Master of Science / Department of Industrial & Manufacturing Systems Engineering / David H. Ben-Arieh / In present competitive market, there is growing concern for ascertaining and fulfilling the individual customer’s wants and needs. Therefore, the focus of manufacturing has been shifting from mass production to mass customization, which requires the manufacturers to introduce an increasing number of products with shorter life span and at a lower cost. Also, another challenge is to manage the variety of products in an environment where demands are stochastic and the lead times to fulfill those demands are short. The focus of this thesis is to develop and investigate platform based production strategies, as opposed to producing each product independently, which would ensure the economic production of the broader specialized products with small final assembly time and under demand uncertainty. The thesis proposes three different platform based production models. The first model considers the economic production of products based on a single platform and with forecasted demands of the products. The model is formulated as a general optimization problem that considers the minimization of total production costs. The second model is the extension of the first model and considers the production of products based on multiple platforms and considers the minimization of total production costs and the setup costs of having multiple platforms. The third model is also an extension of the first model and considers the demands of the products to be stochastic in nature. The model considers the minimization of total production costs and shortage costs of lost demands and holding cost of surplus platforms under demand uncertainties. The problem is modeled as a two stage stochastic programming with recourse. As only the small instances of the models could be solved exactly in a reasonable time, various heuristics are developed by combining the genetic evolutionary search approaches and some operations research techniques to solve the realistic size problems. The various production models are validated and the performances of the various heuristics tailored for the applications are investigated by applying these solution approaches on a case of cordless drills.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Integer programming (IP) has been and continues to be widely used by industries to minimize cost and effectively manage resources. Faster computers and innovative IP techniques have enabled the solution to many large-scale IPs. However, IPs are NP-hard and many IPs require exponential time to solve. Lifting is one of the most widely used techniques that helps to reduce computational time and is widely applied in today's commercial IP software. Lifting was first introduced by Gomory for bounded integer programs and a theoretical and computationally intractible technique to simultaneously lift sets of variables was introduced by Zemel in 1978. This thesis presents a new algorithm called the Maximal Simultaneous Lifting Algorithm (MSLA), to simultaneously uplift sets of binary integer variables into a cover inequality. These lifted inequalities result in strong inequalities that are facet defining under fairly moderate assumptions. A computational study shows that this algorithm can find numerous strong inequalities for random Knapsack (KP) instances. The pre-processing time observed for these instances is less than 1/50th of a second, which is negligible. These simultaneously lifted inequalities are easy to find and incorporating these cuts to KP instances reduced the solution time by an average of 41%. Therefore, implementing MSLA should be highly beneficial for large real-world problems.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Malgorzata J. Rys / Emergency Medical Systems (EMS) are designed to handle emergencies. Fortunately, most emergencies faced have only one patient. The every day system is not designed to respond to emergencies in which there are many casualties. Due to natural disasters and terrorist attacks that have occurred over the past decade, mass-casualty disaster response plans have become a priority for many organizations, including EMS. The resources available for constructing such plans are limited. Physical simulations or practices of the plan are often performed; however, it is not until a disaster strikes that the capabilities of the plan are truly realized. In this paper, it is proposed that discrete-event simulations are used as part of the planning process. A computer simulation can test the capability of the plan under different settings and help planners in their decision making. This paper looks at the creation of a discrete-event simulation using ARENA software. The simulation was found to accurately simulate the response to the Greensburg tornado that occurred May of 2008. A sensitivity analysis found that the simulation results are dependent upon the values assumed for Volunteer Injury Rate, Injury Level, Information Dissemination Rate and Transportation Decision variables. When a disaster occurs, the local resources are overwhelmed and outside aide must be called in. Decision rules for when to request more outside ambulances and when to release them to send them home are evaluated. The more resources that are made available, the quicker patients receive medical care. However, when outside ambulances are called in, they are putting their home area at risk because it no longer has complete (or any) ambulance coverage. As the percent of coverage decreases, the amount of time that victims spend waiting for ambulances also decreases. Many decision rules were evaluated, resulting in various combinations of ambulance wait times and average percent coverage. It is up to Disaster Planners to determine how much of an additional wait can be assumed by the disaster victims to prevent outside districts from taking on unwarranted risk of low coverage.

