Doctor of Philosophy / Department of Industrial & Manufacturing Systems Engineering / Shuting Lei / Laser-assisted machining (LAM) is a promising non-conventional machining technique for advanced ceramics. However, the fundamental machining mechanism which governs the LAM process is not well understood so far. Hence, the main objective of this study is to explore the machining mechanism and provide guidance for future LAM operations. In this study, laser-assisted milling (LAMill) of silicon nitride ceramics is focused. Experimental experience reveals that workpiece temperature in LAM of silicon nitride ceramics determines the surface quality of the machined workpiece. Thus, in order to know the thermal features of the workpiece in LAM, the laser-silicon nitride interaction mechanism is investigated via heating experiments. The trends of temperature affected by the key parameters (laser power, laser beam diameter, feed rate, and preheat time) are obtained through a parametric study. Experimental results show that high operating temperature leads to low cutting force, good surface finish, small edge chipping, and low residual stress. The temperature range for brittle-to-ductile transition should be avoided due to the rapid increase of fracture toughness. In order to know the temperature distribution at the cutting zone in the workpiece, a transient three-dimensional thermal model is developed using finite element analysis (FEA) and validated through experiments. Heat generation associated with machining is considered and demonstrated to have little impact on LAM. The model indicates that laser power is one critical parameter for successful operation of LAM. Feed and cutting speed can indirectly affect the operating temperatures. Furthermore, a machining model is established with the distinct element method (or discrete element method, DEM) to simulate the dynamic process of LAM. In the microstructural modeling of a β-type silicon nitride ceramic, clusters are used to simulate the rod-like grains of the silicon nitride ceramic and parallel bonds act as the intergranular glass phase between grains. The resulting temperature-dependent synthetic materials for LAM are calibrated through the numerical compression, bending and fracture toughness tests. The machining model is also validated through experiments in terms of cutting forces, chip size and depth of subsurface damage.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Chih-Hang Wu / In recent years the stock markets have shown tremendous volatility with significant spikes and drops in the stock prices. Within the past decade, there have been numerous jumps in the market; one key example was on September 17, 2001 when the Dow industrial average dropped 684 points following the 9-11 attacks on the United States. These evident jumps in the markets show the inaccuracy of the Black-Scholes model for pricing options. Merton provided the first research to appease this problem in 1976 when he extended the Black-Scholes model to include jumps in the market. In recent years, Kou has shown that the distribution of the jump sizes used in Merton’s model does not efficiently model the actual movements of the markets. Consequently, Kou modified Merton’s model changing the jump size distribution from a normal distribution to the double exponential distribution. Kou’s research utilizes mathematical equations to estimate the value of an American put option where the underlying stocks follow a jump-diffusion process. The research contained within this thesis extends on Kou’s research using Monte Carlo simulation (MCS) coupled with least-squares regression to price this type of American option. Utilizing MCS provides a continuous exercise and pricing region which is a distinct difference, and advantage, between MCS and other analytical techniques. The aim of this research is to investigate whether or not MCS is an efficient means to pricing American put options where the underlying stock undergoes a jump-diffusion process. This thesis also extends the simulation to utilize copulas in the pricing of baskets, which contains several of the aforementioned type of American options. The use of copulas creates a joint distribution from two independent distributions and provides an efficient means of modeling multiple options and the correlation between them. The research contained within this thesis shows that MCS provides a means of accurately pricing American put options where the underlying stock follows a jump-diffusion. It also shows that it can be extended to use copulas to price baskets of options with jump-diffusion. Numerical examples are presented for both portions to exemplify the excellent results obtained by using MCS for pricing options in both single dimension problems as well as multidimensional problems.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Graph Theory is a widely studied topic. A graph is defined by two important features: nodes and edges. Nodes can represent people, cities, variables, resources, products, while the edges represent a relationship between two nodes. Using graphs to solve problems has played a major role in a diverse set of industries for many years. Integer Programs (IPs) are mathematical models used to optimize a problem. Often this involves maximizing the utilization of resources or minimizing waste. IPs are most notably used when resources must be of integer value, or cannot be split. IPs have been utilized by many companies for resource distribution, scheduling, and conflict management. The node packing or independent set problem is a common combinatorial optimization problem. The objective is to select the maximum nodes in a graph such that no two nodes are adjacent. Node packing has been used in a wide variety of problems, which include routing of vehicles and scheduling machines. This thesis introduces several new graph structures, cliqued hole, odd bipartite hole, and odd k-partite hole, and their corresponding valid inequalities for the node packing polyhedron. These valid inequalities are shown to be new valid inequalities and conditions are provided for when they are facet defining, which are known to be the strongest class of valid inequalities. These new valid inequalities can be used by practitioners to help solve node packing instances and integer programs.