When should a replicating shop stop copying itself and start making goods?
research/selfrep-reinvest
Optimal split of a replicating printer shop's time between copies and goods: copy flat out, then switch one e-folding time (about 50 h) before the horizon; constant splits get 9–27% of that value, smooth ramps no better. Cash-limited cases switch about 50 h from the end. All inputs assumed. Stylised.
What it found
Builds on the selfrep-growth fleet model. A fluid optimal-control model splits machine time between building copies and making goods, scored on the total value of goods over 600 h. Copying flat out and then switching to goods one e-folding time (1/k = W/(1−f), 50 h with no failures) before the horizon matches the closed form; the best constant split earns only 9–27% of that value, and smooth ramps are no better than the sharp switch. When imports or goods sales fund vitamins, cash binds throughout and the switch lands about 50 h from the end. Every input is assumed, the fleet is a continuous fluid, goods demand is unlimited and the final fleet is worth nothing. Stylised. Piecewise policies are local search, not a proof of optimality.
A figure from its own output
Paper, code and results
More in Self-replicating manufacturing
- How much imported material can recycling save a self-replicating printer shop?Mass and energy balance of plastic and aluminium recycling for one RepRap copy (stylised, assumed process parameters): vitamins stay about 75% of imported mass, recycling the shop's own scrap cuts imports a median 3%, and only retired-machine plastic changes the plastic import much.
- How many printer copies does it take for a shop's recycling machines to repay their own imports?Payback of recycling machines with their own assumed part lists (stylised): about 100 printer copies on the shop's own scrap, 12–31 if retired machines' plastic is recycled.
- Does pricing a shop’s imports, instead of weighing them, change when its recycling machines repay themselves?Recycler payback priced instead of weighed (stylised, assumed prices): plastic pair 98–111 printer copies on own scrap, furnace 203, 10–26 with retired plastic.
- What is the closed form of a replicating shop’s smooth switch from copying to goods, and does it match dynamic programming?Closed-form optimal copy share for a replicating printer shop with a saturating goods market (Pontryagin singular arc: goods output grows linearly, last 1/k hours all goods); earns 99.96–100% of the dynamic-programming policy's value. Necessary conditions only; all inputs assumed. Stylised.
- When the goods market saturates, does a replicating shop’s bang-bang switch turn smooth?Reinvestment of a replicating printer shop when the goods market saturates, checked by dynamic programming: bang-bang is optimal with linear revenue, but with market capacity below about 10^4 machine-hours per hour the optimum ramps the copy share down over 90–300 h and bang-bang loses 4.5–7%. All inputs assumed. Stylised.
- What fleet can a replicating printer shop sustain when its machines wear out?Fleet a replicating printer shop sustains when machines wear out (stylised, assumed inputs): short-lived machines die out from one seed; recycling gains need a correction for builds cut short.
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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.