2) The company decided that the project in the previous problem has to be expedi
ID: 363320 • Letter: 2
Question
2) The company decided that the project in the previous problem has to be expedited in order to optimize (minimize) the project cost. Expediting can be used to trade direct cost for indirect cost, since expediting the project reduces the indirect cost of the project by a fixed amount per day, while expediting an activity increases its total direct cost. The Accounting Department found that indirect costs amount to $100 per day, while activity direct costs as well as their normal and expedited times are given in the table below.
Activity
Normal
Time
(days)
Expedited
Time
(days)
Normal
Cost
($)
Expedited
Cost
($)
A
32
26
200
500
B
21
20
300
375
C
30
30
200
200
D
45
40
200
800
E
26
20
700
1,360
F
28
24
1,000
1,160
G
20
18
400
550
From this table you can compute the direct cost incurred by expediting an activity by one day.
Answer the following questions:
2.1) (25 points) What is the optimal time to complete the project?
2.2) (25 points) What is the optimal project cost?
Activity
Normal
Time
(days)
Expedited
Time
(days)
Normal
Cost
($)
Expedited
Cost
($)
A
32
26
200
500
B
21
20
300
375
C
30
30
200
200
D
45
40
200
800
E
26
20
700
1,360
F
28
24
1,000
1,160
G
20
18
400
550
Explanation / Answer
The optimal time to complete the project is 73 days. Consider the following information:
Activity Normal Time (days) Expedited Time (days) Normal Cost ($) Expedited Cost ($) Cost/ day ($)
A 32 26 200 500 50
B 21 20 300 375 75
C 30 30 200 200 -
D 45 40 200 800 120
E 26 20 700 1,360 110
F 28 24 1,000 1,160 40
G 20 18 400 550 75
Cost/day = (Expedited Cost – Normal Cost)/(Normal Time – Expedited Time)
Critical path : AEG : duration = 78
CFG : duration = 78
The company shoudl expedite activity G by 1 day, then the duration becomes 77 days and $75 is added to the total cost of the project. This also adds A-D as a critical path. Next expedite A & E by 2 days each, so the completion time now is 73 days while adding an additional cost of $ 90 per day to the total cost of the project.
The optimal project cost is $ 75 + 90 + 187.5+ 646.15+ 380= $1378.65
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