smc-6916-10-Precedence Tables

Networks, STD2 N3 EQ-Bank 30

A project involves nine activities, `A` to `I`.

The immediate predecessor(s) of each activity is shown in the table below.

\begin{array} {|c|c|}
\hline \ \ \textbf{Activity}\ \ & \textbf{Immediate} \\ & \textbf{predecessor(s)} \\
\hline \rule{0pt}{2.5ex} A \rule[-1ex]{0pt}{0pt} & - \\
\hline \rule{0pt}{2.5ex} B \rule[-1ex]{0pt}{0pt} & A \\
\hline \rule{0pt}{2.5ex} C \rule[-1ex]{0pt}{0pt} & A \\
\hline \rule{0pt}{2.5ex} D \rule[-1ex]{0pt}{0pt} & B \\
\hline \rule{0pt}{2.5ex} E \rule[-1ex]{0pt}{0pt} & B, C \\
\hline \rule{0pt}{2.5ex} F \rule[-1ex]{0pt}{0pt} & D \\
\hline \rule{0pt}{2.5ex} G \rule[-1ex]{0pt}{0pt} & D \\
\hline \rule{0pt}{2.5ex} H \rule[-1ex]{0pt}{0pt} & E, F \\
\hline \rule{0pt}{2.5ex} I \rule[-1ex]{0pt}{0pt} & G, H \\
\hline \end{array}

A directed network for this project will require a dummy activity.

Sketch the network diagram, clearly identifying the dummy activity. (3 marks)

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Show Worked Solution

`text(Sketch network diagram:)`

`text(The dummy activity needs to be drawn)`

`text(from the end of activity)\ B\ text(to the start)`

`text(of activity)\ E.`

Networks, STD2 N3 2019 HSC 26

A project requires activities `A` to `F` to be completed. The activity chart shows the immediate prerequisite(s) and duration for each activity.

By drawing a network diagram, determine the minimum time for the project to be completed. (3 marks)

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Determine the float time of the non-critical activity. (1 mark)

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a. `text(15 hours)`

b. `text(3 hours)`

Show Worked Solution

`text(Scanning forwards:)`

`text(Minimum time = 2 + 6 + 2 + 4 + 1 = 15 hours)`

`text{(Scanning forwards and backwards is highly recommended but not}`

`text{required in the network diagram.)}`

b. `text(Critical Path is)\ ABDEF.`

♦♦ Mean mark 30%.

`text(Non-critical activity is)\ C.`

`text(Float time)=5-2=3\ text(hours)`

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.

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

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

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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.

Sketch the network diagram. (3 marks)

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

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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 EQ-Bank 32

An engineering project requires activities `A` to `G` to be completed, as shown in the table.

The minimum completion time for the project is 25 days and the critical path includes activities `B, D, E` and `F`. The float for activity `G` is two days and the float for activity `C` is four days.

Find the possible duration for each of the activities `A, C, F` and `G`. Include a network diagram in your answer. (5 marks)

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`text(Duration of)\ F = 1\ text(day)`

`text(Duration of)\ G = 4\ text(days)`

`text(*Understand why there are many possibilities for the duration of)`

`A and C, text(provided they add up to 20 days and)\ A\ text(is not longer)`

`text{than 7 days (or a new critical path is created)}.`

Show Worked Solution

`text(Sketch the network:)`

`text{Critical path information included in the network (where EST = LST)}`

`F\ text(is on critical path)rightarrow text(no float)`

`:.\ text(Duration of)\ F= 25-24 = 1\ text(day)`

`text(Duration of)\ G`	`=\ text(LST of next activity − EST of)\ G-text(float)`
	`= 25-19-2= 4\ text(days)`

`text(The float of)\ C\ text{is 4 days (given)}`

`:.\ text(Duration of)\ C`	`=\ text(LST of)\ F-text(EST of)\ C-4`
	`= 24-text(EST of)\ C-4`
	`= 20-text(EST of)\ C`

`text(EST of)\ C =\ text(Duration of)\ A\ \ (A\ text(has no prerequisites))`

`=>\ text(Duration of)\ A +\ text(Duration of)\ C = 20\ text(days)`

`:.\ text(Possible durations of)\ A\ text(and)\ C\ text(are:)`

`A = 5\ text(days), C = 15\ text(days)`

`text(*Understand why there are many possibilities for the duration of)`

`A and C, text(provided they add up to 20 days and)\ A\ text(is not longer)`

`text{than 7 days (or a new critical path is created)}.`

Networks, STD2 N3 EQ-Bank 31

An engineering project requires activities `A` to `G` to be completed, as shown in the table.

