Chapter $16$

Use the information provided in the Table $1$ and the network diagram in Figure $1$ for the following problems.

Activity Normal Time$($weeks$)$ Normal Cost $($$$)$ Crash Time $($weeks$)$ Crash Cost $($$$)$ Maximum weeks Reduced Crash Cost per Week $($$$)$

A $455039502450$

B $565047502150$

C $7850413504550$

D $71550522003100$

E $71800523003550$

F $62506125011050$

G $81550618503350$

$1.$ Using the informatiChapter $16$

Use the information provided in the Table $1$ and the network diagram in Figure $1$ for the following problems.

Activity Normal Time$($weeks$)$ Normal Cost $($$$)$ Crash Time $($weeks$)$ Crash Cost $($$$)$ Maximum weeks Reduced Crash Cost per Week $($$$)$

A $455039502450$

B $565047502150$

C $7850413504550$

D $71550522003100$

E $71800523003550$

F $62506125011050$

G $81550618503350$

$1.$ Using the information given,

$**$Ideology for Problem $1$ is sourced from textbook page $586,$ Table $16\mathrm{.}6($Reid and Sanders, $2023).**$

o Calculate the completion time of the project.

Path $1$: A$-$B$-$E$-$G$-$H $=4+3+5+4+3=19$ weeks

Path $2$: A$-$C$-$E$-$G$-$H $=4+5+5+4+3=21$ weeks

Path $3$: A$-$C$-$F$-$G$-$H $=4+5+6+4+3=22$ weeks

Path $4$: A$-$D$-$F$-$G$-$H $=4+2+6+4+3=19$ weeks

Completion Time $=($longest production path$)=22$ weeks

o Identify the activities on the critical path.

Activities on the Critical Path $=$ A$,$C$,$F$,$G$,$H

$2.$ Using the information given and the project completion time calculated in Problem $1,$ reduce the completion time of the project $3$ weeks in the most economical way.

The least expensive critical path activity to crash is activity G$.$ Based on the above table, we can crash activity G for a maximum of $3$ weeks at a cost of $$350$ per week.

Total Crash Cost to reduce time of project completion by $3$ weeks $=$ $$350*3$ weeks $=$ $$1,050$

$3.$ Using the information given and the project completion time calculated in Problem $1,$ calculate the minimum time for completing the project possible.on given,

$**$Ideology for Problem $1$ is sourced from textbook page $586,$ Table $16\mathrm{.}6($Reid and Sanders, $2023).**$

o Calculate the completion time of the project.

Path $1$: A$-$B$-$E$-$G$-$H $=4+3+5+4+3=19$ weeks

Path $2$: A$-$C$-$E$-$G$-$H $=4+5+5+4+3=21$ weeks

Path $3$: A$-$C$-$F$-$G$-$H $=4+5+6+4+3=22$ weeks

Path $4$: A$-$D$-$F$-$G$-$H $=4+2+6+4+3=19$ weeks

Completion Time $=($longest production path$)=22$ weeks

o Identify the activities on the critical path.

Activities on the Critical Path $=$ A$,$C$,$F$,$G$,$H

$2.$ Using the information given and the project completion time calculated in Problem $1,$ reduce the completion time of the project $3$ weeks in the most economical way.

The least expensive critical path activity to crash is activity G$.$ Based on the above table, we can crash activity G for a maximum of $3$ weeks at a cost of $$350$ per week.

Total Crash Cost to reduce time of project completion by $3$ weeks $=$ $$350*3$ weeks $=$ $$1,050$

$3.$ Using the information given and the project completion time calculated in Problem $1,$ calculate the minimum time for completing the project possible.