Solving a Real-Life Distributor’s Pallet Loading Problem

Abstract

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.

Mixed Palletizing for Smart Warehouse Environments: Sustainability Review of Existing Methods

“…In particular, one matheuristic approach for solving palletizing problems has two phases. Firstly, classical 2D packing algorithms define the number of layers, and secondly, the calculated layers are packed on pallets by means of a specialized mixed integer linear programming model solved with Gurobi solver [18]. In the same way, a two-step strategy algorithm is proposed where an Extreme Point heuristic algorithm is utilized to group items into layers, while an exact method algorithm stacks layers to form pallets [44].…”

“…A literature search was conducted on databases such as Google Scholar, Science Direct, arXiv, the Institute of Electrical and Electronics Engineers (IEEE), Multidisciplinary Digital Publishing Institute (MDPI), and Scopus. More than 200 scientific papers were searched and reviewed related to their relevance, in accordance with which this procedure appears under various names, like "palletising" [7][8][9], "palletizing" [10][11][12], "palletisation" [13,14], "palletization" [6,15,16], "pallet loading problem" [17][18][19], "pallet placement" [13,14,20], and "3D Bin Packing Problem" (pallet version as opposed to packing packages and loading containers) [21,22]. To address this ongoing issue, a typology was proposed in 1990 [23] and in 2007 [24] by researchers that concerns the area of Cutting and Packing problems.…”

“…Mixed palletizing is a Three-Dimensional Bin Packing Problem (3DBPP) where items are rectangular boxes that are to be fitted orthogonally into as few rectangular containers of identical size as possible [24]. A Distributor's Pallet Packing/Loading Problem is a term that also appears in the literature, with the intent of distinguishing it from its Manufacturer counterpart, where all boxes are identical [18]. In all proposed solutions, there are constraints present (geometry, weight, stability [25], compression [21], center of gravity [26][27][28], shipment cost [29], fragility [30], packing sequence [31], load bearing [32,33], and profit optimization [34]) that make computations even more complex.…”

Application of Machine Learning Methods for Pallet Loading Problem

“…Barros et al [6] studied the complexity of an arrangement of cargo in a pallet and proved through principal component analysis and multiple linear regression that the number of boxes is a strong predictor of complexity in this challenging problem. Moreover, the Distributor's Pallet Loading Problem (DPLP) is an NP-hard problem and has multiple layers of complexity stemming from various constraints imposed on it, such as the stability of a layer to sustain upper layers, the compression limit of each layer to sustain the weight of the layers placed on top of it, and the weight limit imposed by the company carrying out the packaging [7]. Nonetheless, loading boxes onto a container in such a manner that the 3D volume is utilized to the maximum is also a computationally demanding problem since it requires addressing various constraints, such as the orientations in which a box can be loaded as well as stability constraints [8].…”

Numerical and Evolutionary Optimization 2021

“…In [1], Dell'Amico and Magnani consider a pallet loading problem subject to stability requirements for which they propose a novel two-phase metaheuristic approach. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm.…”