6-1 Project Crashing Crashing: shortening duration of activities. Because Some activities were delayed Client is willing to pay more for earlier completion Crashing changes the schedule for remaining activities It has impact on schedules for all the subcontractors Often introduces unanticipated problems The faster an activity is completed, the more it costs There is always a lower bound on task duration 06/10/22 Ardavan Asef-Vaziri 6-1
Project Crashing. Crashing: shortening duration of activities. Because Some activities were delayed Client is willing to pay more for earlier completion Crashing changes the schedule for remaining activities It has impact on schedules for all the subcontractors - PowerPoint PPT Presentation
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6-1
Project Crashing
Crashing: shortening duration of activities. Because Some activities were delayed Client is willing to pay more for earlier completion
Crashing changes the schedule for remaining activities It has impact on schedules for all the subcontractorsOften introduces unanticipated problemsThe faster an activity is completed, the more it costsThere is always a lower bound on task duration
04/21/23 Ardavan Asef-Vaziri 6-1
6-2
Linear Time / Cost Tradeoff
Time
Cost
Crash point
Normal point
Normal time =Crash time =
Normal cost =
Crash cost =
tjNtj
c
Cjc
CjN
Slope (bj) = increase in cost from reducing task duration by one time unit
Time Normal - TimeCrash
Cost Normal -Cost Crash Slope
04/21/23 Ardavan Asef-Vaziri -4
6-3
Crashing Algorithm
Assume each task can be crashed one day at a time (simplifying assumption, but not necessary)
Crash only critical activities. Crashing other activities can only increase cost without changing project duration
To decrease project duration by one day, the critical path or paths must decrease by one day.
1. Find the critical path or paths
2. If there is no other critical activity which could still be reduced, and shorten the critical path. Stop.
3. Crash the cheapest critical activity (or combination of activities) to shorten the critical path (or paths) by one day.
1Activity Predecesor Time(N) Time(C) Cost(N) Cost(C) C/T Left
a - 6 5 60 90 30 1b - 7 4 50 150 33.3 3c a 6 4 100 160 30 2d a 7 7 30 30 - -e b 5 4 70 85 15 1f c 9 7 40 120 40 2g d,e 7 4 50 230 60 3
6-7
Crashing to 19 Days
Activities a,c, & f are still on the critical path a cannot be crashed any more c is the least-cost choice. Lower c’s normal time by one day. The critical path is unchanged The critical time has been lowered to 19 days The cost of the project is $400+ 30(a) + 30(c) = $460
All activities are now critical. 3 paths; acf, adg, and beg a cannot be crashed any more. The only way to crash
acf is to crash c or f. c is cheaper. Regarding path adg, a and d cannot be crashed. The
only way to crash adg is to crash g Crashing g automatically crashes path beg. Crash c and g by 1 at cost of 30+60 = 90 The critical time has been lowered to 18 days The cost of the project is $400+ 30(a) + 30(c2) + 60(g) =
All activities are critical There are three paces acf, adg, and beg Crash f and g by 1 at cost of 60 +40 = 100 The critical time has been lowered to 17 days The cost of the project is $400+ 30(a) + 30(c2) +