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programs (IP) are used in companies and organizations across the world to reach financial and time-related goals most often through optimal resource allocation and scheduling. Unfortunately, integer programs are computationally difficult to solve and in some cases the optimal solutions are unknown even with today’s advanced computing machines. Lifting is a technique that is often used to decrease the time required to solve an IP to optimality. Lifting begins with a valid inequality and strengthens it by changing the coefficients of variables in the inequality. Often times, this technique can result in facet defining inequalities, which are the theoretically strongest inequalities. This thesis introduces a new type of lifting called synchronized simultaneous lifting (SSL). SSL allows for multiple sets of simultaneously lifted variables to be simultaneously lifted which generates a new class of inequalities that previously would have required an oracle to be found. Additionally, this thesis describes an algorithm to perform synchronized simultaneous lifting for a binary knapsack inequality called the Synchronized Simultaneous Lifting Algorithm (SSLA). SSLA is a quadratic time algorithm that will exactly simultaneously lift two sets of simultaneously lifted variables. Short computational studies show SSLA can sometimes solve IPs to optimality that CPLEX, an advanced integer programming solver, alone cannot solve. Specifically, the SSL cuts allowed a 76 percent improvement over CPLEX alone.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Malgorzata J. Rys / During the last several decades, the number of drivers and the number of senior citizens driving on U.S highways has increased significantly along with the number of traffic signs. The median age of the drivers has also increased due to the aging population. Traffic signs provide a plethora of necessary information - directions, guidance, warnings, regulations, and recreation. With today's congestion and higher speed, it's very important to recognize the need for brighter and easier to read signs to increase safety among drivers. In the recent years, there has been innovation in the field of traffic engineering, giving rise to numerous innovations in retro-reflective sheeting materials and fonts. It is important to identify the combination of font and retro-reflective sheeting material, which performs best by increasing the legibility distance between the driver and the sign during both day and night time conditions. The objective of the research was to determine the combination of font (among Clearview 5-W, Series E-Modified and Clearview 5-W-R) and retro-reflective sheeting materials (DG3, Type 4 and Type 1) that produces maximum legibility distance. The objective was also to study the safety benefits of the Clearview font. Both field and computer based tests were carried out to find out which combination of font and retro-reflective material produced maximum legibility distance. From field tests it was found that the Clearview 5-W-R font along with Type 1 reflective material produced the maximum legibility distance in day time conditions, whereas Clearview 5-W-R along with Type 4 reflective material produced the maximum legibility distance at night conditions. It was also seen that while the Type 1 sheeting material performed well during day time, it failed to produce good results during night time. In fact it ended up as the worst performing sheeting material during night time. Based on these observations, it is recommended to use the Clearview 5-W-R in combination with Type 4 retro-reflective sheeting as it showed the most consistent performance compared to all other combinations of fonts and DG3 or Type 1 retro-reflective material.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Chih-Hang Wu / The fast advancement in computer technologies in the recent years has made the use of simulation to estimate stock/equity performances and pricing possible; however, determining the optimal exercise time and prices of American options using Monte-Carlo simulation is still a computationally challenging task due to the involved computer memory and computational complexity requirements. At each time step, the investor must decide whether to exercise the option to get the immediate payoff, or hold on to the option until a later time. Traditionally, the stock options are simulated using Monte-Carlo methods and all stock prices along the path are stored, and then the optimal exercise time is determined starting at the final time period and continuing backward in time. Also, as the number of paths simulated increases, the number of simultaneous equations that need to be solved at each time step grow proportionally. Currently, two theoretical methods have emerged in determining the optimal exercise problem. The first method uses the concept of least-squares approach in linear regression to estimate the value of continuing to hold on to the option via a set of randomly generated future stock prices. Then, the value of continuing can be compared to the payoff at current time from exercising the option and a decision can be reached, which gives the investor a higher value. The second method uses the finite difference approach to establish an exercise boundary for the American option via an artificially generated mesh on both possible stock prices and decision times. Then, the stock price is simulated and the method checks to see if it is inside the exercise boundary. In this research, these two solution approaches are evaluated and compared using discrete event simulation. This allows complex methods to be simulated with minimal coding efforts. Finally, the results from each method are compared. Although a more conservative method cannot be determined, the least-squares method is faster, more concise, easier to implement, and requires less memory than the mesh method. The motivation for this research stems from interest in simulating and evaluating complicated solution methods to the optimal exercise problem, yet requiring little programming effort to produce accurate and efficient estimation results.

Doctor of Philosophy / Department of Industrial & Manufacturing Systems Engineering / Shuting Lei / This study experimentally and numerically investigates laser assisted milling (LAMill) of silicon nitride ceramics. Experiments are conducted to study the machinability of Si3N4 under LAMill. The effects of temperature on cutting forces, tool wear, surface integrity, edge chipping and material removal mechanisms are investigated. It is shown that when temperature increases, cutting force and tool wear are significantly decreased, surface integrity is improved, chip size is increased and material removal demonstrates more plastic characteristics. The mechanisms of edge chipping at elevated temperature are investigated theoretically and experimentally. When temperature is above the softening point and below the brittle/ductile transition temperature, the mechanism is mainly through softening. When temperature is above the brittle/ductile transition temperature, toughening mechanism contributes significantly to the reduced edge chipping. The coupled effect of softening and toughening mechanisms shows that temperature range between 1200 to 1400°C has the most significant effect to reduce edge chipping. Distinct element method (DEM) is applied to simulate the micro-mechanical behavior of Si3N4. First, quantitative relationships between particle level parameters and macro-properties of the bonded particle specimens are obtained, which builds a foundation for simulation of Si3N4. Then, extensive DEM simulations are conducted to model the material removal of machining Si3N4. The simulation results demonstrate that DEM can reproduce the conceptual material removal model summarized from experimental observations, including the initiation and propagation of cracks, chip formation process and material removal mechanisms. It is shown that material removal is mainly realized by propagation of lateral cracks in machining of silicon nitride. At the elevated temperature under laser assisted machining, lateral cracks are easier to propagate to form larger machined chips, there are fewer and smaller median cracks therefore less surface/subsurface damage, and crushing-type material removal is reduced. The material removal at elevated temperature demonstrates more plastic characteristics. The numerical results agree very well with experimental observations. It shows that DEM is a promising method to model the micro-mechanical process of machining Si3N4.

Doctor of Philosophy / Department of Industrial & Manufacturing Systems Engineering / Zhijian Pei / Titanium alloy is one of the most important materials used in major segments of industries such as aerospace, automobile, sporting goods, medical and chemical. Market survey has stated that the titanium shipment in the USA has increased significantly in last two decades, indicating its increased usage. Industries are always under tremendous pressure to meet the ever-increasing demand to lower cost and improve quality of the products manufactured from titanium alloy. Similar to titanium alloys, silicon carbide and dental ceramics are two important materials used in many applications. Rotary ultrasonic machining (RUM) is a non-traditional machining process that combines the material removal mechanisms of diamond grinding and ultrasonic machining. It comprises of a tool mounted on a rotary spindle attached to a piezo-electric transducer to produce the rotary and ultrasonic motion. No study has been reported on RUM of titanium alloy, silicon carbide and dental ceramics. The goal of this research was to provide new knowledge of machining these hard-to-machine materials with RUM for further improvements in the machining cost and surface quality. A thorough research has been conducted based on the feasibility study, effects of tool variables, effects of machining variables and wheel wear mechanisms while RUM of titanium alloy. The effects of machining variables (such as spindle speed, feed rate, ultrasonic vibration power) and tool variables (grit size, diamond grain concentration, bond type) have been studied on the output variables (such as cutting force, material removal rate, surface roughness, chipping size) and the wheel wear mechanisms for titanium alloy. Feasibility of machining silicon carbide and dental ceramics is also conducted along with a designed experimental study.

