Question

For a construction project, the project team has come up with the following set of activities with their durations and costs $($see Table below$).$ For simplicity, the crash cost of the activities per day is assumed to be linear. The indirect cost is $$48k$ per day.

$\backslash$table$[[$Activity$,$IPA,$\backslash$table$[[$Normal Duration$],[($Days$)]],\backslash$table$[[$Normal Direct$],[$Cost $($k$)]],\backslash$table$[[$Crash Duration$],[($Days$)]],\backslash$table$[[$Crash Direct$],[$Cost $($k$)]]],[$A$,-,7,140,6,210],[$B$,-,5,100,5,100],[$C$,$A$,3,90,2,140],[$D$,$A$,5,100,3,130],[$E$,$A$,5,60,4,100],[$F$,$C$,4,120,3,140],[$G$,$D$,$ F$,6,180,4,240],[$H$,$E$,7,150,5,200],[$J$,$B$,2,40,2,40],[$K$,$E$,$ J$,5,120,4,160],[$L$,$G$,$ H$,$ K$,4,80,4,80],[$M$,$E$,$ J$,8,180,5,240]]$

Using the information provided in the table, please:

a$.$ Draw the Activity$-$On$-$Arrow $($AOA$)$ network diagram $(30$ marks$)$

b$.$ Identify the critical path $($or critical paths$)(5$ marks$)$

c$.$ Calculate the total duration and the total cost of the project $(5$ marks$)$

d$.$ Calculate the total float time of each non$-$critical activity $(5$ marks$)$

If the project team wants to shorten the project duration by two days, please:

a$.$ For each day of shortening of the project, determine the activity $($or activities$)$ that would be the most appropriate to crash for the optimal cost effectiveness of the project; and re$-$calculate the total cost of the project after each day of shortening. $(40$ marks$)$

b$.$ Draw the AOA network diagram after the two$-$day crash. $(10$ marks$)$

c$.$ Identify the critical path $($or critical paths$)$ of the AOA network diagram after the two$-$day crash. $(5$ marks$)$For a construction project, the project team has come up with the following set of activities with their

durations and costs $($see Table below$).$ For simplicity, the crash cost of the activities per day is

assumed to be linear. The indirect cost is $$48$k per day.

Activity IPA Normal Duration

$($Days$)$

Normal Direct

Cost $($k$)$

Crash Duration

$($Days$)$

Crash Direct

Cost $($k$)$

A $-71406210$

B $-51005100$

C A $3902140$

D A $51003130$

E A $5604100$

F C $41203140$

G D$,$ F $61804240$

H E $71505200$

J B $240240$

K E$,$ J $51204160$

L G$,$ H$,$ K $480480$

M E$,$ J $81805240$

$1.$ Using the information provided in the table, please:

a$.$ Draw the Activity$-$On$-$Arrow $($AOA$)$ network diagram $(30$ marks$)$

b$.$ Identify the critical path $($or critical paths$)(5$ marks$)$

c$.$ Calculate the total duration and the total cost of the project $(5$ marks$)$

d$.$ Calculate the total float time of each non$-$critical activity $(5$ marks$)$