Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programs (IPs) are a commonly researched class of decision problems. These problems are used in various applications to help companies, governments, or individuals make better decisions by determining optimal resource allocations. While IPs are practical tools, they require an exponential amount of effort to solve, unless P = NP. This fact has led to much research focused on reducing the time required to solve IPs. Cutting planes are a commonly used tool for reducing IP solving time. Lifting, a process of changing the coefficients in an inequality, is often employed to strengthen cutting planes. When lifting, the goal is often to create a facet defining inequality, which is theoretically the strongest cutting plane. This thesis introduces two new lifting procedures for the Node Packing problem. The Node Packing problem seeks to select the maximum number of nodes in a graph such that no two nodes are adjacent. The first lifting method, the Simultaneous Lifting Expansion, takes two inequalities and combines them to make a stronger cut. It works for any two general classes of inequalities, as long as the requisite graph structures are met. The second method, the Cliques On Odd-holes Lifting (COOL) procedure, lifts from an odd-hole inequality to a facet defining inequality. COOL makes use of the Odd Gap Lifting procedure, an efficient method for finding lifting coefficients on odd holes. A computational study shows COOL to be effective in creating cuts in graphs with low edge densities.

Master of Science / Industrial & Manufacturing Systems Engineering / David H. Ben-Arieh / Telemental health systems, a form of telemedicine, use electronic communication media to provide patients in remote locations access to psychological and psychiatric specialists. The structure of telemental health systems has a major impact on their performance. Discrete-event simulations offer useful results concerning capacities and utilization of specific resources. Simulation, however, cannot provide theoretical properties of analyzed systems. Petri net representations of systems can overcome this shortfall, offering a wide range of easily-analyzed and useful properties. Their ability to model resource conflict, parallel activities, and failure modes fits nicely with the reality of telemental health systems. Analysis of behavioral properties of Petri nets can provide meaningful information for system analysts. The most useful properties include net boundedness, liveness, and non-reachability of certain undesirable states. The thesis discusses methods to find all these properties. Specifically, it provides property-preserving net reductions to facilitate analysis of boundedness and liveness and describes an integer programming model to solve reachability and coverability problems. Moreover, this thesis outlines a simulation analysis of synchronous and asynchronous telemental health systems. The paper then describes a Petri net model of a generic telemental health delivery system. The paper subjects the model to an integer programming model and net reduction. The integer programming model indicated that the number of resources in the system remains static, full utilization of resources at a given time is possible, conflict over resources is possible, and improper work prioritization is possible within the model. Net reduction and analysis with open-source software showed that the model is bounded and live. These results can aid telemedicine system architects in diagnosing potential process issues. Additionally, the methods described in the paper provide an excellent tool for further, more granular analysis of telemedicine systems.

Doctor of Philosophy / Department of Industrial and Manufacturing Systems Engineering / Shuting Lei / Shuting Lei / Femtosecond (fs) laser ablation possesses unique characteristics for micromachining, notably non-thermal interaction with materials, high peak intensity, precision and flexibility. In this dissertation, the potential of fs laser ablation for machining polyurea aerogel and scribing thin film solar cell interconnection grooves is studied. In a preliminary background discussion, some key literature regarding the basic physics and mechanisms that govern ultrafast laser pulse interaction with materials and laser micromachining are summarized. First, the fs laser pulses are used to micromachine polyurea aerogel. The experimental results demonstrate that high quality machining surface can be obtained by tuning the laser fluence and beam scanning speed, which provides insights for micromachining polymers with porous structures. Second, a new fs laser micro-drilling technique is developed to drill micro-holes in stainless steel, in which a hollow core fiber is employed to transmit laser pulses to the target position. The coupling efficiency between the laser and the fiber is investigated and found to be strongly related to pulse energy and pulse duration. Third, the