Honest FFD Scope - Bin Packing: First-Fit Decreasing, Step by Step

FFD is a heuristic in general, so this book separates the heuristic from the certificate.

highlighted = computed this step

Not an FFD proof

FFD does not always find an optimal packing on every instance.

\text{FFD is a heuristic in general}

Proof here

Here, optimality comes from the lower bound matching the bins used.

\text{certificate: lower bound}=2=\text{bins used}

Not modeled

This one-dimensional model does not include item rotation, multiple bin sizes, weights, uncertainty, or online arrivals.

\text{outside scope: richer packing settings}

Honesty note

FFD is a heuristic in general. This packing is optimal only because the exact lower-bound certificate matches the two bins used here. Pixel positions are rounded for layout; every item size, fill, total size, and bound is exact.

\text{exact certificate for this pinned instance}