The main objective in the one-dimensional cutting stock problem (1D-CSP) is to minimize material costs. In practice, it is useful to focus on auxiliary objectives, one of which is to reduce the number of different cutting patterns. This paper discusses the classical integer IDCSP, where only one type of stock object is included. Meanwhile, the demands of various items must be precisely satisfied in the constraints. In other words, no overproduction or underproduction is allowed. Therefore, to solve this issue, a variable-to-constant method based on a new mathematical model is proposed. In addition, we integrate the approach with two other representative methods to demonstrate its effectiveness. Both benchmark instances and real instances are used in the experiments, and the results show that the methodology is effective in reducing patterns. In particular, in terms of the solutions to the real-life instances, the proposed approach presents a 31.93 to 37.6% pattern reduction compared to other similar methods (including commercial software).
Keywords: column generation; cutting; cutting pattern; cutting stock; optimization algorithms.