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.

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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