FA-95085 / Warehouse slotting and bin packing / Member archive

Slot fit: utilization rounded instead of floored · case 05

Cube utilization is overstated by one basis point on fractional values.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

slot [width, depth, height], unit [w, d, h]. Upright units may only rotate in the horizontal plane; others may take any of the 6 axis orientations. Vertical layers = height // unit height, capped at max_stack when max_stack > 0 (0 = unlimited). Units = best over orientations of (W//a)*(D//b)*layers. Utilization in basis points = floor(units*unit volume*10000/slot volume).

Why this case matters

Slot sizing converts product cube into units per location for slotting and replenishment.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
generated mix 26	`[56, 8167]`	`[56, 8166]`	Failed

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