Problem $1$: Given the information provided below $($predecessors$,$ normal time, normal cost, crash time $($the minimum duration$)$ and crash cost $($the cost if crashed to the minimum duration$)$ for an nine$-$activity $($a to i$)$ project$)$ answer the questions $($a$)$ through $($e$)$ using this template. You need to provide enough explanations to show evidence that you have understood this topic.

Activity Predecessor Normal Time Normal Cost Crash Time Crash Cost

a $-4$ $ $502$ $ $150$

b a $4$ $ $402$ $ $200$

c b $7$ $ $704$ $ $160$

d c$,$ f $2$ $ $201$ $ $50$

e c $3$ $ $302$ $ $100$

f b $8$ $ $805$ $ $290$

g d$,$ e $5$ $ $503$ $ $100$

h f $6$ $ $602$ $ $180$

i g$,$ h $3$ $ $503$ $ $50$

$($a$).$ Create the network diagram in the application of your choice and then insert a screen shot of the diagram here. The diagram can be created easily in MS Word using the Insert Shapes function.

$[$a$]$

$|$

$[$b$]$

$|$

$[$c$]------[$e$]$

$||$

$[$f$]-------|$

$||$

$[$d$]------[$g$]$

$|$

$[$h$]$

$|$

$[$i$]$

Identify the critical path of the network, the time, and cost of the normal level of activity for the project:

$$ The critical path $($or paths$)$ is:

Path $1$: a $->$ b $->$ c $->$ d $->$ g $->$ i

Duration: $4+4+7+2+5+3=25$ days

Path $2$: a $->$ b $->$ c $->$ e $->$ g $->$ i

Duration: $4+4+7+3+5+3=26$ days

Path $3$: a $->$ b $->$ f $->$ d $->$ g $->$ i

Duration: $4+4+8+2+5+3=26$ days

Path $4$: a $->$ b $->$ f $->$ h $->$ i

Duration: $4+4+8+6+3=25$ days

The critical path is Path $2$ and Path $3$:

Critical Paths: a $->$ b $->$ c $->$ e $->$ g $->$ i and a $->$ b $->$ f $->$ d $->$ g $->$ i

$$ The project duration: $26$ days

$$ The project cost is: $$450$

The normal project cost is calculated by summing the normal costs of all activities: $50+40+70+20+30+80+50+60+50=450$

$($b$).$ Calculate the crash cost$-$per$-$day $($all activities may be partially crashed$).$ Enter your response to question $1($b$)$ in the table provided below

Activity Normal Time Normal Cost Crash Time Crash Cost Crash Cost$/$Day$1$

a $4$ $$502$ $$150(15050)/(42)=50$

b $4$ $$402$ $$200(20040)/(42)=80$

c $7$ $$704$ $$160(16070)/(74)=30$

d $2$ $$201$ $$50(5020)/(21)=30$

e $3$ $$302$ $$100(10030)/(32)=70$

$1$ Assume that each task$$s crash costs are linear, ie that each day a task is crashed has an equal cost.

PMAN$635$

Project Cost, Schedule, and Resource Management

f $8$ $$805$ $$290(29080)/(85)=70$

g $5$ $$503$ $$100(10050)/(53)=25$

h $6$ $$602$ $$180(18060)/(62)=30$

i $3$ $$503$ $$50000($Cannot be crashed$)$

$($c$).$ Find the optimal way to crash the project by one day.

To crash the project by one day, we should choose the least expensive option along the critical path:

Path $2$: a $->$ b $->$ c $->$ e $->$ g $->$ i

Crashing options: e$,$ c$,$ b$,$ a

Least cost: Crashing c or d $($$$30/$day$)$

Path $3$: a $->$ b $->$ f $->$ d $->$ g $->$ i

Crashing options: f$,$ d$,$ b$,$ a

Least cost: Crashing c or d $($$$30/$day$)$

$$ What is the projected project cost?

$$ What is the projected project duration?

$$ What is the critical path $($or paths$)?$

$$ What task or tasks were crashed?

Explain the results of your calculations.

$($d$).$ Find the optimal way to crash the project by two days.

$$ What is the projected project cost?

$$ What is the projected project duration?

$$ What is the critical path $($or paths$)?$

$$ What task or tasks were crashed?

Explain the results of your calculations.

$($e$).$ Calculate the shortest completion time for the project.

$$ What is the projected project cost?

$$ What is the projected project duration?

$$ What is the critical path $($or paths$)?$

$$ What task or tasks were crashed?

Explain the results of your calculations.