Does a resale value for the finished fleet still end copying late when the goods market saturates?
research/selfrep-terminalmarket
A resale value s per 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.
What it found
Follow-up to selfrep-terminal and selfrep-satmarket: a backward dynamic programme with terminal reward s per machine on the saturating-market fluid model (W = 50 h, failure 0, horizon 600 h, all inputs assumed). With a linear market the DP reproduces the closed-form switch of selfrep-terminal. As the market capacity c falls, a small s moves the optimum from an early switch to copying until the horizon (c = 1000: switch near 400 h at s = 0, none at s = 12.5), and a policy tuned for s = 0 earns only 14% of the optimum. Where the final fleet is large the DP is not reliable: a bang-bang switch beats its policy by up to 0.7%, so it is a lower bound there. Stylised and preliminary; the resale value is assumed and does not itself saturate.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
- 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.
- How many parts should a replicating printer print per plate to double its shop fastest?How many parts per print plate double a replicating printer shop fastest (stylised, assumed inputs): with no changeover one part per plate wins (43.2 h doubling), with 0.25 h per plate four parts (46.4 h), with 0.5 to 1 h eleven parts; pooled fleets stay 7.6 to 15.5% ahead of one copy per printer.
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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.