Robust optimization and data-driven modeling of tissue paper packing considering cargo deformation

Abstract

This paper considers the container loading problem (CLP) for efficient packing of low density tissue paper products, for which, volume, instead of weight, is the key driver for logistic decision-making. Tissue products are susceptible to deformation during the packing process. However, this aspect is usually overlooked when defining the optimal packing policy. In this work, we take this aspect into account and develop a novel methodology for CLP optimization of tissue paper products. The deformation is modeled as a function of known product characteristics and packing process variables using data-driven models. Several modeling approaches are compared, including those based on variable selection, regularization and projection to latent variables. The data-driven model is then included into a Mixed Integer Non Linear Programming (MINLP) CLP. A worst-case robust optimization approach is considered, resulting in solutions that are robust against data-driven model uncertainty. The methodology is applied to a real case study from a portuguese tissue paper mill concerning the packing of toilet paper rolls in wood shipping pallets. Predicted results show an average gain of 4 to 7% in load density in the worst-case scenario, compared to current practice. The deformation model is validated experimentally on the industrial site, by testing optimal configurations which show gains in load density up to 40%. The methodology can be easily extended to other tissue paper products as well as any low density product showing reversible deformation during packing.