Year
2025
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Committee Chairperson
Dr. Daniela Genova
Second Advisor
Dr. Zornitza Prodanoff
Third Advisor
Dr. Kening Wang
Abstract
The Bin Packing problem is a classic and widely studied optimization problem that arises naturally in applications like manufacturing, logistics, and memory allocation, where space and resource constraints are critical. In this thesis, we first demonstrate the NP-completeness of Bin Packing via a reduction from Three-Dimensional Matching, establishing its foundational complexity. We then survey core heuristics for the one-dimensional case and extend our analysis to two and three-dimensional variants, including both offline and online strategies. Special attention is given to stochastic bin packing, where item sizes are modeled as random variables drawn from distributions such as uniform, truncated normal, and multinomial. Our experimental results show that classical heuristics can vary significantly in efficiency depending on the underlying distribution, revealing both limitations and potential adjustments needed for real-world, uncertain environments.
Suggested Citation
Ambrose, Kyle T., "Analysis of bin packing variants" (2025). UNF Graduate Theses and Dissertations. 1356.
https://digitalcommons.unf.edu/etd/1356
Included in
Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Theory and Algorithms Commons