Thesis (Ph. D.)--University of Florida, 2004. / Title from title page of source document. Document formatted into pages; contains 135 pages. Includes vita. Includes bibliographical references.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 50-52). Also available in electronic version.

Thesis (M.S.)--University of Florida, 2005. / Title from title page of source document. Document formatted into pages; contains 61 pages. Includes vita. Includes bibliographical references.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 56-58). Also available in electronic version.

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaf 34).

During the last decade, there have been major advances in solving a class of large-scale real world combinatorial optimization problems. Such problems are formulated as Travelling Salesman Problems (TSP), some involving up to thousands of cities. These achievements, mainly due to the use of so called polyhedral techniques, have established the importance of the polyhedral study for various combinatorial optimization problems. This thesis studies polyhedral structures of two well known combinatorial problems: (i) precedence constrained single machine scheduling and (ii) TSP, both Symmetric TSP (STSP) and Asymmetric TSP (ATSP). These problems are of both theoretical interest and practical importance. Better knowledge of the polyhedral descriptions of these problems may facilitate the polyhedral study of more complex scheduling and routing problems. For the scheduling problem, we present two classes of facetial inequalities, which suffice to describe the linear system of the scheduling problem when the precedence constraints are series-parallel. We also propose a cutting plane procedure based on these facet cuts. The computational results show the procedure yields feasible schedules with relative deviations from the optimum less than 0.25% on the average and less than 1% in the empirical worst case. For TSPs, we explore a Hamiltonian path approach to the polyhedral study. We propose various facet extension techniques for deriving large classes of facets from known facets. In the STSP case, we propose new clique lifting results. In the ATSP case, we develop a Tree Composition method, which generates all non-spanning clique tree facetial inequalities. / Business, Sauder School of / Graduate

published_or_final_version / Mathematics / Master / Master of Philosophy

Approved for public release; distribution is unlimited / Surgical technicians at Naval hospitals provide a host of services related to surgical procedures that include handing instruments to surgeons, assisting operating room nurses, prepping and cleaning operating rooms, and administrative duties. At the Naval Medical Center San Diego (NMCSD), there are 83 surgical technicians that must be scheduled for these duties. The three military and one civilian hospital interviewed for this thesis manually schedule these duties. Weaknesses of these manual schedules exposed during interviews at these hospitals include assignment inequities and the time needed to create them. This thesis reports on an optimization based and spreadsheet implemented tool developed to schedule surgical technicians for both daily and weekly duties at a Naval hospital. We demonstrate the tool for the surgical technician department at NMCSD. The schedulers at NMCSD verify the utility of the developed tool and cite a drastic reduction in the time required to generate timely, equitable, and accurate schedules. The study also investigates historical operating room usage data and makes suggestions for improving scheduling practices based on these data. / Commander (Select), United States Navy

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