Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science


Shier, Douglas R

Committee Member

Adams , Warren P

Committee Member

Dean , Brian C

Committee Member

Warner , Daniel D


We investigate several geometric packing problems (derived from an industrial setting) that involve fitting patterns of regularly spaced disks without overlap. We first derive conditions for achieving the feasible placement of a given set of patterns and construct a network formulation that, under certain conditions, allows the calculation of such a placement. We then discuss certain related optimization problems (e.g., fitting together the maximum number of patterns) and broaden the field of application by showing a connection to the well-known Periodic Scheduling Problem. In addition, a variety of heuristics are developed for solving large-scale instances of these provably difficult packing problems. The results of extensive computational testing, conducted on these heuristics, are presented.