Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Committee Chair/Advisor

Adams, Warren

Committee Member

Gupte , Akshay

Committee Member

Saltzman , Matthew


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.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.