 7 and time 16, explain why it is not possible to complete this project with just 3 workers in the minimum time.

The network in Figure 7 shows the activities that need to be undertaken to complete a maintenance project. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. The numbers in circles are the events. Each activity requires one worker. The project is to be completed in the shortest possible time.

Complete the precedence table for this network in the answer book.

Explain why each of the following is necessary.

The dummy from event 6 to event 7.

The dummy from event 8 to event 9.

Complete Diagram 2 in the answer book to show the early and the late event times.

State the critical activities.

Calculate the total float on activity K. You must make the numbers used in your calculation clear.

Calculate a lower bound for the number of workers needed to complete the project in the minimum time.