Schaefer, Andrew J.2021-05-032021-05-032021-052021-04-28May 2021Brown, Seth. "A Gilmore-Gomory Construction of Integer Programming Value Functions." (2021) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/110397">https://hdl.handle.net/1911/110397</a>.https://hdl.handle.net/1911/110397In this thesis, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. We use a Gilmore-Gomory approach to find parametrized IP value functions over a restricted set of variables. We introduce the notion of maximal connected \color{black}subsets of level sets - volumes in which changes to the constraint right-hand side have no effect on the value function - and relate these structures to IP value functions and optimal solutions.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Value functionlevel setparametrized optimizationThesis2021-05-03