Supplemental Problem 2 Your company has signed a contract to complete a specific
ID: 450636 • Letter: S
Question
Supplemental Problem 2
Your company has signed a contract to complete a specific project for a customer. The normal completion time for each task is shown on the nodes in the following network diagram. Later, the customer wanted the project sooner than the initially agreed upon time. The normal cost, the crash time and crash cost are given in the table below:
Activity
Normal Time
Normal Cost
Crash Time
Crash Cost
(days)
(days)
A
7
$1,000
5
$1,400
B
7
1,400
6
1,450
C
8
2,000
5
2,450
D
8
1,200
7
1,400
E
6
900
3
1,800
F
6
2,500
5
2,600
G
4
1,800
2
2,400
H
3
1,300
2
1,500
I
6
600
5
950
a. Determine the critical path and the normal completion time of the project.
b. What is the total normal completion cost for the project?
c. Suppose the customer requests that the project be completed one day sooner.
Which activities would you not consider to crash and why?
d. Now, suppose that the customer would like the project completed four days sooner than the normal completion time.
(i) Identify the activities that you would crash, and
(i) Indicate the cost of crashing each activity.
Activity
Normal Time
Normal Cost
Crash Time
Crash Cost
(days)
(days)
A
7
$1,000
5
$1,400
B
7
1,400
6
1,450
C
8
2,000
5
2,450
D
8
1,200
7
1,400
E
6
900
3
1,800
F
6
2,500
5
2,600
G
4
1,800
2
2,400
H
3
1,300
2
1,500
I
6
600
5
950
Explanation / Answer
Answer: Activity Normal Time Normal Cost Crash Time Crash Cost Cost slope (days) (days) A 7 $1,000 5 $1,400 $400 B 7 1,400 6 1,450 C 8 2,000 5 2,450 D 8 1,200 7 1,400 200 E 6 900 3 1,800 F 6 2,500 5 2,600 G 4 1,800 2 2,400 600 H 3 1,300 2 1,500 I 6 600 5 950 350 The various paths are: Time ADGI 25 BEGI 23 BEHI 22 CFHI 23 The critical path is ADGI. Total normal cost of completition is = $12,700 Normal time to complete = 25 days if the project is crashed by one day Then the time = 24 days If the project is to be crashed by one day then : the activity G should be crashed by one day: So the cost of crash = $600 Therefore toal cost after crashing = $13,300 If the project is to be crashed by 4 days then : the activity ADGI should be crashed by one day: So the cost of crash = $1,550 Therefore toal cost after crashing = $14,250
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