How far below a clairvoyant schedule is online pick dispatch in a robotic waste-sorting cell?

research/infra-sortbound

Follow-up to infra-sortvalue: an exact dynamic-programming bound on the best possible pick schedule (agreeable deadlines make arrival order optimal) shows highest-value-first dispatch reaches 96.5% of the clairvoyant optimum at 6 items/m and 93.9% at 10, FIFO 94.7% and 89.6%, and that the largest headroom (about 10 to 11%) sits at faster belts and slower arms, not at the loads where pick order helped most. A rolling-horizon rule that re-solves the schedule with a 1 s look ahead recovers most of it: 99.7% of the optimum at 6 items/m and 98.0% in the hardest cells.

8 tests

What it found

infra-sortvalue compared greedy pick orders with each other and asked how much headroom a better schedule would leave. Because every item has the same reach window, deadlines are in arrival order, so the best schedule for a single arm is a subsequence of the called items in arrival order, and a Pareto dynamic program over (finish time, value) solves it exactly; finish times on a grid, rounded up and down, bracket the optimum (width under 0.1 % of value at a 5 ms grid). A brute-force search over every subset and order agrees on 25 random small instances. On identical simulated arrival streams (TACO class mix, assumed values, 40 runs, paired), highest-value-first reaches 99.5 % of the optimum at 1 item/m, 96.5 % at 6 and 93.9 % at 10, against 99.4, 94.7 and 89.6 % for FIFO; value-per-second matches value-first. The gap is largest where the cell is overloaded in time rather than in items: 10 % (FIFO 11 %) at 0.75 m/s belt speed and 9 % for a 0.4 m/s arm, and it vanishes for a 5 m/s arm or a 0.25 m/s belt. Item values, arm speed, detector, grasp and reach are assumed (as in infra-sortvalue), the clairvoyant bound knows every arrival and travel time in advance, and a real cell is not measured. Added: a rolling-horizon rule (exact re-planning each time the arm is free, over the queue plus items arriving within L seconds) reaches 97.5 % of the optimum with queue only and 99.7 % with a 1 s look ahead at 6 items/m, and 98.0 % at both 0.75 m/s belt and 0.4 m/s arm; the look ahead sees called items exactly, so this is an upper estimate for a real upstream camera.

A figure from its own output

Figure produced by research/infra-sortbound: load — infra-sortbound/experiments/load.svg, written by the project's own experiment code.

Paper, code and results

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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.