This dissertation examines characteristics of a class of semi-infinite linear programming problems designated as C/C semi-infinite linear programming problems. Semi-infinite programming problems which belong to this class are problems of the form [See document] where S is a compact, convex subset of Euclidean m space and u_i : S→R, i=1,...,n are strictly concave functions while u _n+1 : S→R is convex. Certain properties of the C/C semi-infinite linear programming problems give rise to efficient solution techniques. The solution techniques are given as well as examples of their use. Of significant importance is the intimate relationship between the class of C/C semi-infinite linear programming problems and certain convex fuzzy set programming problems. The fuzzy set programming problem is defined as [See document] The convex fuzzy set programming problem is transformed to an equivalent semi-infinite linear programming problem. Characterizations of the membership functions are given which cause the equivalent semi-infinite linear programming problems to fall within the realm of C/C semi-infinite linear programming problems. Some extensions of the set inclusive programming problem are also given. / Ph. D.

This dissertation deals with a class of nonconvex mathematical programs called Extreme Point Mathematical Programs (EPMP). These problems are generalizations of certain Integer Programming problems and also find their application in other nonconvex programs like the Concave Minimization problem. The research addresses the design and analysis of algorithms for EPMP. However, most of the ideas are quite general and apply to a wider class of mathematical programs including the Generalized Lattice Point Problem. We obtain a variety of cutting plane algorithms and analyze the convergence of such algorithms. Insightful examples of nonconvergence are also provided. Two finitely convergent algorithms are also presented. One of these is a cutting plane based procedure while the other is a branch and bound scheme. Computational experience with both algorithms is given. / Ph. D.

Call number: LD2668 .T4 1979 D46 / Master of Science

This research examines certain modifications of the mathematical programming models to improve their classificatory performance. These modifications involve the inclusion of second-order terms and secondary goals in mathematical programming models. A Monte Carlo simulation study is conducted to investigate the performance of two standard parametric models and various mathematical programming models, including the MSD (minimize sum of deviations) model, the MIP (mixed integer programming) model and the hybrid linear programming model.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: p. 212-214. / by Robert Hunter Halstead, Jr. / Ph.D.

Abstract not available

Bibliography: p.63-65.

Motivated by operational issues in real-world glass manufacturing, this thesis addresses a problem of laying out and sequencing the orders so as to minimize wasted glass, called scrap. This optimization problem combines aspects of traditional cutting problems and traditional scheduling and sequencing problems. In so far as we know, the combination of cutting and scheduling has not been modeled, or solved. We propose a two-phase approach: snap construction and constructing cutting and offload schedules. Regarding the second phase problem, we introduce FGSP (float glass scheduling problem), and provide its solution structure, called coveys. We analyze simple sub-models of FGSP considering the main elements: time, unit, and width. For each model, we provide either a polynomial time algorithm or a proof of NP-completeness. Since FGSP is NP-complete, we propose a heuristic algorithm, Longest Unit First (LUF), and analyze the worst case performance of the algorithm in terms of the quality of solutions; the worst case performance bound is {1+(m-1)/m}+{1/3-1/(3m)} where m is the number of machines. It is 5/3 when m=2. For the real-world problem, we propose two different methods for snap construction, and we apply two main approaches to solve cutting and offloading schedules: an MIP approach and a heuristic approach. Our solution approach produces manufacturing yields greater than 99%; current practice is about 95%. This is a significant improvement and these high-yield solutions can save millions of dollars.

The goal of a network interdiction problem is to model competitive decision-making between two parties with opposing goals. The simplest interdiction problem is a bilevel model consisting of an 'adversary' and an interdictor. In this setting, the interdictor first expends resources to optimally disrupt the network operations of the adversary. The adversary subsequently optimizes in the residual interdicted network. In particular, this dissertation considers an interdiction problem in which the interdictor places radiation detectors on a transportation network in order to minimize the probability that a smuggler of nuclear material can avoid detection. A particular area of interest in stochastic network interdiction problems (SNIPs) is the application of so-called prioritized decision-making. The motivation for this framework is as follows: In many real-world settings, decisions must be made now under uncertain resource levels, e.g., interdiction budgets, available man-hours, or any other resource depending on the problem setting. Applying this idea to the stochastic network interdiction setting, the solution to the prioritized SNIP (PrSNIP) is a rank-ordered list of locations to interdict, ranked from highest to lowest importance. It is well known in the operations research literature that stochastic integer programs are among the most difficult optimization problems to solve. Even for modest levels of uncertainty, commercial integer programming solvers can have difficulty solving models such as PrSNIP. However, metaheuristic and large-scale mathematical programming algorithms are often effective in solving instances from this class of difficult optimization problems. The goal of this doctoral research is to investigate different methods for modeling and solving SNIPs (optimization) and PrSNIPs (prioritization via optimization). We develop a number of different prioritized and unprioritized models, as well as exact and heuristic algorithms for solving each problem type. The mathematical programming algorithms that we consider are based on row and column generation techniques, and our heuristic approach uses adaptive tabu search to quickly find near-optimal solutions. Finally, we develop a group of hybrid algorithms that combine various elements of both classes of algorithms. / text

Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Thomas, Robin; Committee Co-Chair: Cook, William J.; Committee Member: Dvorak, Zdenek; Committee Member: Parker, Robert G.; Committee Member: Yu, Xingxing.