[1] Yi Junmin, Wang Dupeng, Zhou Jing, et al. Impact of box ratio and pinwheel pattern on the pallet loading problem [J]. Journal of Southeast University (English Edition), 2009, 25 (2): 267-270. [doi:10.3969/j.issn.1003-7985.2009.02.026]

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Impact of box ratio and pinwheel pattern on the pallet loading problem()

货物长宽比及转轮样式对托盘装箱问题的影响

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 2

Page:

267-270

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2009-06-30

Info

Title:

Impact of box ratio and pinwheel pattern on the pallet loading problem

货物长宽比及转轮样式对托盘装箱问题的影响

Author(s):

Yi Junmin^{1, 2}, Wang Dupeng¹, Zhou Jing¹

¹School of Management and Engineering, Nanjing University, Nanjing 210093, China
²Department of Industrial Engineering and Logistics, East China Jiaotong University, Nanchang 330013, China

伊俊敏^{1, 2}, 王笃鹏¹, 周晶¹

¹南京大学工程管理学院, 南京 210093; ²华东交通大学工业工程与物流系, 南昌 330013

Keywords:

packing;  pallet loading problem;  loading pattern;  box ratio;  pinwheel pattern

装箱;  托盘装箱问题;  装箱样式;  长宽比;  转轮样式

PACS:

O221.7;O157.3

DOI:

10.3969/j.issn.1003-7985.2009.02.026

Abstract:

The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem(PLP)is identified after a survey on the loading pattern.The definitions, elements, categories, generating algorithms of the pinwheel pattern are discussed and a uniform symmetric pinwheel notation is proposed.Based on the forming geometry of a pinwheel, the pinwheel structure is analyzed in terms of the innate box ratio, the box/block orientation and the box number by combinatorial and geometrical methods.A revised data set for the PLP with an area ratio range from 1 to 76 and a box ratio range from 1 to 10 is proposed.All pinwheel instances with this data set are calculated, and box ratio range is obtained for each possible pinwheel pattern, which can be found for all non-prime numbers of boxes.And a high box ratio makes an optimal pinwheel pattern more likely appear.Results identify the impact of the above pinwheel pattern and the box ratio on the pallet loading problem.

在对托盘装箱问题的装箱样式进行调查后, 研究了解决托盘装箱问题的一种具有优势的转轮装箱样式.对该样式的定义、组成要素、分类和产生的算法进行了讨论, 并提出一种对称式转轮样式的统一命名方式.基于转轮样式的几何形成条件, 运用组合与几何学的方法, 就货物本身的长宽比特性、货物取向和单层货物数量对转轮样式的结构影响进行了讨论, 提出了托盘装箱问题的修改数据集:面积比范围为1~76, 货物长宽比范围为1~10.并计算了这一数据集下所有箱数为非质数的转轮样式实例, 以及每一可能转轮样式的货物长宽比范围.计算结果显示货物长宽比越大越有可能获得转轮样式的最优解, 表明转轮样式和货物长宽比的确影响托盘装箱问题.

References:

[1] Alvarez-Valdes R, Parrenob F, Tamarita J M.A branch-and-cut algorithm for the pallet loading problem [J].Computers and Operations Research, 2005, 32(11):3007-3029.
[2] Martins G H A, Dell R F.Solving the pallet loading problem [J].European Journal of Operational Research, 2008, 184(2):429-440.
[3] Morabito R, Morales S R.A simple and effective recursive procedure for the manufacturer’s pallet loading problem [J].Journal of the Operational Research Society, 1998, 49(8):819-828.
[4] Arenales M, Morabito R.An and/or-graph approach to the solution of two-dimensional non-guillotine cutting problems [J].European Journal of Operational Research, 1995, 84(3):599-617.
[5] Scheithauer G, Terno J.The G4-heuristic for the pallet loading problem [J].Journal of the Operational Research Society, 1996, 47(4):511-522.
[6] Bolz H A, Hagemann G E.Material handling handbook [M].New York:Ronald Press, 1958:214-216.
[7] Carpenter H, Dowsland W B.Practical considerations of the pallet-loading problem [J].Journal of the Operational Research Society, 1985, 36(6):489-497.
[8] Dowsland K A.A combined data-base and algorithmic approach to the pallet-loading problem [J].Journal of the Operational Research Society, 1987, 38(4):341-345.
[9] Dowsland K A.The three-dimensional pallet chart [J].Journal of the Operational Research Society, 1984, 35(10):895-905.
[10] Neliβen J.New approaches to the pallet loading problem [R/OL].(1993-08-19)[2008-01-12].ftp://ftp.informatik.rwth-aachen.de/pub/reports/others/pallet.ps.gz.

Memo

Memo:

Biographies: Yi Junmin(1969—), male, graduate, associate professor;Zhou Jing(corresponding author), female, doctor, professor, jzhou@nju.edu.cn.
Foundation item: The National Natural Science Foundation of China(No.70571033, 70831002).
Citation: Yi Junmin, Wang Dupeng, Zhou Jing.Impact of box ratio and pinwheel pattern on the pallet loading problem[J].Journal of Southeast University(English Edition), 2009, 25(2):267-270.

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