Formal problem

3D Bin Packing

Load boxes into the fewest fixed-size containers/bins.

Also called: 3D Bin Packing · 삼차원 빈 패킹 · Container packing

Last verified: 2026-05-27

Definition

Load cuboid items, without overlap, into identical 3D containers to minimize the number of containers used.

Example

Suppose a container $2\times2\times2$ and five $1\times1\times2$ boxes. Standing one box in each of the four cells of the container's $2\times2$ floor fills it by volume (four boxes); the fifth spills into a second container. The minimum is 2 containers (total volume $10 > 8$ ). In practice, constraints such as stability, load bearing, and loading order are added.

Family

A higher-dimensional generalization of 2D Bin Packing, adding practical constraints such as stability, load bearing, and loading order (see container loading).

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Claims & evidence

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Relationship	Claim	Equiv.	Evidence	Sources
generalizes2D Bin Packing	3D bin packing is a higher-dimensional generalization of 2D bin packing and shares many constructive and search methods.	E2	B	AAn improved typology of cutting and packing problems
uses methodBranch and Bound	Exact approaches to 3D bin packing / container loading have been reported with branch-and-bound formulations.	—	B	AConstraints in container loading – A state-of-the-art review
uses methodGenetic Algorithm	Container loading / 3D bin packing has been widely addressed with metaheuristics such as genetic algorithms.	—	B	AConstraints in container loading – A state-of-the-art review
uses methodReinforcement Learning	RL-based 3D packing/loading has been reported recently, but its industrial maturity is not verified here. [unverified]	—	D	—

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