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container loading problem based on robotic loader system: An optimization approach

EXPERT SYSTEMS WITH APPLICATIONS 2024年 236卷

作者： Jiao, Guoshuai Huang, Min Song, Yang Li, Haobin Wang, Xingwei Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Natl Univ Singapore Dept Ind Syst Engn & Management Singapore 117576 Singapore Northeastern Univ Coll Comp Sci & Engn Shenyang 110169 Liaoning Peoples R China

With the development of intelligent logistics technology, some companies began to use robots instead of humans to load cargo. This paper studies a novel container loading problem based on robotic loader system (CLP-RLS). Different from the existing robot-packable pattern in the literature, the robotic loader system in this paper consists of a depalletizing robot, an automatic telescopic roller line and a loading robot, in which the loading robot will enter the carriage along with the automatic telescopic roller line. In CLP-RLS, it is necessary to consider not only many practical constraints already in the literature, including load balancing, orientation, stability, and multi-drop but also two new constraints related to robotic loader system: pallet continuity constraint (the loading sequence of cargo on the same pallet is continuous) and robot position constraint (the robot can only load cargo incrementally from the front to the back of the truck). Due to the difficulty in modeling CLP-RLS and the large scale of the real-case instances, we present a tree search approach based on wall-building to solve CLP-RLS, intending to find a feasible loading scheme for the RLS to minimize the length required to load all cargo. The effectiveness of the proposed approach is verified through both real-case instances and numerical instances.

关键词： Intelligent logistics container loading problem Robotic loader system Tree search Heuristic

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A block-building constraint programming model for the container loading problem

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COMPUTERS & OPERATIONS RESEARCH 2025年 182卷

作者： Liu, Chang Smith-Miles, Kate Wauters, Tony Costa, Alysson M. Univ Melbourne Sch Math & Stat Melbourne Australia CODeS Leuven Dept Comp Sci Gebroeders Smetstr 1 B-9000 Ghent Belgium Univ Melbourne ARC Training Ctr Optimisat Technol Integrated Meth Melbourne Australia

The container loading problem involves packing a set of given rectangular boxes into a larger rectangular container of fixed size, with the objective of maximizing the volume of the loaded boxes. Most of the literature on the container loading problem and its variants proposes heuristic approaches that can find good solutions quickly. Current exact methods are mostly limited to mixed-integer programming (MIP) formulations, which often struggle to obtain good solutions for large problem instances. In this paper, we introduce two exact constraint programming models for the container loading problem. The first model uses integer and binary variables to assign boxes to valid positions and orientations within the container. The second model enhances this by incorporating the concept of block-building, commonly used in heuristic methods. Extensive computational experiments on classical benchmark instances from the literature show that the solutions obtained with the proposed models significantly outperform those achieved with existing MIP models. We also perform an instance space analysis of the proposed models to map the models' performances across problem instances, providing deeper insights into the strengths and weaknesses of the block-building approach.

关键词： Packing container loading problem Constraint programming Mathematical modeling Block building Instance space analysis

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Exact decomposition approaches for a single container loading problem with stacking constraints and medium-sized weakly heterogeneous items

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2024年 125卷

作者： Delorme, Maxence Wagenaar, Joris Tilburg Univ Dept Econometr & Operat Res Tilburg Netherlands

We consider a real -world three-dimensional container loading problem in which the objective is to maximize the volume of the items packed into a single vehicle. While container loading problems have been extensively studied in the literature, our case study displays a set of item features (rotation, medium-sized dimensions, stackability, weak heterogeneity) that was not often considered together in previous research papers. In fact, we show that some of these features can be exploited in an innovative way to derive more effective exact algorithms. We first describe a compact integer programming model to solve the problem exactly together with a number of ad hoc reduction procedures and modeling tricks to enhance the empirical performance of the model. We then present a sequential approach where one generates item columns in a first stage and then solves a two-dimensional knapsack problem afterwards and show that each of the two components is NP -hard. Thereafter, we introduce a set of exact algorithms based on Benders' decomposition. We identify three ways to split the problem decisions (deciding if an item should be packed, in which column, in which x-coordinate, and in which y-coordinate) into the classical master -subproblem framework and we observe trough an extensive set of computational experiments on both real and randomly generated instances that not all decomposition methods are as competitive as the others. We conclude our work by showing how relevant extensions of the problem related to item fragility and customer visit order can be taken into account. Overall, this work aims at establishing a bridge between the theoretical field of two-dimensional packing problems and the more practical field of container loading problems.

