Accelerated Benders Decomposition for Variable-Height Transport Packaging Optimisation

TL;DR

This paper introduces an accelerated Benders decomposition approach for optimizing variable-height transport packaging, significantly reducing computation time and memory usage in large-scale 3D bin-packing problems.

Contribution

It presents novel acceleration techniques, including a KD-Tree algorithm and analytical transformations, to efficiently solve large-scale mixed integer problems in packaging optimization.

Findings

Achieved about three hours solution time on a laptop for a problem with over seven billion variables.

Implemented a KD-Tree algorithm to avoid exhaustive grid evaluation.

Realized a three order of magnitude speedup in runtime and significant memory savings.

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.