Constructing PERT Charts

In a PERT chart, task A has an earliest start time of $\displaystyle 0$ and a duration of $\displaystyle 4$ days.
Task B follows task A and has a duration of $\displaystyle 6$ days.
Calculate the earliest start time of task B.

Task E cannot begin until both task C and task D are complete.
Task C has an earliest start time of $\displaystyle 12$ days and a duration of $\displaystyle 5$ days.
Task D has an earliest start time of $\displaystyle 9$ days and a duration of $\displaystyle 6$ days.
Calculate the earliest start time of task E.

Task B must be finished before both task C and task D can begin.
Task C has a duration of $\displaystyle 4$ days and a latest end time of $\displaystyle 20$ days.
Task D has a duration of $\displaystyle 5$ days and a latest end time of $\displaystyle 22$ days.
Calculate the latest end time of task B.

State the three values recorded in each node of a PERT chart.

Explain why the forward scan takes the maximum value when a task has more than one preceding task.

Explain why the backward scan takes the minimum value when a task is followed by more than one task.

A project has the following tasks.
A: no preceding task, $\displaystyle 5$ days
B: preceded by A, $\displaystyle 7$ days
C: preceded by A, $\displaystyle 3$ days
D: preceded by B and C, $\displaystyle 4$ days
Carry out a forward scan to find the earliest start time of each task, and state the earliest completion time of the project.

A company provides a team of workers to re-roof a house.

The table shows the list of tasks required to complete this job, the time required for each task, and the order in which the tasks are to be completed.

Task	Description	Preceding task	Time (hours)
A	Transport materials to location	None	3
B	Construct scaffolding	A	7
C	Remove old tiles	B	4
D	Take old tiles to recycling site	C	1
E	Inspect roofing	C	2
F	Purchase required number of roof tiles	D	1
G	Replace roofing felt	E	4
H	Replace roofing tiles	F, G	6
I	Remove scaffolding	H	3
J	Clean up	H	2

(a) Complete the PERT chart showing the earliest start time and the latest completion time for each task.

(b) The roofing company works for 9 hours each day on this job. State the minimum number of days that the company will require to complete this job.

(c) Construct a Gantt chart, without float times, for this job.

In a cooking competition, a contestant has 80 minutes to make a crème brûlée.

There are several tasks that need to be completed to make the crème brûlée. The contestant's timings for each task are shown.

Task	Description	Preceding task	Time (minutes)
A	heat oven	none	8
B	gather ingredients and prepare bowls	none	10
C	whisk egg yolks and sugar	B	5
D	heat double cream in pan	B	4
E	add cream to egg yolk mixture	C, D	2
F	sieve mixture and put into bowls	E	4
G	put bowls into oven and cook	A, F	35
H	tidy workspace	F	12
I	sprinkle caster sugar over each bowl and caramelise	G	3
J	plate up and serve	I	5

(a) Complete the PERT chart below to allow the contestant to determine the earliest start time and latest completion time for each task.

When the contestant puts the bowls into the oven, they realise the oven has not been heated.

(b) Determine whether they can still finish on time. Give a reason for your answer.

A ship is being repaired. The propeller must be removed for the repair to be carried out. The table shows the list of tasks required to complete this job, the time required for each task, and the order in which the tasks must be completed.

Task	Description	Preceding task	Duration (hours)
A	Disconnect electrics	none	2
B	Remove oils from system	A	12
C	Remove rudder	A	24
D	Disconnect oil pipes and hoses	A	8
E	Prepare oil pipes and hoses to be reconnected	D	4
F	Remove propeller blades	B, C, E	14
G	Disconnect propeller stern seals	B, C, E	12
H	Disconnect propeller shaft coupling	B, C, E	8
I	Remove propeller shaft coupling and internal pipes	F, G, H	6
J	Take out propeller shaft	I	8

(a) Complete the PERT chart showing the earliest start time and the latest completion time for each task.

(b) Construct a Gantt chart without float times for this job.

(c) Determine the critical path and the minimum time required to complete the job.

During the job there are difficulties disconnecting the propeller shaft coupling (task H).

(d) Determine the maximum time that can be taken to disconnect the propeller shaft coupling without delaying the total completion time of the job.