关键词： container loading problem Operations research applications Exact algorithms Integer linear programming Benders' decomposition

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The container loading problem with cargo stability: a study on support factors, mechanical equilibrium and grids

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ENGINEERING OPTIMIZATION 2021年第7期53卷 1192-1211页

作者： Oliveira, Liliane de Azevedo de Lima, Vinicius Loti de Queiroz, Thiago Alves Miyazawa, Flavio Keidi Univ Fed Goias Inst Math & Technol Catalao Brazil Univ Estadual Campinas Inst Comp Campinas Brazil

Approaches based on mechanical equilibrium are described for handling cargo stability in the container loading problem. This problem is expressed as an integer programming model and solved with a branch-and-cut algorithm. Cutting planes are added to avoid generating unstable packings. Three grids of points are used to pack items, and then their weakness and advantages, when combined with the cargo stability, are discussed. Computational results on 180 instances from the literature show that the support factor underestimates the solution, as the proposed approaches allowed stable packings with a higher volume.

关键词： container loading problem cargo stability equilibrium of material bodies support factor integer linear programming

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The development of the refrigerated-container loading problem model for perishable fishery products considering internal temperature distribution

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS 2023年第1期10卷 Article: 2051092页

作者： Rusdiansyah, Ahmad Adetio, Irza Rachmadiar Dewi, Ratna Sari Inst Teknol Sepuluh Nopember Dept Ind & Syst Engn Surabaya Indonesia

The paper aims to develop a refrigerated-container loading problem (R-CLP) model for perishable fishery products in a cold chain. The novelty of this study is to enhance the models and algorithms of CLP to deal with two different temperatures in reefers: those of cargoes and those of containers. This research considers synchronising the required optimum temperature of products and the internal temperature distribution of reefers to minimise the quality deterioration of the products. The objective of the R-CLP is to minimise total loading costs while fulfiling quality requirement of the products. The quality requirement is based on the temperature distribution inside the reefer, which was obtained by computational fluid dynamics (CFD) simulation. The model includes traditional loading constraints of CLP. Moreover, this research has developed a heuristics algorithm that deals with various types of products, cargo box dimensions and temperature distribution data. A prototype application has been developed to simulate the loading plan visually using an application prototype named REFLOAD. The numerical experiment shows the ability of the model to minimise the quality loss while maintaining the utilisation of the reefer. The R-CLP algorithm can reduce the total loading costs to about 16% compared with those of CLP algorithm.

关键词： container loading problem refrigerated container perishable products computational fluid dynamics fishery products quality deterioration

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A MILP Approach for the Multi-Drop container loading problem Resolution in Logistics 4.0 29

A MILP Approach for the Multi-Drop Container Loading Problem...

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29th Mediterranean Conference on Control and Automation (MED)

作者： Cavone, Graziana Carli, Raffaele Troccoli, Giorgio Tresca, Giulia Dotoli, Mariagrazia Polytech Bari Dept Elect & Informat Engn Bari Italy

ISBN: (纸本)9781665422581

This paper addresses the multi-drop container loading problem (CLP), i.e., the problem of packing multiple bins -associated to multiple deliveries to one or more customers- into a finite number of transport units (TUs). Differently from the traditional CLP, the multi-drop CLP has been rarely handled in the literature, while effective algorithms to automatically solve this problem are needed to improve the efficiency and sustainability of internal logistics. To this aim, we propose a novel algorithm that solves a delivery-based mixed integer linear programming formulation of the problem. The algorithm efficiently determines the optimal composition of TUs by minimizing the unused space, while fulfilling a set of geometric and safety constraints, and complying with the delivery allocation. In particular, the proposed algorithm includes two steps: the first aims at clustering bins into groups to be compatibly loaded in various TUs;the latter aims at determining the optimal configuration of each group in the related TU. Finally, the proposed algorithm is applied to several realistic case studies with the aim of testing and analysing its effectiveness in producing stable and compact TU loading configurations in a short computation time, despite the high computational complexity of the multi-drop CLP.

关键词： container loading problem Multi-drop MILP Optimization Logistics

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A hybrid adaptive large neighborhood search algorithm for the large-scale heterogeneous container loading problem

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期189卷 115909-115909页

作者： Li, Ying Chen, Mingzhou Huo, Jiazhen Tongji Univ Sch Econ & Management Shanghai 201804 Peoples R China Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China

This paper aims to solve the large-scale heterogeneous container loading problem (HCLP), which is an extensive form of the multiple container loading problem, in a limited time. The target is to choose a set of containers of different sizes to accommodate all products and minimize the wasted space rate. Although the heterogeneous container selection problem is a general problem in the logistics industry, few related studies have been conducted. This study also considers some practical constraints, such as weight limits and suspension constraints. A hybrid adaptive large neighborhood search (HALNS) algorithm, which includes a set of original destroy-repair operators, especially for heterogeneous container selection problems, and integrates a heuristic packing algorithm, is proposed to solve the problem in an acceptable time. To verify the efficiency of the proposed algorithm, computational experiments on real-world instances from a multinational logistics company are performed, and the results are compared with those of other existing algorithms. The results indicate that the proposed algorithm outperforms other algorithms for the HCLP.

