PackingSolver
A state-of-the-art solver for cutting and packing problems
Nesting, cutting optimization, load planning etc
Online solver · Documentation · Ask a question
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 rectangleguillotineTwo-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 rectangleTwo-dimensional rectangles Item rotations · defects · maximum weight of a bin · unloading constraints |
|
Boxes boxThree-dimensional boxes Item rotations · maximum weight of a bin |
|
Box stacks boxstacksThree-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 onedimensionalOne-dimensional items Nesting length · maximum number of items in a bin · maximum weight of a bin · maximum weight after an item |
|
Irregular shapes irregularTwo-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.
1 maintainer
Metadata
1 maintainer
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