fs laser with various energy, pulse durations, and scanning speeds has been utilized to pattern Indium Tin Oxide (ITO) glass for thin film solar cells. The groove width decreases with increasing pulse duration due to the shorter the pulse duration the more effective of the energy used to material removal. In order to fully remove ITO without damaging the glass, the beam scanning speed need to precisely be controlled. Fourth, fs laser has been utilized to scribe Molybdenum thin film on Polyimide (PI) flexible substrate for Copper Indium Gallium Selenide (CIGS) thin film solar cells. The experimental parameters and results including ablation threshold, single- and multiple-pulse ablation shapes and ablation efficiency were discussed in details. In order to utilize the advantages of the fs lasers, the fabrication process has to be optimized for thin film patterning and structuring applications concerning both efficiency and quality. A predictive 3D Two Temperature Model (TTM) was proposed to predict ablation characteristics and help to understand the fs laser metal ablation mechanisms. 3D temperature field evolution for both electrons and lattice were demonstrated. The ablation model provides an insight to the physical processes occurring during fs laser excitation of metals. Desired processing fluence and process speed regime can be predicted by calculating the ablation threshold, ablation rate and ablation crater geometry using the developed model.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Jessica L. Heier Stamm / Gifts-in-kind (GIK) donations negatively affect the humanitarian supply chain at the point of receipt near the disaster site. In any disaster, as much as 50 percent of GIK donations are irrelevant to the relief efforts. This proves to be a significant issue to humanitarian organizations because the quantity and type of future GIK are uncertain, making it difficult to account for GIK donations at the strategic planning level. The result is GIK consuming critical warehouse space and manpower. Additionally, improper treatment of GIK can result in ill-favor of donors and loss of donations (both cash and GIK) and support for the humanitarian organization. This thesis proposes a robust facility location approach that mitigates the impact of GIK by providing storage space for GIK and pre-positions supplies to meet initial demand. The setting of the problem is strategic planning for hurricane relief along the Gulf and Atlantic Coasts of the United States. The approach uses a robust scenario-based method to account for uncertainty in both demand and GIK donations. The model determines the location and number of warehouses in the network, the amount of pre-positioned supplies to meet demand, and the amount of space in each warehouse to alleviate the impact of GIK. The basis of the model is a variant of the covering facility location model that must satisfy all demand and GIK space requirements. A computational study with multiple cost minimizing objective functions illustrates how the model performs with realistic data. The results show that strategic planning in the preparedness phases of the disaster management cycle will significantly mitigate the impact of GIK.

Doctor of Philosophy / Department of Industrial and Manufacturing Systems Engineering / Zhijian Pei / Donghai Wang / The U.S. economy has been depending on petroleum-based liquid transportation fuels (such as gasoline, diesel, and jet fuels). Currently, about 50% of petroleum used in the U.S. is imported. Petroleum is a finite and non-renewable energy source and its use emits greenhouse gases. Therefore, it is extremely important to develop domestic sustainable alternatives for petroleum-based liquid transportation fuels. Ethanol produced from cellulosic biomass can be such an alternative. However, several technical barriers have hindered large-scale, cost-effective manufacturing of cellulosic ethanol. One such barrier is related to the low density of cellulosic feedstocks, causing high cost in their transportation and storage. Another barrier is low efficiency in conversion of cellulose to fermentable sugar (pretreatment and enzymatic hydrolysis are two major conversion processes), causing high cost in pretreatment and enzymatic hydrolysis of cellulosic biomass. Ultrasonic vibration-assisted (UV-A) pelleting increases both density and sugar yield of cellulosic feedstocks. Incorporating UV-A pelleting into cellulosic ethanol manufacturing may help realize cost-effective manufacturing of cellulosic ethanol. This PhD dissertation consists of 13 chapters. An introduction is given in Chapter 1. Chapter 2 presents a literature review on related topics. Experimental studies regarding effects of input parameters (such as particle size, pressure, and ultrasonic power) on output parameters (density, durability, stability, and sugar yield) are presented in Chapters 3–4. In Chapters 5–6, comparisons are made between UV-A pelleting and ring-die pelleting (a traditional