关键词： container loading problem Hybrid adaptive large neighborhood search Heuristic packing algorithm

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An optimization approach for a complex real-life container loading problem

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2022年 107卷 102559-102559页

作者： Gajda, Mikele Trivella, Alessio Mansini, Renata Pisinger, David HEC Lausanne Dept Operat CH-1015 Lausanne Switzerland Swiss Fed Inst Technol Inst Transport Planning & Syst CH-8092 Zurich Switzerland Univ Brescia Dept Informat Engn I-25123 Brescia Italy Tech Univ Denmark DTU Management DK-2800 Lyngby Denmark

We consider a real-world packing problem faced by a logistics company that loads and ships hundreds of trucks every day. For each shipment, the cargo has to be selected from a set of heterogeneous boxes. The goal of the resulting container loading problem (CLP) is to maximize the value of the cargo while satisfying a number of practical constraints to ensure safety and facilitate cargo handling, including customer priorities, load balancing, cargo stability, stacking constraints, positioning constraints, and limiting the number of unnecessary cargo move operations during multi-shipment deliveries. Although some of these constraints have been considered in the literature, this is the first time a problem tackles all of them jointly on real instances. Moreover, differently from the literature, we treat the unnecessary move operations as soft constraints and analyze their trade-off with the value maximization. As a result, the problem is inherently multi-objective and extremely challenging. We tackle it by proposing a randomized constructive heuristic that iteratively combines items in a preprocessing procedure, sorts them based on multiple criteria, uses randomization to partially perturb the sorting, and finally constructs the packing while complying with all the side constraints. We also propose dual bounds based on CLP relaxations. On large-scale industry instances, our algorithm runs in a few seconds and outperforms (in terms of value and constraints handling) both the solutions constructed manually by the company and those provided by a commercial software. The algorithm is currently used by the company generating significant economic and CO2 savings. (C) 2021 Published by Elsevier Ltd.

关键词： container loading problem Real-life constraints Randomized constructive heuristic Industry collaboration

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Analysis of the Impact of Physical Internet on the container loading problem 12th

Analysis of the Impact of Physical Internet on the Container...

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12th International Conference on Computational Logistics (ICCL)

作者： Ferreira, Ana Rita Ramos, Antonio G. Silva, Elsa Polytech Porto INESC TEC Porto Portugal Polytech Porto Sch Engn Porto Portugal INESC TEC Porto Portugal

ISBN: (纸本)9783030876722;9783030876715

In the Physical Internet supply chain paradigm, modular boxes are one of the main drivers. The dimension of the modular boxes has already been subject to some studies. However, the usage of a modular approach on the container loading problem has not been accessed. In thiswork, we aim to assess the impact of modular boxes in the context of the Physical Internet on the optimization of loading solutions. A mathematical model for the CLP problem is used, and extensive computational experimentswere performed in a set of problem instances generated considering the Physical Internet concept. From this study, it was possible to conclude for the used instances that modular boxes contribute to a higher volume usage and lower computational times.

关键词： Physical internet Modular boxes container loading problem

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A beam search algorithm for the biobjective container loading problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期286卷 417-431页

作者： Araya, Ignacio Moyano, Mauricio Sanchez, Cristobal Pontificia Univ Catolica Valparaiso Escuela Ingn Informat Ave Brasil 2950 Valparaiso V Region Chile

In this work we deal with a biobjective variant of the single container loading problem. The problem consists in packing a set of boxes into a large box or container. In addition to the usual objective related to maximize the volume utilization, we include a second objective consisting on maximizing the total profit (e.g., weight or priority) of the loaded boxes. We propose to adapt bsg, a state-of-the-art single-objective algorithm for solving the biobjective problem. bsg can be seen as an incomplete version of a breadth first search in which each level of the search tree is restricted to a fixed number of promising nodes. In order to select the most promising nodes, the algorithm constructs a solution from them by using a greedy algorithm and evaluates the objectives. To deal with two objectives, we propose to select nodes by using well-known multi-objective criteria based on dominance and crowding distance related to the greedy evaluations. We go a little bit further and orient the greedy algorithm to one objective or the other by using a mechanism which changes the configuration of the heuristic function dynamically. The proposal is compared with bsg in a set of well-known instances reporting a 24% increase in the hypervolume indicator. Compared to other biobjective approaches, the reported results are also promising. Codes and test instances are available in: https://***/rilianx/Metasolver#bo-bsg (C) 2020 Elsevier B.V. All rights reserved.

关键词： multiobjective optimization container loading problem beam search greedy

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