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starts with a list of m orders, each requiring q j {\displaystyle q_{j}} pieces, where j = , ... , m {\displaystyle j= ,\ldots ,m} . we then construct a list of all possible combinations of cuts (often called "patterns"). let n {\displaystyle n} be the number of those patterns. we associate with each pattern
a positive integer variable x i {\displaystyle x_{i}} , representing how many times pattern i {\displaystyle i} is to be used, where i = , ... , n {\displaystyle i= ,\ldots ,n} . the linear integer program is then: min ∑ i = n c i x i {\displaystyle \min \sum _{i= }^{n}c_{i}x_{i}} s.t. ∑ i = n a i j...
https://en.wikipedia.org/wiki/Cutting_stock_problem