7.05e Cascade charts: scheduling and effect of delays

\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]

\includegraphics{figure_5} The network in Figure 5 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. The early and late event times are to be shown at each vertex and some have been completed for you.

1. Calculate the missing early and late times and hence complete Diagram 2 in your answer book. [3]
2. List the two critical paths for this network. [2]
3. Explain what is meant by a critical path. [2]

The sum of all the activity times is 110 days and each activity requires just one worker. The project must be completed in the minimum time.

1. Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working. [2]
2. List the activities that must be happening on day 20. [2]
3. Comment on your answer to part (e) with regard to the lower bound you found in part (d). [1]
4. Schedule the activities, using the minimum number of workers, so that the project is completed in 30 days. [3]

(Total 15 marks)

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]