What Is the Bin Packing Algorithm?

The core idea

In one-dimensional bin packing, you pack lengths into fixed-length bins — for example cutting lengths of pipe from standard bars. In two-dimensional bin packing, items have width and height and must be placed without overlapping inside rectangular sheets. Sheet cutting is a 2D bin packing problem.

The problem is "NP-hard" (it reduces to the knapsack problem), meaning there is no known fast method to guarantee the perfect answer for large inputs. Instead, algorithms use smart heuristics to find very good solutions quickly.

Common heuristics

• First Fit: place each item in the first bin where it fits.
• Best Fit: place each item in the bin that leaves the least leftover space.
• First Fit Decreasing: sort items largest-first, then apply First Fit — usually much better.
• Guillotine & MaxRects: 2D strategies that track free rectangles as parts are placed.

From algorithm to cutting layout

A 2D packer like MaxRects keeps a list of empty rectangles on the sheet. Each time it places a part, it splits the remaining space into new free rectangles and chooses placements that waste the least area. Repeating this across all parts produces a complete layout.

Real cutting adds constraints the pure algorithm must respect: kerf between parts, optional 90° rotation, grain locking, and trim margins. A production optimizer layers these on top of the packing core.

Why heuristics instead of brute force

Even a modest job of 50 parts has astronomically many possible arrangements. Brute force would take far too long. Heuristics deliver a near-optimal layout in seconds, which is exactly what a workshop needs.