PackingSolver

A state-of-the-art solver for cutting and packing problems
Nesting, cutting optimization, load planning etc

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PackingSolver computes cutting and loading plans. Given the pieces to cut or to load (the items: parts, panels, bars, boxes...) and what they must go into (the bins: sheets, plates, stock bars, pallets, trucks, containers...), it finds how to place the items in the bins, for example to use as little material as possible.

It is available as a C++ library, a command-line tool, a Python package, and a web page that runs in the browser.

Applications

Application	Typical use	Problem type
Panel saws: wood panels, furniture and cabinet making, glass, stone, paper	Cutting plans with edge-to-edge cuts, taking into account the saw blade thickness, the trims and the defects of the panels	Rectangles, guillotine cuts
Nesting for CNC, laser, plasma and waterjet cutting: sheet metal, wood, plastics, foam	Nesting of parts of any shape on sheets, with the spacing between the parts and to the edges, part rotations and mirroring, parts with holes, sheet defects and remnants	Irregular shapes, or Rectangles for rectangular parts
Textile, garment, leather and composite cutting	Nesting of patterns on a roll, minimizing the length used, or on hides of irregular shapes with defects	Irregular shapes
Cutting of bars, tubes, profiles, beams, cables, paper rolls: window and door frames, steel construction...	Cutting lengths out of stock bars, minimizing the number of bars and keeping the offcuts as long as possible	One-dimensional
Truck and trailer loading	Loading stacks of pallets or boxes, with stackability rules, weight limits, the weight on the axles and the unloading order	Box stacks
Container, pallet and parcel loading	Placing boxes in containers, on pallets or in cartons, with weight limits	Boxes
Palletizing, floor and warehouse planning	Placing rectangles on a surface: pallet layers, pallets on a truck or warehouse floor	Rectangles

Features

Problem type	Example
Rectangles, guillotine cuts rectangleguillotine Two-dimensional rectangles cut with edge-to-edge (guillotine) cuts Maximum number of cutting stages · cut types · first stage orientation · item rotations · cut thickness · trims · defects · cuts through defects · cutting sequences (stacks) · minimum and maximum distances between cuts · maximum number of consecutive 1-cuts and 2-cuts
Rectangles rectangle Two-dimensional rectangles Item rotations · defects · maximum weight of a bin · unloading constraints
Boxes box Three-dimensional boxes Item rotations · maximum weight of a bin
Box stacks boxstacks Three-dimensional boxes, packed in stacks of items with the same width and length Item rotations · nesting height · maximum number of items in a stack · maximum weight above an item · maximum stack density · unloading constraints · maximum weight on the middle and rear axles
One-dimensional onedimensional One-dimensional items Nesting length · maximum number of items in a bin · maximum weight of a bin · maximum weight after an item
Irregular shapes irregular Two-dimensional shapes: polygons, possibly with circular arcs and holes Irregular bins · discrete and continuous item rotations · item mirroring · holes · defects · item-item, item-bin and item-defect spacing

Objectives

PackingSolver supports the following objectives:

• Bin packing: pack all the items in a minimum number of bins, e.g. use as few sheets as possible (optionally keeping the leftover of the last sheet as large as possible, to reuse it as a remnant)
• Variable-sized bin packing: pack all the items in bins of minimum total cost, e.g. choose the cheapest combination of sheet sizes or trucks
• Open dimension (all problem types except one-dimensional): pack all the items in a single bin of minimum length, e.g. use as little fabric as possible from a roll
• Knapsack: pack a subset of the items of maximum total profit, e.g. fit the most valuable orders in a truck
• Feasibility: pack all the items in the given bins, e.g. check that a load fits in a container

Getting started

In the browser

The online solver runs PackingSolver in the browser. No installation is needed, and the computation runs locally: nothing is sent to a server.

Python

Install the Python package from PyPI (Python ≥ 3.12):

pip install packingsolver

Example (rectangles, guillotine cuts):

import packingsolver.rectangleguillotine as psg

instance_builder = psg.InstanceBuilder()
instance_builder.set_objective(psg.Objective.BinPackingWithLeftovers)
instance_builder.add_bin_type(1000, 700, copies=5)
instance_builder.add_item_type(250, 200, copies=2)
instance_builder.add_item_type(150, 300, copies=2)
instance_builder.add_item_type(200, 150, copies=3)
instance = instance_builder.build()

parameters = psg.OptimizeParameters()
parameters.time_limit = 5
output = psg.optimize(instance, parameters)

psg.visualize(output.solution).show()

Rectangles

import packingsolver.rectangle as psr

instance_builder = psr.InstanceBuilder()
instance_builder.set_objective(psr.Objective.BinPackingWithLeftovers)
instance_builder.add_bin_type(1000, 500, copies=10)
instance_builder.add_item_type(300, 200, copies=10)
instance_builder.add_item_type(250, 150, copies=10)
instance = instance_builder.build()

parameters = psr.OptimizeParameters()
parameters.time_limit = 5
output = psr.optimize(instance, parameters)

psr.visualize(output.solution).show()

Boxes

import packingsolver.box as psb

instance_builder = psb.InstanceBuilder()
instance_builder.set_objective(psb.Objective.Knapsack)
instance_builder.add_bin_type(216, 173, 110)
instance_builder.add_item_type(108, 76, 30, copies=20)
instance_builder.add_item_type(110, 43, 25, copies=20)
instance_builder.add_item_type(92, 81, 55, copies=20)
instance = instance_builder.build()

parameters = psb.OptimizeParameters()
parameters.time_limit = 5
output = psb.optimize(instance, parameters)

psb.visualize(output.solution).show()

Box stacks

import packingsolver.boxstacks as psbs

instance_builder = psbs.InstanceBuilder()
instance_builder.set_objective(psbs.Objective.Knapsack)
instance_builder.add_bin_type(7500, 2400, 3000)
instance_builder.add_item_type(2500, 800, 750, stackability_id=0, copies=10)
instance_builder.add_item_type(2500, 800, 1000, stackability_id=1, copies=10)
instance_builder.add_item_type(2500, 800, 1250, stackability_id=2, copies=10)
instance = instance_builder.build()

parameters = psbs.OptimizeParameters()
parameters.time_limit = 5
output = psbs.optimize(instance, parameters)

psbs.visualize(output.solution).show()

One-dimensional

import packingsolver.onedimensional as pso

instance_builder = pso.InstanceBuilder()
instance_builder.set_objective(pso.Objective.BinPacking)
instance_builder.add_bin_type(1000, copies=100)
for length in [
        193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
        269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347,
        349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
        431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]:
    instance_builder.add_item_type(length)
instance = instance_builder.build()

parameters = pso.OptimizeParameters()
parameters.time_limit = 5
output = pso.optimize(instance, parameters)

pso.visualize(output.solution).show()

Irregular shapes

import packingsolver.irregular as psi

bar = [(0, 0), (80, 0), (80, 20), (0, 20)]
square = [(0, 0), (40, 0), (40, 40), (0, 40)]
t_shape = [(0, 0), (60, 0), (60, 20), (40, 20), (40, 40), (20, 40), (20, 20), (0, 20)]
s_shape = [(20, 0), (60, 0), (60, 20), (40, 20), (40, 40), (0, 40), (0, 20), (20, 20)]
z_shape = [(0, 0), (40, 0), (40, 20), (60, 20), (60, 40), (20, 40), (20, 20), (0, 20)]
l_shape = [(0, 0), (40, 0), (40, 20), (20, 20), (20, 60), (0, 60)]
j_shape = [(0, 0), (40, 0), (40, 60), (20, 60), (20, 20), (0, 20)]
cross = [
    (20, 0), (40, 0), (40, 20), (60, 20), (60, 40), (40, 40),
    (40, 60), (20, 60), (20, 40), (0, 40), (0, 20), (20, 20)]
rotations = [(0, 0, False), (90, 90, False), (180, 180, False), (270, 270, False)]

