How much does a smooth copy-then-sell policy beat a single switch for the replicating shop, certified without interpolation?
research/selfrep-exactdp
An interpolation-free DP (the table equals its own policy's value to 1e-14): with no resale value and a saturating market a three-phase policy beats the best single switch by 4.7% (c = 1e4) to 7.1% (c = 1e3), while a resale value of 50 makes one switch optimal; a stylised fluid model, preliminary.
What it found
Follow-up to selfrep-dpgrid, whose DP table sat 2–13% below the value of its own policy. This project chooses a control set whose steps land exactly on a geometric fleet grid, so no interpolation is needed and the table equals the policy value to 1e-14. On the same fluid model (W = 50 h, failure 0, horizon 600 h, all inputs assumed) a single copy-then-goods switch is optimal when machines keep a resale value of 50 each. With no resale value and a saturating goods market, a three-phase policy (full copying, an intermediate share, then goods) beats the best switch by 4.7% (capacity 1e4) and 7.1% (capacity 1e3); with a resale value of 12.5 and capacity 1e4 the gain is 6.5%, and only appears once the control set is fine enough. Stylised, with a fixed Euler step and no cash constraint; preliminary.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
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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.