A Tree Search Algorithm for Solving the Container Loading Problem

This study focuses on a real-world case that is defined as an extension of the container loading problem (CLP) with weakly heterogeneous types of boxes. A company producing plastic cups wants to increase its efficiency in container loading operations. To solve the problem, a hybrid approach including a static rule to rank orders and integer nonlinear programming (INLP) models is developed. INLP models form box sizes according to the properties of the cups, and determine the position of the boxes in layers while simultaneously minimizing the layer-depth. The presented approach is tested on real-world cases and benchmark data sets. The results show that simultaneously forming boxes and solving the CLP increases the effectiveness of container loading operations.

The container loading problem (CLP) has been studied for maximising container space utilization as a method of lowering costs and increasing supply chain efficiency. This paper presents an approach to the CLP, in which a container is to be filled with a selection of cargoes from an available set so that the volume utilization of the container is maximized. By minimizing the outer volume of all the cargoes placed, tight arrangement of the cargoes can be achieved. Genetic algorithm (GA) with adaptive chromosome length formation has been used to find the optimum solution for the arranged cargoes to be placed with minimum space utilization. Two experiments have been conducted, to simulate the space optimization with fixed and unfixed number of cargoes. Our findings show that the GA with adaptive chromosome length proposes better arrangements of cargoes to give optimum space utilization for the container with 93.4% fitness difference percentage than the first generation’s fitness value.KeywordsSpace optimizationContainer loading problemGenetic algorithm

The correct layout of goods, objects or cargo, in the container's available space is considered a complex task. The study was motivated by the need to implement a solution to optimise container use in a steel industry company in the South of Brazil. This article has contributed to synthesising research on the three-dimensional container loading problem, highlighting classifications, constraints, and algorithms used in its resolution. A framework is presented and may be used as a road map for practical implementation as used in this research. As a practical contribution, this article presents several instances of one actual case application. Results showed reducing of formatting loads processing time in comparison with the traditional company approach.

Container loading problem is a kind of constrained three-dimensional bin packing problem in transportation industry. Container loading problem is complex combinatorial optimization problem, and the problem is NP-hard. The multiple container loading problem considered in this paper considered loading multiple containers simultaneously. In the problem the cargoes loaded are strongly heterogeneous cargoes. According to the complexity and the characters of multiple container problem as knapsack loading problem with strongly heterogeneous cargoes, scatter search algorithm is designed to solve the problem. Scatter search is a kind of metaheuristic algorithm based on population evolution which has been successfully applied in many fields of combinatorial optimization. Multiple neighborhood structures are used in the proposed scatter search algorithm, so the search effective of the algorithm and the quality of the obtained solutions can be improved. The simulations based on ample numerical examples show the effectiveness of the algorithm.

The multiple container loading problem with preference

This paper presents a novel hybrid approach for solving the Container Loading (CL) problem based on the combination of caving degree (CD) algorithm and variable neighborhood descent (VND) algorithm. More precisely, the first constructive phase is based on a caving degree (CD) heuristic developed for the single container loading problem. In the second improvement phase, four new moves are designed and combined in a VND structure. The resulting hybrid CD/VND algorithm is simple and quite fast and the extensive computational results on test instances from the literature show that the quality of the solutions is equal to or better than that obtained by the best existing heuristic procedures.

A caving degree approach for the single container loading problem

The paper presents a genetic algorithm (GA) for the container loading problem. The main ideas of the approach are first to generate a set of disjunctive box towers and second to arrange the box towers on the floor of the container according to a given optimization criterion. The loading problem may include different practical constraints. The performance of the GA is demonstrated by a numerical test comparing the GA and several other procedures for the container loading problem.

