Application of Machine Learning Methods for Pallet Loading Problem

Because of continuous competition in the corporate industrial sector, numerous companies are always looking for strategies to ensure timely product delivery to survive against their competitors. For this reason, logistics play a significant role in the warehousing, shipments, and transportation of the products. Therefore, the high utilization of resources can improve the profit margins and reduce unnecessary storage or shipping costs. One significant issue in shipments is the Pallet Loading Problem (PLP) which can generally be solved by seeking to maximize the total number of boxes to be loaded on a pallet. In many previous studies, various solutions for the PLP have been suggested in the context of logistics and shipment delivery systems. In this paper, a novel two-phase approach is presented by utilizing a number of Machine Learning (ML) models to tackle the PLP. The dataset utilized in this study was obtained from the DHL supply chain system. According to the training and testing of various ML models, our results show that a very high (>85%) Pallet Utilization Volume (PUV) was obtained, and an accuracy of >89% was determined to predict an accurate loading arrangement of boxes on a suitable pallet. Furthermore, a comprehensive analysis of all the results on the basis of a comparison of several ML models is provided in order to show the efficacy of the proposed methodology.

Complexity Constraint in the Distributor’s Pallet Loading Problem

This paper presents a study on the complexity of cargo arrangements in the pallet loading problem. Due to the diversity of perspectives that have been presented in the literature, complexity is one of the least studied practical constraints. In this work, we aim to refine and propose a new set of metrics to measure the complexity of an arrangement of cargo in a pallet. The parameters are validated using statistical methods, such as principal component analysis and multiple linear regression, using data retrieved from the company logistics. Our tests show that the number of boxes was the main variable responsible for explaining complexity in the pallet loading problem.

Solving a Real-Life Distributor’s Pallet Loading Problem

We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected. The stability requirement imposes the following: (a) to load at level k+1 a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding α times the area of the layer of level k (where α≥1), and (b) to limit with a given threshold the difference between the highest and the lowest box of a layer. The compression constraint defines the maximum weight that each layer k can sustain; hence, the total weight of the layers loaded over k must not exceed that value. Some stability and compression constraints are considered in other works, but to our knowledge, none are defined as faced in a real-life problem. We present a matheuristic approach which works in two phases. In the first, a number of layers are defined using classical 2D bin packing algorithms, applied to a smart selection of boxes. In the second phase, the layers are packed on the minimum number of pallets by means of a specialized MILP model solved with Gurobi. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm.