Comparison of the most popular methods of loading

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With the rapid development of China's market economy, logistics activities are increasingly showing its importance. Distribution, as an important link in logistics, has increasingly received widespread attention. Distribution includes many links such as sorting, assembly, handling, loading and transportation of goods, among which loading is the key link in the whole distribution link, "Rational distribution" has become an internal requirement of today's logistics development

in actual transportation, for the safety and convenience of products, many products are loaded into rectangular wooden boxes or cartons of various sizes after production, and then these boxes are loaded into containers for transportation. Here, the problem we study is the placement and arrangement of a batch of rectangular goods in containers, In order to maximize the utilization rate of container space, generally speaking, this kind of problem is called three-dimensional packing problem

2 classification and factors to be considered of container loading problem

container loading problem is divided into two categories according to the limited and unlimited number of containers: (1) the number of containers is unlimited, and the goods must be loaded completely, so as to minimize the number of containers used; (2) The number of containers is limited, and the number of goods exceeds the loading capacity of the container. It is required that the total volume of the loaded goods reach the maximum, so as to maximize the space utilization rate

according to the type of goods loaded, it can be divided into three categories: (1) the types of all goods (volume, three-dimensional size, etc.) are the same; (2) The types of goods are different, and there are many types, while the quantity of each type of goods is small; (3) The types of goods are different, but the types are few, and the quantity of each type of goods is large, and the third type can seek the optimal loading scheme by combining the solutions of the first and second types. Therefore, the container loading problem can also be divided into two types according to the same and different types of goods

at the same time, the constraints to be considered are: (1) the load-bearing (fragility) of the goods themselves, heavy rather than light (2) for goods in different locations, try to meet the "first come and then load", Facilitate the handling and unloading when arriving at each station (3) some goods must be isolated, and the machine noise is large. Some goods should not be mixed with other goods, such as food and chemical products; Some dangerous goods are isolated or repacked according to the national regulations on the transportation of dangerous goods (4) the maximum bearing weight is not allowed to be exceeded (5) the deviation between the center of gravity and the geometric centroid should not be too large (6) the stability of cargo stacking, etc.

3 research methods and analysis and comparison of container loading problems

as mentioned earlier, container loading problems can be divided into two categories: limited and unlimited containers, while in practical application, the second category of problems is relatively common, Therefore, the second kind of problem is analyzed here

3.1 loading of the same type of goods

the model of this kind of loading is relatively simple. The main research method is to put the goods in order (the length of the goods is parallel to the length of the container) and then horizontally (the length of the goods is perpendicular to the length of the container to enhance the transformation and upgrading of enterprises) or horizontally and then in order according to the known length and width of the goods and containers, and calculate the utilization rate of these two loading forms, Choose the appropriate loading method

for this kind of problem, the container stowage model is given. The row/column constraint method is applied to container stowage, which simplifies the calculation steps. For the same example, the cargo size is 25cm × 35cm × 50cm, container size 2.28M × 2.38m × 11.9m, using the above two methods respectively, the loading results are obtained: the volume utilization rate of the former is 96.95%, and the latter reaches 97.22%. It can be seen that the latter has better loading effect for this example

3.2 loading of different types of goods

this type of loading mainly depends on the idea of spatial decomposition, thus deriving a series of algorithms, For example: heuristic algorithm trigeminal tree space segmentation algorithm

genetic algorithm and other

3.2.1 trigeminal tree space segmentation algorithm. This algorithm selects a main commodity through the combination of the utilization of commodities in all directions in three-dimensional space, and then combines it with other commodities by changing the quantity of this commodity in one direction, so as to optimize the actual utilization of space; Then deal with the remaining scattered space through the integration of space to meet the requirements of optimal loading. This method is applicable to the loading of goods with small types and large quantities of each type. Using this method, the volume utilization rate of container loading can reach more than 90%

3.2.2 heuristic algorithm. This algorithm is a common algorithm in container loading. Based on the trigeminal tree space segmentation algorithm, a heuristic algorithm based on space decomposition is designed, And when loading goods, the layout is carried out according to the sequencing and positioning rules. The so-called sequencing rules are the sequence of loading goods. The main sequencing rules are: sequencing according to the decreasing area of the bottom of the object; Descending order according to the longest side of the object and descending order according to the volume of the object, among which the third most commonly used positioning rule refers to the layout positioning rule of goods, mainly including: angle occupying strategy, that is, the object is first placed in a corner of the layout space; The placement strategy starts from a corner and is placed in order along one side of the layout space; First place along the four sides of the layout space, and then fill the center. Usually, the corner occupying strategy is adopted. The heuristic algorithm designed after adding sequencing rules and positioning rules is effective for the loading situation with a large variety of goods and a small number of goods in each type. The hierarchical heuristic algorithm is adopted. Each layer is determined by a goods selected with certain rules (called layer definition box LDB), and each layer is decomposed in space, Each sub space formed by gradually loading may have several placement forms, which change. Therefore, the cleaning after each use is very critical. The placement form of the box can obtain more loading methods, so that the best scheme can be taken in a wider range. However, each box takes into account all possible placement forms, which requires a lot of calculation and is difficult to realize. By changing the placement form of LDB on each layer, the relevant data of that layer can be changed, It is feasible to update the loading method and select the layer with the highest space utilization rate as the optimal loading scheme of this layer.

for the same example:

the result is that the volume utilization rate of the former can reach 82.8%, and that of the latter is 85.25%, It can be seen that the effect of the latter is better for this example

3.2.3 genetic algorithm. This algorithm is an adaptive global optimization probability search algorithm formed by simulating the genetic and evolution process of organisms in the natural environment. It uses genetic algorithm as a tool to deal with multi-objective problems through the weight coefficient change method and constraints through the penalty function method, Thus, the genetic algorithm is more suitable for solving the complex container loading problem than the space segmentation algorithm and heuristic algorithm, which creates infinite possibilities for the design of the complex double-layer structure

4 Conclusion

from the above, it can be found that there are still many problems in the research of container loading problem, for example, when there are too many goods to be packed, it may lead to "combination explosion", and in consideration of constraints, Sometimes, in order to simplify the solution, constraints are usually simplified, which reduces the practical application ability of the model. Through literature review, it is found that genetic algorithm, as a randomized search algorithm, has a strong global search ability and is more suitable for solving container loading problems. Of course, genetic algorithm itself has many shortcomings. Therefore, at present, it is based on genetic algorithm and improved, It can become a feasible idea to solve the container problem

information source: logistics technology

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