Thesis (Ph. D.)--Auburn University, 2009. / Abstract. Vita. Includes bibliographical references (p. 109-117).

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Erera, Martin; Committee Chair: Nemhauser, George; Committee Chair: Savelsbergh, Martin; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M.S. in Operation Research)--Naval Postgraduate School, June 2005. / Thesis Advisor(s): Javier Salmeron. Includes bibliographical references (p. 75). Also available online.

Στην παρούσα Διπλωματική Εργασία θα ασχοληθούμε με το πασίγνωστο πρόβλημα της Παραγοντοποίησης Ακεραίων. Η προσέγγιση μας είναι από τη μεριά της Επιστήμης των Υπολογιστών και της Υπολογιστικής Πολυπλοκότητας. Προσπαθούμε να κατανοήσουμε γιατί η Παραγοντοποίηση Ακεραίων θεωρείται ένα υπολογιστικά δύσκολο πρόβλημα και να δούμε τις πρακτικές εφαρμογές και συνέπειες αυτής της θεώρησης. / In the present Diploma Thesis we are going to deal with the very well known problem of Integer-Factoring. Our approach is from the side of Computer Science and Computational Complexity. We are trying to understand why Integer-Factoring is widely considered as a hard problem to solve and see the practical applications of this consideration.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd W. Easton / Jessica L. Heier Stamm / Locomotives in the U.S. use over 3 billion gallons of fuel each year and faster refueling can increase rail network capacity without the infrastructure cost associated with new terminals or tracks. This thesis introduces the locomotive refueling system configuration problem (LRSCP), which seeks to improve efficiency in refueling yards through new technologies or policies. This research also creates two new methods to solve LRSCP. The first method uses an integer program to solve the off-line LRSCP and develop a static refueling policy. The train refueling integer program, TRIP, maximizes the weighted number of train combinations that can be refueled without delay. TRIP is optimized and its outputs are used as inputs to a simulation developed in Simio® for testing and validation. The second method creates an integrated integer program and simulation to solve the on-line LRSCP and produces a dynamic refueling policy. This tool, built in Python, incorporates a different integer program, the strike line integer program (SLIP), into the simulation. SLIP determines the optimal refueling assignment for each incoming train. The simulation incorporates SLIP’s solution for testing and validation. This tool is truly integrated and requires approximately 300 instances of SLIP to simulate a single day. Based on experimental results, solving either TRIP or SLIP and incorporating the optimal refueling policy improves railyard operations by 10 to 30%. This impact is statistically significant and increases the capacity of a railyard. Additionally, it impacts other important parameters such as time spent in the yard and the maximum queue for the railyard. Furthermore, there is a significant decrease in wasted time and an improvement to railyard efficiency. Implementing either method should increase a railyard’s capacity and significantly increase revenue opportunities.

We introduce a new pure integer rounding heuristic, ZI Round, and compare this heuristic to recent extremely fast pure integer rounding heuristic Simple Rounding. Simple Rounding was introduced in the non-commercial code SCIP. ZI Round attempts to round each fractional variable while using row slacks to maintain primal feasibility. We use the MIPLIB 2003 library for the test set. The average time in our run per instance for both Simple Rounding and ZI Round was 0.8 milliseconds, but ZI Round found more feasible solutions with a the same or better objective value. Also the average time to solve the lp relaxation per instance was 2.2 seconds, so these two rounding heuristics are several magnitudes faster than other heuristics which must use the lp solver, including diving heuristics.We also show that ZI Round performs well on a set covering class and a railway crew scheduling class.

The design of a chilled water plant involves selecting the size and type of chillers to be employed and determining the operating strategy. The types may include both gas engine and electric motor driven chillers. The issues that have to be considered in the selection problem are to incorporate external and internal factors into the decision making. External factors may include the utility rate schedules, the cooling load profile, and the outdoor temperature profile. Internal factors may include the chiller performance characteristics, initial and maintenance costs, and the chiller(s) operating strategy. A mathematical model representing the chilled water plant design problem is developed. The problem is approached as a mixed integer linear programming problem where non-linear chiller performance curves are transformed into linear constraints through the use of integer variables. The optimization task is to select the best cooling plant configuration and operating strategy to minimize life cycle cost. A solution procedure is developed which decomposes the optimization problem to reduce extensive computation time. Two case studies are provided to investigate the implementation of the mathematical model. / Master of Science

A new minimum spanning tree (MST) based heuristic for clustering biological data is proposed. The heuristic uses MSTs to generate initial solutions and applies a local search to improve the solutions. Local search transfers the nodes to the clusters with which they have the most connections, if this transfer improves the objective function value. A new objective function is defined and used in the heuristic. The objective function considers both tightness and separation of the clusters. Tightness is obtained by minimizing the maximum diameter among all clusters. Separation is obtained by minimizing the maximum number of connections of a gene with other clusters. The objective function value calculation is realized on a binary graph generated using the threshold value and keeping the minimumpercentage of edges while the binary graph is connected. Shortest paths between nodes are used as distance values between gene pairs. The efficiency and the effectiveness of the proposed method are tested using fourteen different data sets externally and biologically. The method finds clusters which are similar to actual ones using 12 data sets for which actual clusters are known. The method also finds biologically meaningful clusters using 2 data sets for which real clusters are not known. A mixed integer programming model for clustering biological data is also proposed for future studies.

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