Review of Dynamic Stability Metrics and a Mechanical Model Integrated with Open Source Tools for the Container Loading Problem

Abstract

Traditional considerations related to dynamic stability constraint in the Container Loading Problem (CLP), such as boxes with insufficient lateral support, have proven to be inaccurate when compared with the results of dynamic simulations where the boxes are subjected to real world conditions. In response to this, two indicators for dynamic stability were introduced; the number of fallen boxes and the number of boxes likely to be damaged in case of acceleration. These indicators, however, have not yet been estimated using a mechanical approach.An open source application (PackageCargo) was developed to calculate, visualize, and save efficient packing patterns to instances of the CLP, including a dynamic simulation environment to obtain performance indicators related the dynamic stability of such patterns. The physics engine used in the application is capable of trading accuracy for simulation speed, and is in most cases non-deterministic. Through PackageCargo we evaluated the accuracy of new dynamic stability metrics.Additionally, a mechanical model that measures dynamic stability without the need to subject the packing pattern to a physics simulation was developed, based on a dynamic analysis of the forces and accelerations acting upon the boxes and using the kinetic parameters of the load such as mass distribution, coefficient of friction, and rigidity.