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Networks, STD2 N3 2024 HSC 39

A project involving nine activities is shown in the network diagram.

The duration of each activity is not yet known.
 

The following table gives the earliest start time (EST) and latest start time (LST) for three of the activities. All times are in hours.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Activity} \rule[-1ex]{0pt}{0pt} & EST & LST \\
\hline
\rule{0pt}{2.5ex} A \rule[-1ex]{0pt}{0pt} & \ \ \ \ \ \ 0\ \ \ \ \ \  & \ \ \ \ \ \ 2\ \ \ \ \ \  \\
\hline
\rule{0pt}{2.5ex} C \rule[-1ex]{0pt}{0pt} & 0 & 1 \\
\hline
\rule{0pt}{2.5ex} I \rule[-1ex]{0pt}{0pt} & 12 & 12 \\
\hline
\end{array}

  1. What is the critical path?   (1 mark)
  2. The minimum time required for this project to be completed is 19 hours.
  3. What is the duration of activity \(I\)?   (1 mark)

  4. The duration of activity \(C\) is 3 hours.
  5. What is the maximum amount of time that could occur between the start of activity \(F\) and the end of activity \(H\)?   (1 mark)

Show Answers Only

a.   \(\text{Critical Path:}\ BEGI\)

b.   \(\text{Duration of}\ I =7\ \text{hours}\)

c.  \(\text{Max time}\ =8\ \text{hours}\)

Show Worked Solution

a.   \(\text{Activity}\ A\ \text{and}\ C: \ LST \gt EST\)

\(\Rightarrow\ \text{Activity}\ A\ \text{and}\ C\ \text{not on critical path.}\)

\(\text{Critical Path:}\ BEGI\)
 

♦ Mean mark (a) 43%.

b.   \(\text{Duration of}\ I = 19-12=7\ \text{hours}\)
 

c.   \(\text{Since}\ C + F + H + I\ \text{is not a critical path:}\)

\(C + F + H + I = 18\ \text{or less (C.P. = 19 hours)}\)

\(3+F+H+7 = 18\ \text{or less}\)

\(\Rightarrow\ F+H = 8\ \text{or less}\)

\(\therefore\ \text{Max time from start of}\ F\ \text{to end of}\ H = 8\ \text{hours}\)

♦♦♦ Mean mark (c) 10%.

Networks, STD2 N3 2021 FUR1 6

The directed graph below shows the sequence of activities required to complete a project.

The time taken to complete each activity, in hours, is also shown.
 

The minimum completion time for this project is 18 hours.

The time taken to complete activity `E` is labelled  `x`.

What is the maximum value of  `x`?   (2 marks)

Show Answers Only

`text(3 hours)`

Show Worked Solution

`text{Consider all possible network paths:}`

`ADHJ \ -> \ text{18 hours}`

`BEJ \ -> \ (12 + x) \ text{hours}`

`CGFEJ \ -> \  (15 + x) \ text{hours}`

`CGIJ \ -> \ text{18 hours}`
 

`text{Minimum completion time = 18 hours}`

`=>\ text{No path can be longer than 18 hours}`

`:. \ x_text{max} = 3 \ text{hours}`

Networks, STD2 N3 2021 HSC 36

A project requires completion of 11 tasks  `A, B, C, . . . , K.`

A network diagram for the project giving the completion time for each task, in minutes, is shown.
 

  1. Find the minimum time to complete the project.   (1 mark)

  2. State the critical path for this project.   (1 mark)

  3. A new task, `X`, is to be added to the project. The earliest starting time for `X` is 17 minutes, the latest starting time for `X` is 18 minutes and `X` has a completion time of 12 minutes.
  4. Add task `X` to the given network diagram above AND state the float time for this task.   (3 marks)

Show Answers Only

a.    `40 \ text{minutes}`

b.    `A – C – D – E – G – J – K`

c.    `text{Float time = 1minute}`

Show Worked Solution
a.    `text{Scanning forwards:}`

♦ Mean mark part (a) 37%.