pelleting method) in terms of pellet properties (density and durability), power consumption, and sugar yield under different conditions. Next, effects of input parameters (such as biomass type, particle size, moisture content, pelleting pressure, and ultrasonic power) on power consumption are studied in Chapters 7–9. Chapter 10 presents an investigation on biomass temperature in UV-A pelleting. Chapter 11 presents an investigation on effects of UV-A pelleting on sugar yield and chemical composition of cellulosic biomass. Chapter 12 presents an investigation on influence of UV-A pelleting on biomass characteristics (such as crystallinity index, thermal properties, and morphological structure). Finally, conclusions are presented in Chapter 13.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd Easton / This thesis introduces the Bay Crane Scheduling (BCS) problem and related BCS algorithm. The purpose of this algorithm is to optimize the assignment of jobs to overhead cranes as well as the sequence in which each crane performs its assigned jobs. This problem is unique from other Overhead Crane Scheduling (OCS) problems through its increased complexity. Up until now, OCS problems involve a set number of cranes operating in a single common area, referred to as a bay, and are unable to pass over each other. The BCS problem involves a varying number of active cranes operating in multiple bays. Each crane is allowed to move from one bay to the next, through specific locations called bridges. This is crucial to completing certain “special” jobs that require two cranes operating in unison to transport an item. The BCS algorithm employs two continuous time simulations in conjunction with an initial job-assignment algorithm and a Simulated Annealing (SA) improvement heuristic in order to minimize the non-productive crane time, while avoiding overloading any crane. To the extent of the author’s knowledge, this is the first time a continuous time simulation has been used to model an OC system. The BCS algorithm was originally developed for a large manufacturing facility, and when it was tested against the facility’s current scheduling methods, it shows a 20% improvement in the overall active crane time required to complete equivalent set of jobs. This improved efficiency is crucial to the manufacturing facility being able to increase its production rate without the addition of new cranes. In addition, BCS is statistically shown to be superior to the current strategy. The results from BCS are substantial and practitioners are encouraged to utilize BCS’s methodologies to improve other overhead crane systems.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Jessica L. Heier Stamm / During public health emergencies, organizations in charge require an immediate and e ffcient method of distributing supplies over a large scale area. Due to the uncertainty of where individuals will choose to receive supplies, these distribution strategies have to account for the unknown demand at each facility. Current techniques rely on population ratios or requests by health care providers. This can lead to an increased disparity in individuals' access to the medical supplies. This research proposes a mathematical programming model, along with a solution methodology to inform distribution system planning for public health emergency response. The problem is motivated by distribution planning for pandemic influenza vaccines or countermeasures. The model uses an individual choice constraint to determine what facility the individual will choose to receive their supplies. This model also determines where to allocate supplies in order to meet the demand of each facility. The model was solved using a decomposition method. This method allows large problems to be solved quickly without losing equity in the solution. In the absence of publicly-available data on actual distribution plans from previous pandemic response e fforts, the method is applied to another representative data set. A computational study of the equity and number of people served depict how the model performed compared to the actual data. The results show that implementing an individual choice constraint will improve the effectiveness of a public health emergency response campaign without losing equity. The thesis provides several contributions to prior research. The first contribution is an optimization model that implements individual choice in a constraint. This determines where individuals will choose to receive their supplies so improved decisions can be made about where to allocate the resources. Another contribution provided is a solution methodology to solve large problems using a decomposition method. This provides a faster response to the public health emergency by splitting the problem into smaller subproblems. This research also provides a computational study using a large data set and the impact of using a model that accounts for individual choice in a distribution campaign.

