张晶蓉,贺占文,周艳杰,李玉民.基于混合整数规划的工厂产品托盘打包及装箱问题研究[J].包装工程,2023,44(17):143-151.
ZHANG Jing-rong,HE Zhan-wen,ZHOU Yan-jie,LI Yu-min.Pallet Packing and Container Loading of Factory Products Based on Mixed Integer Programming Approach[J].Packaging Engineering,2023,44(17):143-151. |
| 基于混合整数规划的工厂产品托盘打包及装箱问题研究 |
| Pallet Packing and Container Loading of Factory Products Based on Mixed Integer Programming Approach |
| 投稿时间：2022-12-02 |
| DOI：10.19554/j.cnki.1001-3563.2023.17.017 |
| 中文关键词: 集装箱 装载 托盘打包 工厂产品 混合整数规划 启发式算法 |
| 英文关键词: container loading pallet packing factory products mixed integer programming heuristic algorithm |
| 基金项目:国家自然科学基金资助项目(72201252);河南省社科规划决策咨询项目(2022JC10);河南省高校智库研究项目(2023ZKYJ21) |
|
| 摘要点击次数: |
| 全文下载次数: |
| 中文摘要: |
| 目的 针对工厂产品的托盘打包及装箱问题，提出一种优化产品在托盘上的布局以及托盘与产品整体在集装箱中的布局方法，以最大化集装箱的空间利用。方法 在满足现实约束的条件下，以最大化产品装载体积为目标建立混合整数规划模型。考虑问题的复杂性，本文将所研究的问题分解为2个子问题，并建立两阶段装载模型进行求解。第1阶段，建立二维集装箱装载模型，确定多种托盘类型在集装箱底面的平面布局;第2阶段，建立三维托盘装载模型，确定产品在托盘上的立体布局。鉴于精确求解该问题耗时较大，本文针对2个子问题设计两阶段启发式算法求解。为验证模型及算法的有效性，采用2组不同规模大小的算例进行测试。结果 算例结果表明，在小、大2种规模算例中，装载率平均差值分别为0和−0.5%，计算时间相差较大，本文提出的模型及算法在合理的时间内获得了最优解或近似最优解。结论 本研究能够为工厂产品的托盘打包及装箱提供快速高效的解决方案。 |
| 英文摘要: |
| The work aims to propose a method to optimize the layout of products on pallets and the layout of pallets and products in containers to maximize container space utilization, thus solving the problem in pallet packing and container loading of factory products. A mixed integer programming model was developed to optimize the volume of the loaded product under realistic constraints. Due to the complexity of the problem, the studied problem was divided into two sub-problems and a two-stage loading model was established for solution. In the first stage, a two-dimensional container loading model was established to determine the plane layout of pallets on the bottom of containers. In the second stage, a three-dimensional pallet loading model was established to determine the 3D layout of products on the pallet. In view of that accurate solution was time-consuming, a two-stage heuristic algorithm was designed to solve the two sub-problems. To verify the effectiveness of the model and algorithm, two groups of examples with different sizes were adopted. The results showed that the average difference of loading rate was 0 and −0.5% in small and large-scale experimental cases, respectively, but the calculation time was quite different. The model and algorithm proposed could obtain the optimal solution or approximate optimal solution in a reasonable time. This study can provide a fast and efficient solution for pallet packing and container loading of factory products. |
|
查看全文
查看/发表评论 下载PDF阅读器 |
| 关闭 |
渝公网安备 50010702501716号