The cutting stock problem with a given sequence of order lengths

This paper considers the one-dimensional cutting stock problem where the demand for a given number of order lengths is to be satisfied from an available supply of stock lengths required for a given set of jobs. Each job requires a specified order length. The sequence in which the jobs are processed is already specified. This paper transforms the one-dimensional cutting stock problem to a shortest route problem and shows that an optimal solution can be found in polynomial time.