A computational improvement to Wang's two-dimensional cutting stock algorithm

Abstract

Wang developed algorithms [ Opns Res. 31, 573–586 (1983)] for the constrained two-dimensional guillotine cutting stock problem. Given a bound on trim waste based on a feasible cutting pattern, her algorithms are guaranteed to generate the optimal guillotine cutting pattern. In this paper, we discuss two algorithms: (1) an algorithm, SPAM, which quickly generates solutions to the constrained two-stage two-dimensional guillotine cutting stock problem, and (2) an enhanced version of Wang's Algorithm One [1] which significantly improves its computational performance. SPAM is used to generate an initial upper bound for the minimum trim waste of the more general (non-staged) constrained guillotine cutting stock problem. Then, this bound is used in both Wang's Algorithm One and the enhanced version of it to solve 120 cutting stock problems. On average, the enhanced version was more than 25 times faster than the original algorithm, and the computational benefits of the enhancements increased as the problem complexity increased.