 


 
`text{Minimum completion time} = 40 \ text{minutes}`
♦ Mean mark part (b) 44%.
 
 
b.   `text{Critical Path:} \ A C D E G J K`
 
 
♦♦ Mean mark part (c) 32%.
c.   
`text{Float time}\ (X)=18-17= 1 \ text{minute}`

Networks, STD2 N3 EQ-Bank 20

A project requires nine activities (A–I) to be completed. The duration, in hours, and the immediate predecessor(s) of each activity are shown in the table below.
 


 

  1. Sketch the network, identifying each activity and its duration.   (2 marks)

  2. Identify the critical path and the minimum completion time of the project.   (2 marks)

Show Answers Only

a. 

 

b.    `text(Critical path is)\ ACFGI.`

`text(20 hours)`

Show Worked Solution

a.    `text(Sketch the network:)`

 

 
b.    `text(Completion time of possible paths:)`

`ABEGI = 4 + 3 + 5 + 4 + 3 = 19\ text(hours)`

`ACFGI = 4 + 7 + 2 + 4 + 3 = 20\ text(hours)`

`ADHI = 4 + 2 + 5 + 3 = 14\ text(hours)`
 

`:.\ text(Critical path is)\ ACFGI.`

`:.\ text{Minimum completion time  = 20 hours}`

Networks, STD2 N3 EQ-Bank 49

A project requires nine activities (A–I) to be completed. The duration, in hours, and the immediate predecessor(s) of each activity are shown in the table below.


 

  1. Sketch the network diagram.   (3 marks)

  2. Find the minimum completion time for this project, in hours.   (1 mark)

Show Answers Only

a.

b.    `20\ text(hours)`

Show Worked Solution

a.    `text(Sketch the network:)`
 

 
b.    `text(Completion time of paths:)`

`ABEGI = 4 + 3 + 5 + 4 + 3 = 19\ text(hours)`

`ACFGI = 4 + 7 + 2 + 4 + 3 = 20\ text(hours)`

`ADHI = 4 + 2 + 5 + 3 = 14\ text(hours)`
 

`:.\ text{Minimum completion time (critical path) = 20 hours}`

Networks, STD2 N3 2012 FUR1 8 MC

networks-fur1-2012-vcaa-8-mc 
 

Eight activities, `A, B, C, D, E, F, G`  and  `H`, must be completed for a project.

The network above shows these activities and their usual duration in hours.

The duration of each activity can be reduced by one hour.

To complete this project in 16 hours, the minimum number of activities that must be reduced by one hour each is

  1. `1`
  2. `2`
  3. `3`
  4. `4`
Show Answers Only

`C`

Show Worked Solution

`text(Two critical paths)\ AFH\ text(and)\ BCFH => 18\ text(hours)`

♦♦ Mean mark 30%.

`text(Paths)\ AEG\ text(and)\ BCEG => 17\ text(hours)`

`text(Reducing)\ A\ text(and)\ B\ text(by 1 hour each reduces each)`

`text(path above by 1 hour.)`

 

`text(Need to reduce)\ AFH\ text(and)\ BCFH\ text(by 1 hour to 16 hours.)`

`=>\ text(Reducing either)\ F\ text(or)\ H\ text(by 1 hour brings the)`

`text(critical path down to 16 hours.)`

`=> C`

Networks, STD2 N3 2006 FUR1 9 MC

The network below shows the activities and their completion times (in hours) that are needed to complete a project.
 


 

The project is to be optimised by reducing the completion time of one activity only.

This will reduce the completion time of the project by a maximum of

  1. 1 hour 
  2. 3 hours
  3. 4 hours
  4. 5 hours
Show Answers Only

`C`

Show Worked Solution

`text(Scanning forward:)`
 


 

`text(Critical path:)`

♦♦♦ Mean mark 17%.
MARKER’S COMMENT: When choosing an activity to crash, take care that a new critical path is not created.

`=> BDCEHJ\ text{(19 hours)}`
 

`text(Other routes not through)\ B,`

`ACEHJ\ text{(15 hours),}\ AFJ\ text{(14 hours)}`
 

`:.\ text(Activity)\ B\ text(could be reduced by 4 hours without)`

`text(a new critical path emerging.)`
 

`=> C`