A Pattern-Generation Algorithm for the One-Dimensional Cutting Problem with Pattern Reduction

Abstract

The one-dimensional cutting stock problem with pattern reduction (CSPPR) is to find a solution with the minimum material cost and minimum number of different cutting patterns (setups). The primary objective is to minimize material cost. In practice, a common auxiliary objective is to reduce the number of setups. In this paper, we develop a bi-objective integer linear programming model for the CSPPR and propose a variable-to-constant (VTC) approach combined with a column generation technique (VTCCG) to generate the pattern set. Three sets of instances are tested in a computational experiment. The results of some instances show a 22.22% material cost saving and a 46.15% pattern reduction compared to the classical column generation technique. Moreover, for some practical instances, our solution can compete with several state-of-the-art heuristics.

Keywords: Cutting, multi-objective optimization, cutting pattern, column generation, optimization algorithms