CPM Project Crashing
Shorten a project by crashing the cheapest critical activities. Extends PERT/CPM with a time–cost tradeoff until you hit a deadline.
Activities
| ID | Predecessors | Normal t | Crash t | Normal $ | Crash $ | Slope $/t |
|---|---|---|---|---|---|---|
| 40.0 | ||||||
| 40.0 | ||||||
| 40.0 | ||||||
| 60.0 |
Why crash?
Crashing shortens project duration by spending extra money on activities. Only crashing activities on the current critical path can reduce project length.
Cost slope
At each step, crash 1 time unit on the critical activity with the lowest finite slope that still has crash room.
Algorithm used here
1) Schedule with CPM (ES/EF/LS/LF). 2) Identify critical path. 3) Pick cheapest crashable critical activity. 4) Reduce its time by 1. 5) Repeat until target duration or no crash room remains.
Limits
This discrete unit-crash heuristic is the standard textbook method. Parallel critical paths may require crashing multiple activities in a coordinated way for true optimality — interpret results as a practical plan.
Network A→B→D and A→C→D. Normal duration 13; crash toward target 10. Activity B is often cheapest to crash first.