Examples
Examples
Try the starting example
- Tasks: name, normal duration, minimum duration, crash cost per time unit, prerequisites
- A,5,4,10,none B,4,2,5,A
- Target project durations to compare
- 7,8,9
- Solver status for first target
- optimal
- Minimum crash cost for first target
- 10
- Crash reductions by task for first target
- A: 0; B: 2
- Achieved duration for first target
- 7
- Minimum theoretical project duration
- 6
- Target-duration cost curve
- 7: 10; 8: 5; 9: 0
Try another scenario
- Tasks: name, normal duration, minimum duration, crash cost per time unit, prerequisites
- A,5,4,10,none B,4,2,5,A
- Target project durations to compare
- 5,6
- Solver status for first target
- infeasible
- Minimum crash cost for first target
- Not applicable
- Crash reductions by task for first target
- Not applicable
- Achieved duration for first target
- Not applicable
- Minimum theoretical project duration
- 6
- Target-duration cost curve
- 5: infeasible; 6: 20
Calculation method
Calculation method
Solver status for first target
Enumerate source-to-sink paths and solve a continuous LP imposing enough total duration reduction on every path to meet the first target.
Minimum crash cost for first target
Minimise sum(reduction×supplied crash-unit cost), subject to each task’s reduction bounds.
Crash reductions by task for first target
Return time removed from each task; unavailable if the first target is infeasible.
Achieved duration for first target
Recompute critical-path duration with the returned reduced task durations.
Minimum theoretical project duration
Critical path with every task at its supplied minimum.
Target-duration cost curve
Repeat the LP for each requested target and expose infeasible targets explicitly.
Symbols and units
- a
- Tasks: name, normal duration, minimum duration, crash cost per time unit, prerequisites
- b
- Target project durations to compare
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- Linear continuous crashing costs, fixed precedence and unlimited resources. Supports at most ten tasks, thirty source-to-sink paths and twenty targets. It does not model discrete acceleration packages, resource contention or nonlinear crash effects.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
YALPS: continuous linear-program constraints and solver statuses ↗
Background reading; this does not imply endorsement or independent review of SumFizz.