Research replication
The anatomy of delivery
Open the exact fictional inputs behind each worked study. Project cases use their companion model; auxiliary cash bridges retain a separate, verifiable calculation.
Return to the paper↗These are illustrative scenarios, not actual project or supplier data. Inputs and method boundaries govern each result.
Illustrative study
Illustrative parallel delivery network
Establish forward/backward dates, float and the selected critical path.
What changes
- Changed: None; authored reference fixture
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative serialised receiving release
Show a dependency revision changing completion while durations remain unchanged.
What changes
- Changed: Receiving works now follows equipment readiness rather than design alone
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative supply duration improvement
Shorten the original critical branch and expose the receiving branch as critical.
What changes
- Changed: Equipment readiness duration estimates only
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative explicit interface decision
Insert a previously omitted release activity and reveal the consequence for downstream completion.
What changes
- Changed: Added readiness decision after assembly and before integrated testing
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative equal critical branches
Show why one selected-path approximation omits parallel-path uncertainty.
What changes
- Changed: Receiving duration distribution assumptions equal supply assumptions
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative earlier target only
Change the selected-path deadline reading without changing the dependency schedule.
What changes
- Changed: Target completion only; no task or dependency changes
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative deterministic task durations
Test the zero-variance conditional deadline boundary.
What changes
- Changed: Each task estimate is fixed at its base most-likely duration; target matches schedule duration
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative zero-duration release milestone
Preserve a discrete readiness event without adding elapsed duration.
What changes
- Changed: A zero-duration root milestone is added as the design predecessor
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
Illustrative bounded critical-path display
Test total critical-path counting separately from the bounded displayed list.
What changes
- Changed: An explicit equal-branch network replaces the base topology; all task durations are deterministic
- Held constant: Every other input retained from the expressly fictional base unless the named fixture declares a different network
- Comparison: Full slate tests serialisation, duration and critical-path switching, inserted interface decision, tied branches, target change and deterministic boundaries.
Limits of the study
- Illustrative finish-to-start DAG with a continuous week basis, no resources, calendars, lags, lead relationships or rework loop.
- PERT means and variance are assumptions; the selected-path normal deadline approximation is not full-graph completion probability, empirical likelihood or guaranteed delivery.
Open this case in the model↗Illustrative study
A short independent activity does not become critical
Keep a supported small positive float distinct from zero when choosing a critical path.
What changes
- Change: Rescale all durations and deadline together.
- Held constant: Two independent deterministic tasks.
- Interpretation: The longer task remains the sole critical path; no stochastic duration distribution is estimated.
Limits of the study
- Artificial durations diagnose arithmetic and do not represent a practical calendar.
- Zero task ranges make this diagnostic deterministic; the general app still omits path switching and duration correlation.
Open this case in the model↗Illustrative study
Two equal canonical decimal path totals
Reproduce exact equality of the supplied decimal0.1 plus0.2 path and the decimal0.3 direct path.
What changes
- Change: Raise only the direct task duration by0.000000001.
- Held constant: Task A, task B and the target deadline.
- Interpretation: The direct path then becomes strictly longer rather than remaining tied by a tolerance.
Limits of the study
- The equality is conditional on canonical input values, not duration measurement certainty.
- The first displayed path remains a selected-path diagnostic, even when several critical paths exist.
Open this case in the model↗