Doctor of Philosophy / Department of Industrial and Manufacturing Systems Engineering / Bradley Kramer / This research shows that industry and company related performance indicators enhance the business valuation process by providing a broader, more encompassing view of overall corporate health and a better understanding of improvement opportunity areas within a company. To incorporate performance indicators in the business valuation process, new methodologies are required to integrate the non-financial and soft data with the typical financial information used in business valuation. This requires a “re-think” of the standard business valuation process and the exploration and application of other methods and analytical techniques. The results of this research are the definition of a problem type and the development of a new business valuation process. The problem structure has as inputs industry specific performance metrics grouped into three primary areas Production Processes, Products/Services and Marketability and Management, a fuzzy logic model with fuzzy and approximate relationships between performance metrics and financial information and crisp financial information as output. The framework for a fuzzy logic model was developed and is used to approximate relationships and model a non-linear environment. The resulting crisp financial information is then input and integrated into the traditional business valuation process. The process was demonstrated with an example production company and with data from two regional airlines. A step-by-step example of the process was provided using the production company example to demonstrate how the results are generated and integrated with DCF business valuation. Heuristics to identify areas to improve company performance were described. Two regional airlines, individually and combined, were tested with actual data using the original fuzzy logic model structure and then the original fuzzy logic model structure was revised and new results generated. Tuning the model showed an improvement in the business valuation process performance. The benefits from this research include the definition of a new class of problems and a process to solve problems of this nature. The insights gained from this research can be applied in major disciplines such as accounting, business and finance, engineering and decision theory.

Doctor of Philosophy / Department of Chemical Engineering / Larry E. Erickson / Over the past decade, nanomaterials have been the subject of enormous interest. Their defining characteristic is a very small size in the range of 1-100 nm. Due to their nanometer size, nanomaterials are known to have unique mechanical, thermal, biological, optical and chemical properties, together with the potential for wide-ranging industrial applications. Here, we synthesized nanocrystalline metal oxides through the sol-gel process and used these materials as desulfurization adsorbents and photocatalysts. Deep desulfurization of fuels has received more and more attention worldwide, not only because of health and environmental consideration but also due to the need for producing ultra-low-sulfur fuels, which can only be achieved under severe operating conditions at high cost using hydrodesulfurization (HDS). Consequently, development of new and affordable deep desulfurization processes to satisfy the decreasing limit of sulfur content in fuels is a big challenge. Sol-gel derived Cu/Al[subscript]2O[subscript]3 and Zn/Al[subscript]2O[subscript]3 adsorbents have been demonstrated to be effective in the removal of thiophene from a model solution. Results showed that Cu[superscript]+ was the active site and thermal treatment under vacuum was critical for Zn/Al[subscript]2O[subscript]3 since a defective, less crystalline spinel led to stronger interaction between zinc ions and thiophene molecules in the adsorption process. The kinetic study suggested that most of the adsorption occurred in the first 30 min, and adsorption equilibrium was attained after 1.5 h. Both adsorbents showed good regenerative property. TiO2 is considered the most promising photocatalyst due to its high efficiency, chemical stability, non-toxicity, and low cost for degradation and complete mineralization of organic pollutants. However, the use of TiO[subscript]2 is impaired because it requires ultraviolet (UV) activation ([Lambda]<387 nm). The shift of optical response of TiO[subscript]2 from the UV to the visible light region would have a profound positive effect on the efficient use of solar energy in photocatalytic reactions. We shifted the optical response of TiO[subscript]2 and improved the photocatalytic efficiency through size modification and transition metal ion and nonmetal atom doping. Experimental results showed that C and V co-doped TiO[subscript]2 catalysts had much higher activity than commercial P25 TiO[subscript]2 towards the degradation of acetaldehyde under visible light irradiation. For the first time, we reported that activities were comparable in the dark and under visible light irradiation for co-doped TiO[subscript]2 with 2.0 wt% V. C and N co-doped TiO[subscript]2 exhibited higher activity for the degradation of methylene blue than pure TiO[subscript]2 under visible light and UV irradiation. Possible mechanisms were discussed based on the experimental results.