Improved Mixed-Integer Models of a Two-Dimensional Cutting Stock Problem

Author

William Lassiter, Clemson UniversityFollow

Date of Award

5-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Committee Chair/Advisor

Adams, Warren

Committee Member

Gupte , Akshay

Committee Member

Saltzman , Matthew

Abstract

This paper is concerned with a family of two-dimensional cutting stock problems that seeks to cut rectangular regions from a finite collection of sheets in such a manner that the minimum number of sheets is used. A fixed number of rectangles are to be cut, with each rectangle having a known length and width. All sheets are rectangular, and have the same dimension. We review two known mixed-integer mathematical formulations, and then provide new representations that both economize on the number of discrete variables and tighten the continuous relaxations. A key consideration that arises repeatedly in all models is the enforcement of disjunctions that a vector must lie in the union of a finite collection of polytopes. Computational results demonstrate a relative performance of the different formulations.

Recommended Citation

Lassiter, William, "Improved Mixed-Integer Models of a Two-Dimensional Cutting Stock Problem" (2014). All Theses. 1944.
https://open.clemson.edu/all_theses/1944