A) what is the project completition date? B) what is the total cost required for
ID: 418077 • Letter: A
Question
A) what is the project completition date? B) what is the total cost required for completing this project on normal time? C) if you wish to reduce the time required to complete this project by 1 week, which activity should be crashed, and how much will this increase the total cost? D) what is the maximum time that can be crashed? of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table: Total Cost Normal Time Crash Time Normal with sor(s) Activity (weeks) (weeks) Cost Crashing Immediate 3 $2,100 $2,800 $2,100 $2,700 $750 $750 $2,400 $2,720 1,000 1,300 $3,000 $4,400 $1,600 $2200 D, E a) Based on the given information regarding the activities for the project, the project length-weeks.Explanation / Answer
Project crashing
Activity
Normal time
Crash time
Normal cost
Crash cost
cost increase
number of weeks got by crashing,
crash cost per week
=crash cost -normal cost
Nc =normal time-crash time
=crash increase /Nc
A
4
3
2100
2800
700
1
700
B
2
1
2100
2700
600
1
600
C
3
3
750
750
0
0
0
D
8
4
2400
2720
320
4
80
E
6
3
1000
1300
300
3
100
F
3
2
1300
4400
3100
1
3100
G
4
2
1600
2200
600
2
300
11250
5620
A) what is the project completition date?
The project comp0letetion depends on the path with the longest duration – the critical path
A-> D-> G = 4+8+4 =16
B->E->G =2+6+4= 12
C->F = 3+3 =6
ADG is the critical path. Project duration- duration of critical path=16 weeks
B) what is the total cost required for completing this project on normal time?
Cost(normal time) = 2100+2100 + 750+2400+1000+3000+1600= $5620
C) if you wish to reduce the time required to complete this project by 1 week, which activity should be crashed, and how much will this increase the total cost?
The crash sequence will start with the cheapest unit-crash-cost item. Then we will progress to the most expensive unit-crash cost item
So, from the table above the cheapest unit-crash-cost item is D and is crashed first for 1 week
Note
For getting 4 weeks advance in activity D , we have to spend additional 320 in addition to normal cost(2720-2400)
Hence for 1 additional week of crashing ,we spend 320/4= $80 per week
D) what is the maximum time that can be crashed? How much would costs increase?
The crash sequence will start with the cheapest unit-crash-cost item. Then we will progress to the most expensive unit-crash cost item
Step 1
So we first crash D now duration of ADG IS 12 WEEKS .
Now,
A->D-> G = 4+4+4 =10
B->E->G =2+6+4= 10
C->F = 3+3 =6
ADG and BEG both are critical paths now.
Additional cost for crashing D for 4 weeks=4 *80= $ 320
Step 2
In the next stage of crashing, it is impossible to crash one activity alone and achieve a reduction in the overall project duration. So we use combination of activities from each path to achieve an equal reduction
The combination that gives the least cost per week is chosen first and then we progress. So we choose G to carsh
A+B cost a total of 700+600 =1300, for crashing per week
A +E cost a total of 700+100=$800 , for crashing per week
G costs 300 per week
G is the lowest . so we choose G for crashing, next
Now
A-> D-> G = 4+4+2 =10
B->E->G =2+6+2= 10
C->F = 3+3 =6
Additional cost for crashing G for 2 weeks=2 *300= $ 600
Cost increase up to this stage = 320+600=$920
Step 3
Now the remaining combinations are
We crash the lowest of these we choose A+E
Now A can be crashed by only one more week, and E can be crashed by three weeks.
We chose the minimal of two so that we reduce the total duration of the two critical paths equally. So we crash both A and E for 1 week
Now
A-> D-> G = 3+4+2 =9
B->E->G =2+5+2= 9
C->F = 3+3 =6
Additional cost for crashing A for 1 week=1 *700= $ 700
Additional cost for crashing E for 1 week=1 *100= $ 100
Cost increase up to this stage = 320+600+ (700+100)=$1720
We have reached the crash limit for the critical path ADG. No further crashing is possible in this path.
There is no use of crashing activities other paths because anyway it will take 9 weeks for ADG.
Hence we stop here.
So the maximum time that can be crashed is 16-9=7 weeks
Cost increase=$1720
Project crashing
Activity
Normal time
Crash time
Normal cost
Crash cost
cost increase
number of weeks got by crashing,
crash cost per week
=crash cost -normal cost
Nc =normal time-crash time
=crash increase /Nc
A
4
3
2100
2800
700
1
700
B
2
1
2100
2700
600
1
600
C
3
3
750
750
0
0
0
D
8
4
2400
2720
320
4
80
E
6
3
1000
1300
300
3
100
F
3
2
1300
4400
3100
1
3100
G
4
2
1600
2200
600
2
300
11250
5620
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