![]() That solution is used as input to the second part of the algorithm, a "Knapsack" algorithm, which searches for an unused pattern that improves the solution, i.e. Specifically, for each part length, cut as many as possible of that length from the longest available stock piece) until enough parts have been cut. ![]() Here we generate enough columns to define a solution, usually not the optimal one. The solution uses a technique called "Delayed Column Generation". Since there may be hundreds (or thousands or millions) of columns, they cannot all be generated. The intersections of the input matrix contain the number of that length (row) which can be cut from that pattern (column). The different lengths required are rows of the solution matrix and the unique cutting patterns are the columns. This is an LP (Linear programming) problem with the complication that the number of different ways to cut each stock piece grows exponentially with the number of lengths required and may get too large for traditional LP techniques. ![]()
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