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The three-dimensional bin packing problem with variable box size
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DOI：10.1016/j.tre.2026.105038.png)
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Abstract
En 中文
Most research on Three-dimensional Bin Packing Problem (3DBPP) treats box size as fixed throughout the packing process. However, in practical packing scenarios, boxes containing garments, bedding items, or plastic foam materials are deformable, exhibiting both compressibility and extensibility. To better capture this reality, we introduce the Three-dimensional Bin Packing Problem with Variable Box Sizes (3DBPP-VBS), which allows changing box sizes during packing. We formulate the problem as a Mixed Integer Linear Programming (MILP) model and develop a beam search-based algorithm (BSA) for its solution. While Gurobi can obtain optimal solutions for small-scale instances, BSA efficiently generates high-quality near-optimal solutions for larger instances within practical computational times. Extensive experimental results on the Martello and BR instances demonstrate that allowing box size variation significantly enhances space utilization, with improvements of 6.06% in small-size Martello instances and 1.22% in large-size BR instances. Our findings highlight the potential value of considering variable box sizes for improving the efficiency of the 3DBPP, particularly in small-scale scenarios such as packaging operations for express delivery and e-commerce companies.
Keywords:
Three-dimensional bin packing problem
Deformable boxes
Mixed Integer linear programming
Beam search
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8.8
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896
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