Compare a common activity with crashing parallel branches
When two critical paths share an activity, shortening that common activity can reduce both paths at once. Compare its marginal cost with the combined cost of shortening one activity on each separate branch. Include indirect daily costs when the objective is minimum total cost rather than merely minimum direct crashing cost. The arithmetic below assumes one-day increments, fixed precedence and no resource conflicts.
Worked practice example
A common activity A takes 4 days, followed by parallel branches B and C of 6 days each, then a common finish activity D of 2 days. Both paths take 12 days. A can be reduced by one day for KSh 900; B and C can each be reduced by one day for KSh 600 and KSh 500 respectively. Site overhead is KSh 1,000 per project day. Compare reaching 11 days.
| Step | Working |
|---|---|
| Normal project duration | A–B–D = 4 + 6 + 2 = 12 days; A–C–D is also 12 days. |
| Common-activity option | Crash A by one day: both paths become 11 days, extra direct cost KSh 900. |
| Separate-branch option | Crash both B and C by one day: both paths become 11 days, extra direct cost 600 + 500 = KSh 1,100. |
| Include overhead | One day saved reduces overhead by KSh 1,000. Net change: −KSh 100 for A, versus +KSh 100 for the branch option. |
Check your method
The common-activity option gives the lower total cost for this one-day target. Crashing B alone leaves the C path at 12 days and saves no overhead. Further reductions require fresh path and capacity checks; the one-day data do not establish a complete minimum-cost schedule for every possible duration.
Try it yourself
If daily overhead were KSh 700 instead, would crashing A by one day reduce total cost?
Show the answer and method
No. Extra direct cost 900 minus overhead saved 700 gives a KSh 200 increase. It would still achieve the 11-day deadline, but it would not save total cost under the stated assumptions.
This written practice example was prepared for Jemshah revision. It is additional practice, not an official examination question or a transcript of the video.