3D Bin Packing

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

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

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).

Claims & evidence

Every relationship is a claim with an evidence grade; applicable problem-to-problem relationships also carry an equivalence level. See the evidence policy.

A–X describes evidence reliability; E0–E4 describes mathematical similarity between problems. The two axes are independent.

Relationships from this entry 4

generalizes
3D Bin Packing to 2D Bin Packing
3D bin packing is a higher-dimensional generalization of 2D bin packing and shares many constructive and search methods.
EvidenceB · Survey / tutorial / community
Equiv.E2 · shared methodology
Sources
- Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems
  Citation details
  Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
uses method
3D Bin Packing to Branch and Bound
Exact approaches to 3D bin packing / container loading have been reported with branch-and-bound formulations.
EvidenceB · Survey / tutorial / community
Sources
- Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review
  Citation details
  Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
uses method
3D Bin Packing to Genetic Algorithm
Container loading / 3D bin packing has been widely addressed with metaheuristics such as genetic algorithms.
EvidenceB · Survey / tutorial / community
Sources
- Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review
  Citation details
  Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
uses method
3D Bin Packing to Reinforcement Learning
RL-based 3D packing/loading has been reported recently, but its industrial maturity is not verified here. [unverified]
EvidenceD · Expert inference
Sources
No source listed

Relationships from this entry
Relationship	Claim	Evidence	Equiv.	Sources
generalizes 3D Bin Packing to 2D Bin Packing	3D bin packing is a higher-dimensional generalization of 2D bin packing and shares many constructive and search methods.	B · Survey / tutorial / community	E2 · shared methodology	Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems Citation details Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.
uses method 3D Bin Packing to Branch and Bound	Exact approaches to 3D bin packing / container loading have been reported with branch-and-bound formulations.	B · Survey / tutorial / community	—	Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review Citation details Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
uses method 3D Bin Packing to Genetic Algorithm	Container loading / 3D bin packing has been widely addressed with metaheuristics such as genetic algorithms.	B · Survey / tutorial / community	—	Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review Citation details Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
uses method 3D Bin Packing to Reinforcement Learning	RL-based 3D packing/loading has been reported recently, but its industrial maturity is not verified here. [unverified]	D · Expert inference	—	No source listed

Relationships to this entry 2

shares method with
Pallet Loading to 3D Bin Packing
Distributor's pallet loading, which stacks boxes on a pallet, is methodologically connected to container loading and 3D bin packing.
EvidenceB · Survey / tutorial / community
Equiv.E3 · structural analogy
Sources
- Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review
  Citation details
  Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
industry instance of
Container Loading to 3D Bin Packing
Container loading is an industrial instance of 3D bin packing, adding practical constraints such as stability, load bearing, and loading order.
EvidenceA · Peer-reviewed / official
Equiv.E1 · same base, different side constraints
Sources
- Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review
  Citation details
  Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.

Relationships to this entry
Relationship	Claim	Evidence	Equiv.	Sources
shares method with Pallet Loading to 3D Bin Packing	Distributor's pallet loading, which stacks boxes on a pallet, is methodologically connected to container loading and 3D bin packing.	B · Survey / tutorial / community	E3 · structural analogy	Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review Citation details Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.
industry instance of Container Loading to 3D Bin Packing	Container loading is an industrial instance of 3D bin packing, adding practical constraints such as stability, load bearing, and loading order.	A · Peer-reviewed / official	E1 · same base, different side constraints	Source grade: A — Peer-reviewed / officialConstraints in container loading – A state-of-the-art review Citation details Bortfeldt, A., Wäscher, G. (2013). Constraints in container loading – A state-of-the-art review. EJOR 229(1):1-20.