A Local Search Approach for One Dimensional Cutting Stock Problem

One dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which has many applications in, e.g., steel, paper and fiber industries. To define an instance of 1D-CSP, we are given sufficient number of stock rolls which have the same length L, and m types of products with given lengths (l1, l2, . . . , lm) and demands (d1, d2, . . . , dm). A cutting pattern is a combination of products cut from a stock roll. A solution to 1D-CSP consists of a set of cutting patterns and the corresponding frequencies, i.e., the number of times each pattern is applied.