Sizing a Hand-Sorting Frame: When One Pass Stops Reaching, and What a Second Pass Costs in Errors

Hand sorting looks like a furniture problem — how big a frame of pigeonholes to build — and is actually a decision about passes, reach and errors. A sorter can work comfortably with at most a stated 48 compartments within reach. An office sorting for 180 delivery rounds therefore cannot sort in one pass; the computed two-pass plan uses 13 first-pass area groups and 14 compartments in all, at a handling time of 135.0 minutes for 900 items. The second pass is not free: at a stated mis-sort rate of 0.8 percent per pass, two passes raise the expected mis-sort share from 0.8 percent to 1.59 percent. The paper tabulates the plan for 12 to 320 rounds and gives the rule: one pass to the reach limit, two passes with a square-root split beyond it, and a third pass only when the frame, not the sorter, is the constraint. SIMULATED, NOT MEASURED.