Project Crashing

Reduces a project’s duration by shortening (crashing) critical activities, trading extra cost for time saved.

• Normal time / normal cost
  An activity’s duration and cost under regular execution.
• Crash time / crash cost
  The minimum achievable duration and its (higher) cost.
• Cost slope
  $\dfrac{\text{crash cost} - \text{normal cost}}{\text{normal time} - \text{crash time}}$. The cost of shortening the activity by 1 time unit.

Crashing Steps

• Find the critical path(s) at normal duration.
• Crash the critical activity with the lowest cost slope, by 1 time unit at a time.
• Recompute the critical path after every crash: a non-critical path can become critical, requiring simultaneous crashing on multiple paths.
• Stop when every activity is at crash time, or when the marginal cost of crashing further exceeds the benefit (e.g. the cost of the delay it avoids).