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Thesis (M.S. in Systems Engineering Management)--Naval Postgraduate School, Sept. 2004. / Thesis Advisor(s): Robert F. Dell. Includes bibliographical references (p. 33-34). Also available online.

Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009. / Committee Co-Chair: George L. Nemhauser; Committee Co-Chair: Shabbir Ahmed; Committee Member: Martin W. P. Savelsbergh; Committee Member: R. Gary Parker; Committee Member: Zonghao Gu.

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Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Baseball is an incredibly complex game where the managers of the baseball teams have numerous decisions to make. The managers are in control of the offense and defense of a team. Some managers have ruined their teams’ chances of a victory by removing their star pitcher too soon in a game or leaving them in too long; managers also choose to pinch hit for batters or pinch run for base runners in order to set up a “favorable match-up” such as a left handed pitcher versus a right handed batter. This research’s goal is to aid managers by providing an optimal positioning of defensive players on the field for a particular batter. In baseball, every ball that is hit onto the field of play can be an out if the fielders are positioned correctly. By positioning the fielders in an optimal manner a team will directly reduce the number of runs that it gives up, which increases the chances of a win. This research describes an integer program that can determine the optimal location of defensive players. This integer program is based off of a random set of hits that the player has produced in the past. The integer program attempts to minimize the expected costs associated with each hit where the cost is defined by a penalty (single, double or triple) or benefit (out) of the person’s hit. By solving this integer program in Opl Studio 4.2, a commercial integer programming software, an optimal defensive positioning is derived for use against this batter. To test this defense against other standard defenses that teams in the MLB currently use, a simulation was created. This simulation uses Derek Jeter’s actual statistics; including his 2009 regular season hit chart. The simulation selects a hit at random according to his hit chart and determines the outcome of the hit (single, double, out, double play, etc.). Once this simulation is complete a printout shows the batter’s statistics; including his average and slugging percentage. VI By comparing the optimized defensive alignment with some commonly used major league alignments, it can be shown that this optimal alignment would decrease Jeter’s average by nearly 13% and decrease his slugging by 35%. It is my opinion that managers should use this tool to help them win more games. These defenses can be seamlessly implemented by any coach or team.

Approved for public release; distribution is unlimited / This thesis explores Benders decomposition for solving interdiction problems on electric power grids, with applications to analyzing the vulnerability of such grids to terrorist attacks. We refine and extend some existing optimization models and algorithms and demonstrate the value of our techniques using standard reliability test networks from IEEE. Our implementation of Benders decomposition optimally solves any problem instance, in theory. However, run times increase as Benders' cuts are added to the master problem, and this has prompted additional research to increase the decomposition's efficiency. We demonstrate empirical speed ups by dropping slack cuts, solving a relaxed master problem in some iterations, and using integer but not necessarily optimal master-problem solutions. These mixed strategies drastically reduce computation times. For example, in one test case, we reduce the optimality gap, and the time that it takes to achieve this gap, from 16% in 75 hours to 5% in 16 minutes. / FUNDED BY: 2002-GT-R-057 / Lieutenant Commander, United States Navy

The Defense Language Institute (DLI) offers 23 beginning language courses and in 2004 began to provide a smaller class size for these courses. Restrictions on when classes can begin and a limited number of instructors prevent all students from being trained in a smaller class. This thesis develops integer linear programs (ILPs) that generate schedules for all student classes and maximize the number of smaller class starts for a given number of instructors. Secondary scheduling goals include avoiding weekly changes to instructor levels and scheduling preferences such as the number of classes to start simultaneously. The ILPs solve in less than one minute and offer a significant improvement in the number of students that may be trained in the smaller class size. Computational results using real data for the Arabic, Chinese-Mandarin, and Persian-Farsi courses verify the ILPs find feasible multiyear schedules that incorporate the DLI's scheduling preferences while exceeding the DLI's published schedule results. For example, the ILPs find schedules for Arabic that train 8%, 34% and 76% of students in the smaller class in 2006, 2007, and 2008, whereas DLI's manual schedules at best can train 8%, 7% and 64%.

The U.S. Army distributes its 51,000 competitive category officers among manning targets specified by location, rank and skill that change over time in response to changing requirements. The officer inventory also changes over time and does not exactly match the manning target requirements. The Army responds to imbalances by redistributing officers in order to provide each location with the minimum required officers while minimizing the number of unfilled targets and excess officers at each location. This thesis focuses on branch officers, branch targets and generalist targets with ranks from Branch Qualified Captain to Colonel. Using data provided by the Army, we formulate an integer programming model called DISTRIBUTOR. When DISTRIBUTOR allows all officers in the inventory to move, it finds only 340 unfilled targets but this requires 4,688 or 28% of the inventory to move. We reduce the number of moves by using DISTRIBUTOR in two sequential steps. The first step optimally distributes officers at each location and identifies the excess officers and unfilled targets at each location. The second step takes the excess officers and distributes them to unfilled targets at other locations. The two-step leaves only 346 targets unfilled (6 more) but requires only 1,373 or 8% of the inventory to move. By allowing rank substitution DISTRIBUTOR can reduce the unfilled targets to 70.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / The possibility of becoming a millionaire attracts over 200,000 daily fantasy sports (DFS) contest entries each Sunday of the NFL season. Millions of people play fantasy sports and the companies sponsoring daily fantasy sports are worth billions of dollars. This thesis develops optimization models for daily fantasy sports with an emphasis on tiered contests. A tiered contest has many different payout values, including the highly sought after million-dollar prize. The primary contribution of this thesis is the first model to optimize the expected payout of a tiered DFS contest. The stochastic integer program, MMIP, takes into account the possibility that selected athletes will earn a distribution of fantasy points, rather than a single predetermined value. The players are assumed to have a normal distribution and thus the team’s fantasy points is a normal distribution. The standard deviation of the team’s performance is approximated through a piecewise linear function, and the probabilities of earning cumulative payouts are calculated. MMIP solves quickly and easily fits the majority of daily fantasy sports contests. Additionally, daily fantasy sports have landed in a tense political climate due to contestants hopes of winning the million-dollar prize. Through two studies that compare the performance of randomly selected fantasy teams with teams chosen by strategy, this thesis conclusively determines that daily fantasy sports are not games of chance and should not be considered gambling. Besides creating the first optimization model for DFS tiered contests, this thesis also provides methods and techniques that can be applied to other stochastic integer programs. It is the author’s hope that this thesis not only opens the door for clever ways of modeling, but also inspires sports fans and teams to think more analytically about player selection.