Constraints in container loading – A state-of-the-art review

Container loading problem (CLP) is a major problem for logistics in distributing cargoes to customers. As cost and time savings are important in shipping management, the process of cargo handling is essential. Cargoes must be effectively packed into a container. This paper, therefore, proposes container loading problem solving using a strategy for positioning non placement heuristics to reduce space between different buildings. Particle Swarm Optimization (PSO) is used to select the orientation of boxes to be packed into a single container to minimize the space which simulated in 3D. The condition for this solution is packing must be placed within the container with no part of the box overhanging the container, and the boxes must be placed parallel to the container surface area or other boxes. Weight and orientation of the box condition are also considered. The experiments are 12 cases. Different sizes of boxes and different sizes of containers are used. The experimental results are satisfied and it can be concluded that varied sizes of boxes are applicable for the space utilization in the container.

This article presents PackageCargo. A modular open-source application developed using the Unity game engine to calculate, visualize, and save efficient packing patterns to instances of the Container Loading Problem (CLP). The packing patterns are obtained through approximate optimization algorithms (metaheuristics). Additionally, the proposed tool allows us to estimate cargo stability metrics through the implementation of mathematical models and verify the results of said models using a simulation environment built with the PhysX library. The goal of this application was to create a usable decision support system suitable for industrial purposes as well as a platform for academic research. It is offering a modifiable framework that can adapt to the necessities of its users, saving them software development time while continuing to extend PackageCargo through community contributions. The resulting application was compared with commercial software solutions. Furthermore, each module was tested using the most successful approaches found in literature as benchmarks. The packing module was compared against the top-performing algorithm published to date, obtaining similar results in similar computational times. The simulation module for cargo stability was benchmarked against high-performance simulation software, validating its accuracy and performance. Accordingly, PackageCargo was found to have a competitive feature set useful in both academic and commercial settings. As future work, it is proposed to combine the different modules to solve more sophisticated variants of the CLP, like the container loading problem constrained to weight distribution profiles.

Formal methodologies and tools for decision support systems – An editorial

In this work, it is presented an exact method to solve the Single Container Loading Problem, which aims at deciding which items should be packed into the container in order to attain the maximum loaded value. The method is derived from the resolution of integer and constraint programming models. One of the integer programming models is a relaxation for the three-dimensional packing problem related to arranging items into the container. Besides that, it is measured how constraints related to priority conditions and vertical and horizontal load cargo stability can impact on the solution. Instances from the literature are solved in order to assess the method behavior in relation to the occupied volume and runtime. It has been observed that the highest volume losses have happened when the priority conditions are taken into consideration, while the runtime has increased when the vertical and horizontal stability constraints are considered.

The paper discusses the complexities of the air cargo loading problem and provides an effective approach based on the proposed heuristic to tackle the problem. The primitive class of problems like general bin packing, cutting stock and knapsack problems can be taken as the basic step towards the air-cargo loading problem. The discussed problem is very different in its nature in respect to the general pallet, container or truck loading problem. Generally, the container loading problems consider only the rectangular type of containers to load the items whereas in case of air-cargos, the shape of containers are very different such as irregular pentagon, hexagon etc. Apart from this, the objective of air cargo loading problem discussed in this paper is based on the minimization of the shipping cost of the container keeping in mind the number of constraints involved in loading. In past research literatures, most of the container loading problems are aimed to pack the container in such a way so that either the number of containers is minimized or the volume of the packed items are maximized. In this paper the objective function includes the shipment cost as the primary goal and the volume and weight of the containers are taken as constraints. A very interesting finding can be noticed in this paper which states that even if the container's volume is properly utilized the cost of shipment may be increased.

This paper presents a Fit Degree based Two-step Lookahead algorithm (FDTL) for the NP hard container loading problem. Several evaluation criteria, the fit degrees, are defined to construct different initial solutions as well as to explore different portions of the search space. Then a two-step lookahead tree search procedure is incorporated for the sufficient search such that the algorithm could find better layouts compared to a one-step lookahead tree search procedure. FDTL is tested on two sets of typical instances: 800 instances as proposed by Bischoff and Ratcliff (1995), and 15 instances as proposed by Loh and Nee (1992). Experiments show that this new algorithm improves among the known algorithms on the space utilization.