Examples
Examples
Try the starting example
- Items: name, length, width, height, quantity (cm)
- Cube,5,5,5,2
- Available cartons: name, length, width, height, quantity (cm)
- Box,10,5,5,1
- Allowed rotations: fixed, base or all
- fixed
- Cartons opened
- 1
- Units packed
- 2
- Units not packed by heuristic
- 0
- Unused opened-carton volume (cm³)
- 0
- Placement proposal
- Box 1: Cube 1 @ 0,0,0 [5×5×5]; Cube 2 @ 5,0,0 [5×5×5]
- Unpacked unit identifiers
- None
Try another scenario
- Items: name, length, width, height, quantity (cm)
- Wide,8,4,2,3
- Available cartons: name, length, width, height, quantity (cm)
- B,10,5,4,1
- Allowed rotations: fixed, base or all
- fixed
- Cartons opened
- 1
- Units packed
- 2
- Units not packed by heuristic
- 1
- Unused opened-carton volume (cm³)
- 72
- Placement proposal
- B 1: Wide 1 @ 0,0,0 [8×4×2]; Wide 2 @ 0,0,2 [8×4×2]
- Unpacked unit identifiers
- Wide 3
Calculation method
Calculation method
Cartons opened
Count cartons actually opened from the supplied finite inventory.
Units packed
Count item units assigned to cartons.
Units not packed by heuristic
Requested units − assigned units under the stated greedy method.
Unused opened-carton volume (cm³)
Opened carton volume − packed item volume.
Placement proposal
Place larger-volume units first in best-fitting disjoint free boxes; after placement split the remaining box into right, front and top regions. Coordinates are relative to carton origin.
Unpacked unit identifiers
List unplaced unit identifiers. A heuristic failure does not prove infeasibility.
Symbols and units
- a
- Items: name, length, width, height, quantity (cm)
- b
- Available cartons: name, length, width, height, quantity (cm)
- c
- Allowed rotations: fixed, base or all
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Finite carton inventory and rectangular rigid item bounding boxes, at most 100 expanded item units. Rotations are fixed, horizontal-base only, or all six orientations. The guillotine-style greedy proposal checks geometric fit; no weight, cushioning, strength, optimality or shipping suitability is inferred.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.