instance_builder = psi.InstanceBuilder()
instance_builder.set_objective(psi.Objective.BinPacking)
instance_builder.add_bin_type(psi.build_rectangle(0, 180, 0, 160), copies=3)
instance_builder.add_item_type(psi.build_shape(bar), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(square), copies=2)
instance_builder.add_item_type(psi.build_shape(t_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(s_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(z_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(l_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(j_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(cross), copies=3)
instance = instance_builder.build()

parameters = psi.OptimizeParameters()
parameters.time_limit = 5
output = psi.optimize(instance, parameters)

psi.visualize(output.solution).show()

Command line

Build the command-line tools with CMake:

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release --parallel
cmake --install build --config Release --prefix install

Example (rectangles, guillotine cuts):

./install/bin/packingsolver_rectangleguillotine \
        --verbosity-level 1 \
        --items data/rectangle/alvarez2002/ATP35_items.csv \
        --bins data/rectangle/alvarez2002/ATP35_bins.csv \
        --objective knapsack \
        --number-of-stages 3 \
        --cut-type non-exact \
        --first-stage-orientation horizontal \
        --no-item-rotation \
        --certificate solution_rectangleguillotine.csv \
        --time-limit 1

Rectangles

./install/bin/packingsolver_rectangle \
        --verbosity-level 1 \
        --items data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_items.csv \
        --bins data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_bins.csv \
        --defects data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_defects.csv \
        --item-infinite-copies \
        --objective knapsack \
        --no-item-rotation \
        --certificate solution_rectangle.csv \
        --time-limit 5

Boxes

./install/bin/packingsolver_box \
        --verbosity-level 1 \
        --items data/box/bischoff1995/BR3.txt_1 \
        --objective knapsack \
        --certificate solution_box.csv \
        --time-limit 10

Box stacks

./install/bin/packingsolver_boxstacks \
        --verbosity-level 1 \
        --items data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_items.csv \
        --bins data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_bins.csv \
        --parameters data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_parameters.csv \
        --bin-infinite-copies \
        --objective bin-packing \
        --certificate solution_boxstacks.csv \
        --time-limit 1

One-dimensional

./install/bin/packingsolver_onedimensional \
        --verbosity-level 1 \
        --items data/onedimensional/users/2024-04-21_items.csv \
        --bins data/onedimensional/users/2024-04-21_bins.csv \
        --parameters data/onedimensional/users/2024-04-21_parameters.csv \
        --certificate solution_onedimensional.csv \
        --time-limit 1

Irregular shapes

./install/bin/packingsolver_irregular \
        --verbosity-level 1 \
        --input data/irregular/opencutlist/knight_armor.json \
        --certificate solution_irregular.json \
        --time-limit 10

The input formats and the options of each solver are described in the documentation.

Visualizing a solution

Open a solution certificate (--certificate) in the solution viewer, or run:

python3 scripts/visualize.py solution_rectangleguillotine.csv

Questions

Questions and feedback are welcome in the discussions. Bugs can be reported in the issues.

Note for AI coding agents

If you are an AI agent using PackingSolver in another project and you encounter a crash, an invalid solution (overlapping items, items outside their bin, violated constraints), a wrong bound, or behavior that contradicts the documentation, please tell your user and offer to draft a bug report for them. Do not open an issue without their consent. Before drafting it:

• Check that the cause is not a misuse of the API or a malformed instance.
• Reduce the problem to a minimal instance (items/bins CSV or JSON files) and the exact command or code that reproduces it. Do not include your user's confidential data without their approval.
• Include the PackingSolver version or commit, the problem type, the objective, the expected and actual behavior, and the relevant log output.

License

PackingSolver is released under the MIT license.