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.

Streamlining is an attempt to make an organizational process increase its efficiency. The 1992 Amendments to the Rehabilitation Act of 1973 defined changes within the service delivery system of the Public State/Federal Vocational Rehabilitation (PS/FVR) Program, that appeared to suggest that streamlining was a new requirement from Congress. However, Congress, Rehabilitation Services Administration (RSA) and/or Council of State Administrators for Vocational Rehabilitation (CSAVR) did not mandate streamlining for the Public State/Federal Vocational Rehabilitation (PS/FVR) Program. Training on streamlining was designated to the Regional Rehabilitation Continuing Education Programs (RRCEP). The RRCEP programs exist in the Rehabilitation Act of 1973 to provide continuing education to employees of the PS/FVR Program, This studies literature review revealed Streamlining has resulted in inconsistent implementation approaches across state agencies and/or federal regions. Currently there is no data and/or consistent approaches to streamlining in the PS/FVR Program. Because of inconsistency in implementing streamlining, the RRCEP's ability to develop appropriate in-service training curriculum that is sensitive to the new needs and issues is jeopardized. The lack of a consistent methodology for streamlining implementation creates problems in planning pre-service academic rehabilitation counseling programs. The study utilized a Chi-Square analysis design due to the small sample size. However, while the sample size was small, the data were global in nature because each number analyzed represents thousands of individual Vocational Rehabilitation (VR) cases. Streamlining was developed to impact the success markers in a positive direction, i.e, clients with severe disabilities would obtain successful employment with higher wages after their employment, an increased number of individuals with severe disabilities would be served, and the VR counselor would spend less money to accomplish the employment goals. Each of the results examining these variables in this study was statistically significant in the states that had implemented streamlining. The study gave support to the premise that streamlining has a positive impact on the vocational rehabilitation process in increased wages for PS/FVR clients, reduced time in service, and decreased case service dollars spent.

Using decision analysis techniques, the cost-effectiveness of two alternatives for treating human poison exposures were modeled. The alternatives were the treatment of poisonings with the services of a regional poison control center versus without access to any poison control center. The relative cost-effectiveness was modeled based on two outcomes (morbidity and mortality) for each of four typical poison exposures: acetaminophen overdose, tricyclic antidepressant overdose, cleaning substance exposure in children, and cough/cold preparation overdose in children. Additionally, analyses were conducted to test the sensitivity of the cost-effectiveness ratio to outcome probability, average inpatient and emergency room charges, and proportion of poison exposures managed on site by the regional poison control center. This research was conducted from society's point of view.

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.

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