The minimum completion time for the project is 40 weeks and the critical path includes activities `A, C, E` and `G`. The float for activity `F` is six weeks and the float for activity `D` is 9 weeks.

Find the possible duration for each of the activities `B, D, F` and `G`. Include a network diagram in your answer. (5 marks)

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`text(Duration of)\ G = 3\ text(weeks)`

`text(Duration of)\ F = 9\ text(weeks)`

`text(There are many possibilities for the duration of)\ B and D`

`text(provided they add up to 28 weeks and)\ B\ text(is not longer)`

`text{than 10 weeks (new critical path)}.`

Show Worked Solution

`text(Sketch network:)`

`text{Critical path added to network (where EST = LST)}`

`G\ text(is on critical path ⇒ no float)`

`:.\ text(Duration of)\ G = 40-37 = 3\ text(weeks)`

`text(Duration of)\ F`	`=40- text(EST of)\ F-text(float)`
	`= 40-25-6= 9\ text(weeks)`

`text(Float of)\ D = 9\ text{weeks (given)}`

`:.\ text(Duration of)\ D`	`=\ text(LST of)\ G-\ text(EST of)\ D-9`
	`= 37-\ text(EST of)\ D-9`
	`= 28-\ text(EST of)\ D`

`text(EST of)\ D =\ text(Duration of)\ B\ \ \ (B\ text(has no prerequisites))`

`text(Duration of)\ B +\ text(Duration of)\ D = 28\ text(weeks)`

`:.\ text(Possible durations of)\ B\ text(and)\ D\ text(are:)`

`B = 1\ text(week), D = 27\ text(weeks)`

`text(*Understand why there are many possibilities for the duration of)`

`B and D, text(provided they add up to 28 weeks and)\ B\ text(is not longer)`

`text{than 10 weeks (or a new critical path is created)}.`

Networks, STD2 N3 2006 FUR2 3

The five musicians are to record an album. This will involve nine activities.

The activities and their immediate predecessors are shown in the following table.

The duration of each activity is not yet known.

Use the information in the table above to complete the network below by including activities `G`, `H` and `I`. (2 marks)

There is only one critical path for this project.

How many non-critical activities are there? (1 mark)

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

Write down the critical path for this project. (1 mark)

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The minimum time required for this project to be completed is 19 hours.

What is the duration of activity `I`? (1 mark)

The duration of activity `C` is 3 hours.

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Determine the maximum combined duration of activities ` F` and `H`. (1 mark)
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b. `5`

c. `B E G I`

d. `text(7 hours)`

e. `text(8 hours)`

Show Worked Solution

b. `text(S)text(ince no time information, possible critical paths are:)`

`ADGI, BEGI\ text(or)\ CFHI\ \ text{(all have 4 activities)}`

`:.\ text(Non-critical activities)= 9-4 = 5`

c. `text(Critical activities have zero float time.)`

♦ Mean mark of parts (c)-(e) (combined) was 36%.

`=> A\ text(and)\ C\ text(are non-critical.)`

`:. B E G I\ text(is the critical path.)`

d. `text(Duration of)\ \ I= 19-12= 7\ text(hours)`

e. `text(Maximum time for)\ F\ text(and)\ H`

♦♦ MARKER’S COMMENT: Many students incorrectly answered 9 hours in part (e).

`=\ text(LST of)\ I–text(duration)\ C – text(slack time of)\ C`

`= 12-3-1= 8\ text(hours)`

Networks, STD2 N3 2011 FUR1 7 MC

Andy, Brian and Caleb must complete three activities in total (K, L and M)

The table shows the person selected to complete each activity, the time it will take to complete the activity in minutes and the immediate predecessor for each activity.

\begin{array}{|l|c|c|c|}
\hline
\textbf{Person} & \textbf{Activity} & \textbf{Duration} & \textbf{Immediate predecessor} \\
\hline
\text{Andy} & K & 13 & - \\
\hline
\text{Brian} & L & 5 & K \\
\hline
\text{Caleb} & M & 16 & L \\
\hline
\end{array}

All three activities must be completed in a total of 40 minutes.

The instant that Andy starts his activity, Caleb gets a telephone call.

The maximum time, in minutes, that Caleb can speak on the telephone before he must start his allocated activity is

`5`
`13`
`18`
`24`

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`D`

Show Worked Solution

`text(Maximum speaking time on phone)`

♦♦ Mean mark 33%.
MARKER’S COMMENT: Many students incorrectly answered the earliest starting time, C.

`= 40-text(duration of)\ M`

`= 40-16= 24\ text(minutes)`

`=> D`

Networks, STD2 N3 2015 FUR1 9 MC

The table below shows, in minutes, the duration, the earliest starting time (EST) and the latest starting time (LST) of eight activities needed to complete a project.