How does a resale value for the finished fleet move the switch from copies to goods?
research/selfrep-terminal
A resale value s per machine at the horizon shortens the goods phase from one e-folding time 1/k to 1/k − s/a; at s ≥ a/k the shop never switches. Grid optimum matches the closed form. All inputs assumed. Stylised.
What it found
Follow-up to selfrep-reinvest. Giving each machine left at the horizon a value s shortens the goods phase from one e-folding time 1/k to 1/k − s/a, so the switch moves later; at s ≥ a/k (50 per machine with no failures, 29% of the assumed vitamin cost) the shop copies to the end. The grid optimum of the Euler simulation agrees with this closed form to within 1 h, and ignoring a terminal value of 12.5–50 per machine costs 3–26% of the optimum. Every input is assumed; cash is free and demand unlimited. Stylised.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
- Does a resale value for the finished fleet still end copying late when the goods market saturates?A resale value
sper machine with a saturating goods market (DP): at capacity c = 1000 machine-hours per hour the copy phase runs to the horizon once s is 12.5 (a quarter of a/k), and the policy that ignores s earns 14% of the optimum; the DP loses to bang-bang by under 1% where the fleet is large, so it is a lower bound there; stylised, preliminary. - Is the dynamic-programming table for the replicating shop with a resale value converged, and can its policy be trusted?Grid-convergence check of the terminal-value DP: the policy's value is stable to about 0.15% from 800 to 1,600 grid points while the table value rises from 8–13% (400 points) to 2–3% (1,600) below it; a stylised fluid model, preliminary.
- How much does a smooth copy-then-sell policy beat a single switch for the replicating shop, certified without interpolation?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.
- How does a falling resale price for the finished fleet change when the shop stops copying?A resale price for the finished fleet that falls with market depth
m(stylised): with an unsaturated goods market the switch moves from 574 h (linear) to 549 h (m = 1e3) and a single switch matches the DP; with a saturating goods market the DP beats the best switch by up to 14%. - How much do the RepRap closure numbers depend on which parts a shop is judged able to make?How much the RepRap closure numbers depend on which parts a shop is judged able to make (stylised, assumed inputs): buying all optimistic lines cuts mass closure from 22% to 17%; making the motors in-house would add 22 points.
- Does sharing part jobs across printers make a replicating printer shop double faster than one copy per printer?Does sharing part jobs across printers beat one copy per printer (stylised, assumed inputs): a pool serving the oldest copy first doubles in 43.2 h against 51.1 h with no import limit, about half the gap to the fluid 34.7 h; with imports binding all policies agree.
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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.