Métodos de análise da complexidade no problema de empacotamento de paletes do distribuidor - Barros, Hugo André de Almeida (2019)
In the pallet loading problem, one of the main goals is to allocate the highest number of boxes as possible, to minimize empty spaces in the pallet. Those empty spaces are called trim-loss. If all boxes have a rectangular shape, which is the most common one, it is possible to pack them so that their faces are coincident with themselves. By doing that, the trim-loss can be minimized. Although loading a pallet may seem linear to most people, some customers impose restrictions that increase the complexity of the pallet loading. Due to that, to evaluate the complexity of a packed pallet, some metrics were created. They consist in an evaluation of a set of parameters that are inherent to the pallet loading process and affect its complexity. After analysing some of those constraints and loading methods enforced by some pickers in a real company, it was possible to obtain samples where the metrics were applied to learn which parameters add the most complexity in the pallet loading process. In the future, after knowing the relevancy of each parameter, the metrics can be used in pallet generation tools to learn how complex is the loading of a certain pallet and study new and easier ways to load the boxes that reduce the complexity of such process. Two statistical tests were then used to analyse the samples retrieved: the principal components analysis and the multiple linear regression. The first is used to combine multiple variables into a smaller set that represents the most relevant information, while the multiple linear regression uses the variables and respective observations to calculate a model that can predict the value of the complexity of a packed pallet in given circumstances. In the first one, it was learned that three principal components were extracted, but since the third one explained a small percentage of the total data variance, it was decided to retain only two components: the box quantities, which explains 41% of the total variance, followed by the box dimensions, explaining 28% of the total variance. The multiple linear regression revealed that the component representing the box quantities, which contains the Number of Box Types, Number of Column Piles, Number of Boxes, Time Spent Packing, and Percentage of Fragile Boxes variables is the component that mostly increase the complexity of pallet cargo arrangements. Although the model can predict the data that was obtained with an average accuracy, some of the coefficients ended up being small, those being related to the components Box Dimensions, which has the Number of Heavy Boxes, Average Box Weight, Average Maximum Width variables, and Height Between Pile and Worker and Number variables, meaning that they aren’t very significant towards evaluating the complexity of a pallet loading process. Using a multiple linear regression with the 9 variables showed that the variable who adds more complexity is the Number of Column Piles. Overall, the results obtained were acceptable, and showed that the variable that adds more complexity is the ones that the pickers see as adding more complexity, and also that the results of the multiple regression with the components match the one using the original variables. It is worth noting that this variable is subjective, meaning that one worker’s perception on the complexity may not match others’ perception. Despite having obtained only one variable being considered as statistically significant towards explaining the complexity in the pallet loading problem, it doesn’t mean it’s the only one that adds complexity.