Doctor of Philosophy / Department of Industrial and Manufacturing Systems Engineering / Shing I. Chang / Profile analysis has drawn attention in quality engineering applications due to the growing use of sensors and information technologies. Unlike the conventional quality characteristics of interest, a profile is formed functionally dependent on one or more explanatory variables. A single profile may contain hundred or thousand data points. The conventional charting tools cannot handle such high dimensional datasets. In this dissertation, six unsolved issues are investigated. First, Chang and Yadama’s method (2010) shows competitive results in nonlinear profile monitoring. However, the effectiveness of removing noise from given nonlinear profile by using B-splines fitting with and without wavelet transformation is unclear. Second, many researches dealt with profile analysis problem considering whether profile shape change only or variance change only. Those methods cannot identify whether the process is out-of-control due to mean or variance shift. Third, methods dealing with detecting profile shape change always assume that a gold standard profile exists. The existing profile shape change detecting methods are hard to be implemented directly. Fourth, multiple nonlinear profiles situation may exist in real world applications, so that conventional single profile analysis methods may result in high false alarm rate when dealing multiple profile scenario. Fifth, Multiple nonlinear profiles situation may be also happened in designs of experiment. In a conventional experimental design, the response variable is usually considered a single value or a vector. The conventional approach cannot deal with when the format of the response factor as multiple nonlinear profiles. Finally, profile fault diagnosis is an important step after detecting out-of-control signal. However, current approaches will lead to large number of combinations if the number of sections is too large. The organization of this dissertation is as following. Chapter 1 introduce the profile analysis, current solutions, and challenges; Chapter 2 to Chapter 4 explore the unsolved challenges in single profile analysis; Chapter 5 and Chapter 6 investigate multiple profiles issues in profile monitoring analysis and experimental design method. Chapter 7 proposed a novel high-dimensional diagnosis control chart to diagnose the cause of out-of-control signal via visualization aid. Finally, Chapter 8 summarizes the achievements and contributions of this research.

Doctor of Philosophy / Department of Industrial and Manufacturing Systems Engineering / Todd Easton / Integer Programming (IP) problems are a common type of optimization problem used to solve numerous real world problems. IPs can require exponential computational effort to solve using the branch and bound technique. A popular method to improve solution times is to generate valid inequalities that serve as cutting planes. This dissertation introduces a new category of cutting planes for general IPs called inequality merging. The inequality merging technique combines two or more low dimensional inequalities, yielding valid inequalities of potentially higher dimension. The dissertation describes several theoretical results of merged inequalities. This research applies merging inequalities to a frequently used class of IPs called multiple knapsack (MK) problems. Theoretical results related to merging cover inequalities are presented. These results include: conditions for validity, conditions for facet defining inequalities, merging simultaneously over multiple cover inequalities, sequentially merging several cover inequalities on multiple variables, and algorithms that facilitate the development of merged inequalities. Examples demonstrate each of the theoretical discoveries. A computational study experiments with inequality merging techniques using benchmark MK instances. This computational study provides recommendations for implementing merged inequalities, which results in an average decrease of about 9% in computational time for both small and large MK instances. The research validates the effectiveness of using merged inequalities for MK problems and motivates substantial theoretical and computational extensions as future research.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd Easton / Integer programming (IP) is a class of mathematical models useful for modeling and optimizing many theoretical and industrial problems. Unfortunately, IPs are NP-complete, and many integer programs cannot currently be solved. Valid inequalities and their respective cuts are commonly used to reduce the effort required to solve IPs. This thesis poses the questions, do valid equality cuts exist and can they be useful for solving IPs? Several theoretical results related to valid equalities are presented in this thesis. It is shown that equality cuts exist if and only if the convex hull is not full dimensional. Furthermore, the addition of an equality cut can arbitrarily reduce the dimension of the linear relaxation. In addition to the theory on equality cuts, the idea of infeasibility conditions are presented. Infeasibility conditions introduce a set of valid inequalities whose intersection is the empty set. infeasibility conditions can be used to rapidly terminate a branch and cut algorithm. Applying the idea of equality cuts to the multi-demand multidimensional knapsack problem resulted in a new class of cutting planes named anticover cover equality (ACE) cuts. A simple algorithm, FACEBT, is presented for finding ACE cuts in a branching tree with complexity O(m n log n). A brief computational study shows that using ACE cuts exist frequently in the MDMKP instances studied. Every instance had at least one equality cut, while one instance had over 500,000. Additionally, computationally challenging instances saw an 11% improvement in computational effort. Therefore, equality cuts are a new topic of research in IP that is beneficial for solving some IP instances.