![]() Therefore, even if a mathematically optimal solution cannot be guaranteed, an algorithm that produces a practical result in a practical amount of time is sought.Ī PC can generate a large number of patterns and select the most efficient one. This is the combinatorial optimization problem. Therefore, it is practically impossible to find the optimal solution, and it is a very difficult problem even using a computer. ![]() The number of combination patterns increases factorially with each additional member, and the calculation time required easily exceeds the history of the universe. However, as mentioned above, this is impossible even with a PC if the number of members is as many as 10. The only way to find the optimal solution is to enumerate and compare all the patterns. What is a combinatorial optimization problem? And, especially when cutting the first large plate, it is important to consider whether to cut longitudinally or shortitudinally, as this will change the efficiency later on. In some cases, it may be more efficient to assign the parts to larger stock plates and remnants. ![]() On the basis of First Fit, for example, for the size of a fixed length boardĪssign which of the parts and which of the parts will fit well together. This eliminates major mistakes.ĭetermine the combination of components that fit together efficiently. In the end, there is no "one-size-fits-all" method, and it is usually a matter of cutting a large piece from as small a stock plate as possible. In the end, there is no "right" way to do it. I also found a "genetic algorithm," which sounds cool, but it's based on a better pattern, and you have to hit a lot more of them. ![]() I don't remember where I read it.Īnother method I found was the Monte Carlo method, but again, it was just a method where if you shoot a lot, you will eventually hit. I tried my best to read up on the method, and was disappointed to find that it was just a matter of cutting from a large part panel, even though it included formulas and a great deal of explanation. This is one of the keywords that came up in various searches to create a plate cutting software. If the member can be rotated or oriented, the pattern will be multipliedfurther.įirst Fit Method - Which part is to be cut from which stock plate (or existing edge material)?.When taking a piece of material, the shape of the end piece will changedepending on whether it is cut longitudinally or shortitudinally first.Decide from which original or leftover material the member is to be taken.The pattern is multiplied by the number of plates and remnants.If there are n pieces, there are n! different orders in which to take thepieces.Let's consider an algorithm for calculating the cutting of severaldifferentsized members from several different types of stock panel.įirst, we decide which members are to be cut. The actual Excel sheet can be downloaded fromĪlgorithm for calculating a highly efficient cutting layout forcuttingplanks with shearing/panel saws, etc. In this case, the yield is higher when the part is oriented vertically. If we change the orientation of the member (swap the horizontal andvertical),we get How many 400*300 pieces can be obtained from an 1800*900mm originalplate? If this is 2-dimensional and all the members are the same "Int" is here assumed to be a function that truncates after the decimalpoint,such as in Excel. To simplify the story, let's first consider a 1D member of the same size.Īssuming the width of the saw is 3mm, how many 200mm can be takenfrom1800mm? However, this can be calculated with Excel. How many pieces of the same size can be taken from one original plate? It isnotpossible to calculate the plate count using only functions. There are macros available, so it is not theoretically impossible.However,dedicated software should be developed for the calculation volume. Because of the combinatorial optimizationproblem,a dedicated application is required. As it turns out, Excel is not suitable forplatecutting calculations.
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