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.

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.

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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In this dissertation, we consider two important problems pertaining to the analysis of transportation systems. The first of these is an approach-dependent, time-dependent, label-constrained shortest path problem that arises in the context of the Route Planner Module of the Transportation Analysis Simulation System (TRANSIMS), which has been developed by the Los Alamos National Laboratory for the Federal Highway Administration. This is a variant of the shortest path problem defined on a transportation network comprised of a set of nodes and a set of directed arcs such that each arc has an associated label designating a mode of transportation, and an associated travel time function that depends on the time of arrival at the tail node, as well as on the node via which this node was approached. The lattermost feature is a new concept injected into the time-dependent, label-constrained shortest path problem, and is used to model turn-penalties in transportation networks. The time spent at an intersection before entering the next link would depend on whether we travel straight through the intersection, or make a right turn at it, or make a left turn at it. Accordingly, we model this situation by incorporating within each link's travel time function a dependence on the link via which its tail node was approached. We propose two effective algorithms to solve this problem by adapting two efficient existing algorithms to handle time dependency and label constraints: the Partitioned Shortest Path (PSP) algorithm and the Heap-Dijkstra (HP-Dijkstra) algorithm, and present related theoretical complexity results. In addition, we also explore various heuristic methods to curtail the search. We explore an Augmented Ellipsoidal Region Technique (A-ERT) and a Distance-Based A-ERT, along with some variants to curtail the search for an optimal path between a given origin and destination to more promising subsets of the network. This helps speed up computation without sacrificing optimality. We also incorporate an approach-dependent delay estimation function, and in concert with a search tree level-based technique, we derive a total estimated travel time and use this as a key to prioritize node selections or to sort elements in the heap. As soon as we reach the destination node, while it is within some p% of the minimum key value of the heap, we then terminate the search. We name the versions of PSP and HP-Dijkstra that employ this method as Early Terminated PSP (ET-PSP) and Early Terminated Heap-Dijkstra (ETHP-Dijkstra) algorithms. All of these procedures are compared with the original Route Planner Module within TRANSIMS, which is implemented in the Linux operating system, using C++ along with the g++ GNU compiler. Extensive computational testing has been conducted using available data from the Portland, Oregon, and Blacksburg, Virginia, transportation networks to investigate the efficacy of the developed procedures. In particular, we have tested twenty-five different combinations of network curtailment and algorithmic strategies on three test networks: the Blacksburg-light, the Blacksburg-full, and the BigNet network. The results indicate that the Heap-Dijkstra algorithm implementations are much faster than the PSP algorithmic approaches for solving the underlying problem exactly. Furthermore, mong the curtailment schemes, the ETHP-Dijkstra with p=5%, yields the best overall results. This method produces solutions within 0.37-1.91% of optimality, while decreasing CPU effort by 56.68% at an average, as compared with applying the best available exact algorithm. The second part of this dissertation is concerned with the Classification and Regression Tree (CART) algorithm, and its application to the Activity Generation Module of TRANSIMS. The CART algorithm has been popularly used in various contexts by transportation engineers and planners to correlate a set of independent household demographic variables with certain dependent activity or travel time variables. However, the algorithm lacks an automated mechanism for deriving classification trees based on optimizing specified objective functions and handling desired side-constraints that govern the structure of the tree and the statistical and demographic nature of its leaf nodes. Using a novel set partitioning formulation, we propose new tree development, and more importantly, optimal pruning strategies to accommodate the consideration of such objective functions and side-constraints, and establish the theoretical validity of our approach. This general enhancement of the CART algorithm is then applied to the Activity Generator module of TRANSIMS. Related computational results are presented using real data pertaining to the Portland, Oregon, and Blacksburg, Virginia, transportation networks to demonstrate the flexibility and effectiveness of the proposed approach in classifying data, as well as to examine its numerical performance. The results indicate that a variety of objective functions and constraints can be readily accommodated to efficiently control the structural information that is captured by the developed classification tree as desired by the planner or analyst, dependent on the scope of the application at hand. / Ph. D.

This dissertation explores mathematical programming optimization models and algorithms for routing and scheduling ships in a maritime transportation system. Literature surveyed on seaborne transportation systems indicates that there is a scarcity of research on ship routing and scheduling problems. The complexity and the overwhelming size of a typical ship routing and scheduling problem are the primary reasons that have resulted in the scarcity of research in this area. The principal thrust of this research effort is focused at the Kuwait Petroleum Corporation (KPC) Problem. This problem is of great economic significance to the State of Kuwait, whose economy has been traditionally dominated to a large extent by the oil sector. Any enhancement in the existing ad-hoc scheduling procedure has the potential for significant savings. A mixed-integer programming model for the KPC problem is constructed in this dissertation. The resulting mathematical formulation is rather complex to solve due to (1) the overwhelming problem size for a typical demand contract scenario, (2) the integrality conditions, and (3) the structural diversity in the constraints. Accordingly, attempting to solve this formulation for a typical demand contract scenario without resorting to any aggregation or partitioning schemes is theoretically complex and computationally intractable. Motivated by the complexity of the above model, an aggregate model that retains the principal features of the KPC problem is formulated. This model is computationally far more tractable than the initial model, and consequently, it is utilized to construct a good quality heuristic solution for the KPC problem. The initial formulation is solved using CPLEX 4.0 mixed integer programming capabilities for a number of relatively small-sized test cases, and pertinent results and computational difficulties are reported. The aggregate formulation is solved using CPLEX 4.0 MIP in concert with specialized rolling horizon solution algorithms and related results are reported. The rolling horizon solution algorithms enabled us to handle practical sized problems that could not be handled by directly solving the aggregate problem. The performance of the rolling horizon algorithms may be enhanced by increasing the physical memory, and consequently, better solutions can be extracted. The potential saving and usefulness of this model in negotiation and planning purposes strongly justifies the acquisition of more computing power to tackle practical sized test problems. An ad-hoc scheduling procedure that is intended to simulate the current KPC scheduling practice is presented in this dissertation. It is shown that results obtained via the proposed rolling horizon algorithms are at least as good, and often substantially better than, results obtained via this ad-hoc procedure. / Ph. D.