The First-Fit Decreasing (FFD) Algorithm

How First-Fit Decreasing works

• Sort all items in decreasing order of size.
• Take the largest remaining item.
• Place it in the first bin (or sheet) that has room.
• If no open bin fits, open a new one.
• Repeat until every item is placed.

Why sort largest-first?

Placing big items first reserves room for them before bins fill with small pieces. Small items can then slot into the gaps left over. Plain First-Fit (without sorting) often strands large items that no longer fit anywhere, wasting space. The "decreasing" step is what makes FFD strong.

How good is FFD?

For the classic 1D bin-packing problem, First-Fit Decreasing never uses more than about 11/9 of the optimal number of bins plus a small constant — a proven worst-case bound. In everyday use it is usually much closer to optimal, which is why it is a common starting point in packing and cutting software.

FFD in 2D cutting

Sheet cutting is two-dimensional, so practical optimizers extend the idea with placement strategies such as guillotine splits or maximal-rectangles tracking. The core insight — place large parts first, fill gaps with small ones — carries straight over from FFD.