Question

Pirmin's bike shop is behind on a custom bike and needs to crash 8 hours of...

Pirmin's bike shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project. Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash.

Activity

Normal

Duration (hr)

Normal

Cost ($)

Crash

Duration (hr)

Crash

Cost ($)

Immediate

Predecessors

A 2 10 2 N/A NONE
B 3 15 2 23 A
C 5 25 4 30 B
D 3 20 1 24 C
E 6 30 4 45 C
F 1 5 1 N/A C,E
G 7 35 6 50 F
H 10 50 7 80 D,G

A. Draw (with a computer application) the network diagram.

B. Calculate the maximum time-savings available on a $25 crash budget.

C. Calculate the cost to crash four hours of savings.

Homework Answers

Answer #1

The project network is as follows:

The network consists of 3 paths as follows:

A-B-C-D-H, duration is 23 days

A-B-C-F-G-H, duration is 28 days

A-B-C-E-F-G-H, duration is 34 days

Determine crashing cost per hour as follows:

Normal Duration (Hr.)

Normal Cost

Crash Duration

Crash Cost

Allowable crashing

Crashing cost per hour

Activity

NT

NC

CT

CC

CC - NC

NT - CT

(CC - NC)/(NT - CT)

A

2

$10

2

NA

$0

0

$0

B

3

$15

2

$23

$8

1

$8

C

5

$25

4

$30

$5

1

$5

D

3

$20

1

$24

$4

2

$2

E

6

$30

4

$45

$15

2

$7.5

F

1

$5

1

NA

$0

0

$0

G

7

$35

6

$50

$15

1

$15

H

10

$50

7

$80

$30

3

$10

TOTALS

$190

Crashing Sequence:

According to crashing principle, crash only critical path and crash the critical activities with lowest crashing cost per hour.

Crashing Sequence

0

1

2

3

4

Critical Paths

A-B-C-E-F-G-H

A-B-C-E-F-G-H

A-B-C-E-F-G-H

A-B-C-E-F-G-H

Lowest crashing cost per week activity (crashing cost)

C ($5/ hour)

E ($7.5/ hr)

E ($7.5/ hr)

B ($8/ hr)

Activity Crashed

None

C

E

E

B

Crashing Duration

0

1

1

1

1

Project duration

34

33

32

31

30

A-B-C-D-H

23

22

22

22

21

A-B-C-F-G-H

28

27

28

28

27

A-B-C-E-F-G-H

34

33

32

31

30

Crash cost

$0

$5

$7.5

$7.5

$8

Cum. Crash cost

$0

$5

$12.5

$20

$28

b.

Crashing activity B by 1 hour, the cumulative crashing cost is increases to $28. To obtain duration for $25 cumulative crashing cost, crash the activity B by fraction of hour. For $25 cost, crash duration = $5/$8 = 0.625 hours.

Thus, if the activity B is crashed by 0.625 hours the cost will increase by $5.

Total project duration will be 30.625 hours.

Maximum time saved for $25 crash budget = 34 hours – 30.625 hours = 3.375 hours

c.

To save four hours or to complete the project in 34 – 4 = 30 hours, the cumulative crash cost is $28. It requires to crash activities C, E, and B by 1, 2 and 1 hours respectively.

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