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 / Todd W. Easton / Integer programs (IPs) are mathematical models that can provide an optimal solution to a variety of different problems. They have been used to reduce costs and optimize organizations. Additionally, IPs are NP-complete resulting in many IPs that cannot be solved. Cutting planes or valid inequalities have been used to decrease the time required to solve IPs. Lifting is a technique that strengthens existing valid inequalities. Lifting inequalities can result in facet defining inequalities, which are the theoretically strongest valid inequalities. Because of these properties, lifting procedures are used in software to reduce the time required to solve an IP. The thesis introduces a new algorithm for exact synchronized simultaneous uplifting over an arbitrary initial inequality for knapsack problems. Synchronized Simultaneous Lifting (SSL) is a pseudopolynomial time algorithm requiring O(nb+n[superscript]3) effort to solve. It exactly uplifts two sets simultaneously into an initial arbitrary valid inequality and creates multiple inequalities of a particular form. This previously undiscovered class of inequalities generated by SSL can be facet defining. A small computational study shows that SSL is quick to execute, requiring on average less than a quarter of a second. Additionally, applying SSL inequalities to a knapsack problem enabled commercial software to solve problems that it could not solve without them.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Jessica L. Heier Stamm / The main goal of public health emergency preparedness efforts is to mitigate the impact of events on the health of the population. However, decision-makers must also remain conscientious of the costs associated with these efforts. Planning is further complicated by uncertainty about the location and volume of demand that will need to be met in an emergency, the speed with which demand must be met, and the potential scarcity of needed items once an emergency occurs. To address these challenges, public health emergency planners often keep inventory stockpiles that are distributed when an event happens. Managing these stockpiles is a difficult task, and inefficient stockpile location and equipment distribution strategies can be costly both in terms of cost and public health impact. This research is motivated by challenges faced by state public health departments in creating stockpile location and equipment distribution strategies. The primary emphasis is on facemasks and respirators used by health workers during an influenza pandemic, but the approach is generalizable to other scenarios. The model proposed here uses a two-stage approach to generate a holistic solution to the problem. The first stage uses a pull distribution strategy to make stockpile location decisions. Additionally, it determines how counties should be assigned to stockpiles to minimize both storage and distribution costs. The second stage adopts a push distribution strategy to determine optimal delivery routes based on the county assignments made in stage one. This stage offers guidance for public health planners who have made location-allocation decisions but who then face a different distribution scenario than what was anticipated in the original planning phase. Recourse methods for managing demand uncertainty are also proposed. A case study of the state of Kansas is conducted using the methods introduced in the thesis. The computational results yield several significant insights into the tradeoffs and costs of various facility location-allocation and vehicle routing decisions: • For the tested range of storage and distribution cost parameters, multiple stockpile locations are preferred over a single location. • In a pull distribution system, storage costs play a greater role in location-allocation decisions than distribution costs. • In the push distribution system, finding an optimal vehicle routing plan is computationally intensive for stockpiles with a large number of assigned counties. • Efficient heuristics perform well to design recourse routing plans when realized demand is greater than expected. • In the event that planners wish to specify routes well in advance, the results of this research suggest adopting a robust routing plan based on higher-than-expected demand levels. This thesis makes three important contributions. The first is an optimization approach that considers multiple distribution strategies. This is especially relevant when stockpiling for an influenza pandemic where stockpiles need to be located significantly before the material is needed, during which time the distribution strategy may change. Second, the case study demonstrates that the proposed methods are applicable to a large-scale problem arising in practice. Finally, this research illustrates for decision-makers the tradeoffs between different stockpile management strategies and between optimal and heuristic methods.

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.