What does a deterministic-duration twin of a lab workcell promise, and how many stations does it buy?

What it found

A batch is split over k parallel stations with a serial arm handover; a twin running every step at its mean picks k = √(W/a) = 8 and promises 16 min. The real makespan uses the exact expected maximum of gamma branches (checked against harmonic numbers and simulation): with exponential branches it averages 1.86× the promise, only 2.6% of runs finish every branch within its mean, and the 95% quantile is 3.03× the promise. Whether the twin also buys the wrong layout depends on how variability scales with splitting: task-level variability makes it under-buy (optimum 12, 24.7% regret on the 95% quantile), while a chain of random unit steps cancels the effect so k = 8 stays optimal yet the real makespan is still 6–59% above the promise. Fitting the branch-time shape needs about 5 real durations to fix the decision and about 50 to make the predicted makespan accurate to 1%. Stylised: one fork-join stage, i.i.d. gamma branches.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.