English

Accelerated Benders Decomposition for Variable-Height Transport Packaging Optimisation

Optimization and Control 2023-08-03 v1

Abstract

This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem as a large-scale mixed integer problem (with over seven billion variables) and demonstrate various acceleration techniques to solve it efficiently in about three hours on a laptop. We present a KD-Tree algorithm to avoid exhaustive grid evaluation of the 3D-bin-packing, provide analytical transformations to accelerate the Benders decomposition, and an efficient implementation of the Benders sub problem for significant memory savings and a three order of magnitude runtime speedup.

Keywords

Cite

@article{arxiv.2308.01104,
  title  = {Accelerated Benders Decomposition for Variable-Height Transport Packaging Optimisation},
  author = {Alain Lehmann and Wilhelm Kleiminger and Hakim Invernizzi and Aurel Gautschi},
  journal= {arXiv preprint arXiv:2308.01104},
  year   = {2023}
}
R2 v1 2026-06-28T11:46:23.042Z