Accelerated Benders Decomposition for Variable-Height Transport Packaging Optimisation

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.