What is the pallet loading problem?
This page is intended for those who may be interested in learning a little more about Pallet Loading and associated problems.
The Pallet Loading Problem in the scientific literature typically refers to the solution of one of two problem types:
An example of the first of these is the packing of identical cardboard cases in layers on a wooden pallet for transportation and storage. The second problem is that encountered when filling a lorry / trailer / shipping container with a variety of cargo.
In most practical situations the identical case problem requires layers of product to be built up. For this reason it can be simplified to that of packing identical smaller rectangles within a larger containing rectangle. This problem may appear very simple to solve, however it can be very difficult to ensure that the solution is the best possible (optimal). Mathematically this problem may be what is termed as NP complete. Even today researchers are carrying out PhD studies on just this problem. For some sets of small and large rectangles it may be possible to produce optimal solutions in a few milliseconds, however by changing (say) the size of the smaller rectangles by a few millimeters the problem may require many hours of computing time.
Given the above comments it is not surprising to learn that the solution to problems involving mixed cargo is even more complex.
The Role of Computer Software.
At the simplest level the role of products such as PALLETMANAGER is to calculate how to maximise the number of identical cases packed within the length, width and height of the pallet space or container. This alone can be very valuable - fitting (say) 5% more product into the available space will save 5% of transportation and storage costs!!
A further role might be to examine the influence of alternate type of case / shrink wrap. New European recycling regulations make this an area of increasing concern.
If it is possible to consider re-designing the case major savings may be possible. Perhaps a case of 24 'cans of baked beans' is currently packed as 3 layers of 8 cans. What if 2 layers of 12 cans were used - the 12 cans on each layer might be arranged in various arrangements (e.g. 6*2; 3*4). Each case design will provide different packaging costs and may be better or worse (in terms of number of cans fitted) when packed on the pallet or into the container.
What if the product size itself can be changed? Here the software needs to help the user by investigating product design changes within limits set by the user. This may require investigating thousands of different designs (perhaps just a few mm. different in size) within a few seconds. For each of these designs the culmination is the calculation of how many cases of the calculated size fit within the loading space - as described above a very complex task.
Problems such as those described above are just a few of those encountered in the general area of Cutting and Packing. The solution techniques used are often highly complex and fall into the subject areas of operational research and mathematics. Those wishing to research the area further may find the SICUP web pages of interest.
The problems described above, in which mathematical solution methods are used in solving business problems, fall into the area know as Operational Research (OR). Some further examples of how OR techniques are applied in business can be found on the website of the British OR Society.
Gower Optimal Algorithms Ltd, Swansea, U.K.
Page last updated 10th December 2015.