Doctor of Philosophy, The Ohio State University, 2008, Geography

The focus of this research is on location problems where potential facility sites are to be located in continuous space and demand is assumed continuously distributed, and includes the continuous p-center and coverage maximization problems. Relevant discrete location models are reviewed for the purpose of comparative analysis, including the vertex p-center problem and the maximal covering locational problem. First, this dissertation explores a simple but effective approach for solving large vertex p-center problems, the results of which are to be used as a benchmark for its continuous space counterpart. By introducing a neighborhood facility set, the p-center problem can be reformulated such that many redundant variables and constraints are removed but characteristics, including optimality, of the problem are preserved. The problem size of the reformulated model can be substantially smaller than in the original form. This enables the use of general-purpose optimization software to solve large vertex p-center instances. Application results are provided and discussed. The dissertation then studies the continuous space p-center problem. A Voronoi diagram heuristic has been proposed for solving the p-center problem in continuous space. However, important assumptions underlie this heuristic and may be problematic for practical applications. These simplifying assumptions include uniformly distributed demand, representing a region as a rectangle, analysis of a simple Voronoi polygon in solving associated one-center problems and no restrictions on potential facility locations. In this dissertation, the complexity of solving the continuous space p-center problem in location planning is explored. Considering the issue of solution space feasibility, this research presents a spatially restricted version of this problem and proposes methods for solving it heuristically. The performance of the heuristic is evaluated by comparison with the discrete p-center problem. Theoretical a (open full item for complete abstract)

Committee: Alan T. Murray PhD (Advisor); Morton E. O'Kelly PhD (Committee Member); Ningchuan Xiao PhD (Committee Member) Subjects: Geography; Operations Research