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(英文)

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.