Computational Performance Evaluation of Column Generation and Generate-and-Solve Techniques for the One-Dimensional Cutting Stock Problem

Authors:
Open Access
Publisher website
Google Scholar
Abstract
The Cutting Stock Problem (CSP) is an optimisation problem that roughly consists of cutting large objects in order to produce small items. The computational effort for solving this problem is largely affected by the number of cutting patterns. In this article, in order to cope with large instances of the One-Dimensional Cutting Stock Problem (1D-CSP), we resort to a pattern generating procedure and propose a strategy to restrict the number of patterns generated. Integer Linear Programming (ILP) models, an implementation of the Column Generation (CG) technique, and an application of the Generate-and-Solve (G&S) framework were used to obtain solutions for benchmark instances from the literature. The exact method was capable of solving small and medium sized instances of the problem. For large sized instances, the exact method was not applicable, while the effectiveness of the other methods depended on the characteristics of the instances. In general, the G&S method presented successful results, obtaining quasi-optimal solutions for the majority of the instances, by employing the strategy of artificially reducing the number of cutting patterns and by exploiting them in a heuristic framework.
Funding Information
  • Fundação Edson Queiroz
  • Universidade de Fortaleza

This publication has 29 references indexed in Scilit: