Project Crashing — Time-Cost Trade-off

Direct and indirect project costs; normal time and cost, crash time and cost; cost slope; total cost curve and optimum duration; steps of crashing a network — crashing critical activities in order of cost slope, parallel critical paths, new critical paths, stopping rules; fast tracking vs crashing; updating networks — with a fully worked crashing problem.

Project Crashing — Time-Cost Trade-off

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📑 Contents (8 sections)

Last reviewed 16 Sept 2026 · 6 min read

Project costs

Cost	Meaning	Behaviour when duration is reduced
Direct costs	Costs directly attributable to activities — materials, labour, equipment for each activity	Increase (overtime, extra shifts, more equipment, costlier methods)
Indirect costs	Overheads — site supervision, office establishment, insurance, interest on capital, general administration, security; also penalties for delay (or bonuses)	Decrease (roughly proportional to duration)

Total cost = direct cost + indirect cost — reducing the duration raises direct cost but lowers indirect cost, so the total cost curve has a minimum at the optimum duration.

Normal and crash points

Normal time ( $T_{n}$ ) — duration under normal working conditions at the lowest direct cost (normal cost $C_{n}$ ).
Crash time ( $T_{c}$ ) — minimum possible duration with maximum resources, at crash cost $C_{c}$ .
Reducing an activity below its crash time is impossible (or only increases cost without saving time).

FormulaCost slope

Cost slope = \frac{C _{c} - C _{n}}{T _{n} - T _{c}}

The extra direct cost per unit time saved (assuming a linear time–cost relationship between normal and crash points).

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