Pirmin's Bike Shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project. Given the project table below calculate the crash cost for 8 hours of time-savings
Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash. Calculate both the maximum time-savings available on a $25 crash budget and the cost to crash four hours of savings.
Activity Normal
Duration (hours) Normal
Cost ($) Crash
Duration (hours) Crash
Cost (S) Immediate
Predecessors
A 2 10 2 0 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 0 C,E
G 7 35 6 50 F
H 10 50 7 80 D,G
The critical path is ABCEFGH with a time of 34 hours. The cost per crash hour for these activities is 8(B), 5(C), 2(D), 7.5(E), 15(G), 10(H). C will be crashed first for a savings of 1 hour. Next E will be crashed for a savings of 2 hours. Then B can be crashed for a savings of 1 hour. Next H will be crashed for a savings of 3 hours, netting 7 hours total at a cost of (5 + 15 + 8 + 30 ) = $58. Only 1 more hour is needed, so G will be crashed for an additional 15 dollars, netting 8 hours saved at a cost of 58 +15 = $73. D was not crashed because it does not lie on the critical path after any amount of crashing (E always > D). With $25 only C and E can be crashed, saving 3 hours of time and spending $20. A fractional component of B could be crashed (5/8 ) of an hour to spend the entire $25, however most students should interpret this question as only whole-hour increments. The cost to crash four hours would be C + E + B crashing = $28.
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