Schaefer, Andrew J2024-01-242024-01-242024-052023-12-04May 2024Karagoz, Aysenur. "Single-Scenario Facet Preservation for Stochastic Mixed-Integer Programs." (2023). Master's thesis, Rice University. https://hdl.handle.net/1911/115396https://hdl.handle.net/1911/115396EMBARGO NOTE: This item is embargoed until 2024-11-01We consider improving the polyhedral representation of the extensive form of an SMIP. Given a facet-defining valid inequality for a single-scenario version of the SMIP, we provide conditions under which the same inequality remains facet-defining for the extensive form. Our main result gives necessary and sufficient conditions for a facet-defining inequality for a single-scenario version to be facet-defining for the extensive form. We then present several implications, which show that various recourse structures from the literature satisfy these conditions. For example, for an SMIP with simple recourse, any single-scenario facet is also a facet for the extensive form. More general recourse structures require additional mild assumptions for these conditions to hold.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.stochastic mixed-integer programmingpolyhedral theoryvalid inequalitiesThesis2024-01-24