Date of Award
12-2024
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair/Advisor
Dr. Cheng Guo
Committee Member
Dr. Boshi Yang
Committee Member
Dr. Yongjia Song
Abstract
The Unit Commitment (UC) problem finds an optimal schedule for a set of generators by minimizing the total operation cost subject to demand and operational constraints. The UC problem is often modeled with a mixed-integer linear program (MILP). We employ the Shapley-Folkman Theorem to provide a bound on the size of fractional solutions of its convex hull relaxation. This result is used to obtain a bound on the optimality gap between the MILP and the convex hull relaxation, which is further tightened using several problem-specific properties of UC. We conduct extensive numerical experiments to study the tightness of this threshold, and how it is impacted by different parameters.
Recommended Citation
Henderson, Lauren, "Bounding the Convex Hull Relaxation of the Unit Commitment Problem with the Shapley-Folkman Theorem" (2024). All Theses. 4435.
https://open.clemson.edu/all_theses/4435