Courses
List of courses required and elective courses in the Interdisciplinary PhD Program in Operations Research with Engineering include:
Division of Economics and Business:
EBGN509: Mathematical Economics
EBGN509: Mathematical Economics
Division of Engineering:
Department of Mathematical and Computer Sciences:
Department of Metallurgical and Materials Engineering:
Department of Mining Engineering:
This course reviews and re-enforces the mathematical and computer tools that are necessary to earn a graduate degree in Mineral Economics. It includes topics from differential and integral calculus; probability and statistics; algebra and matrix algebra; difference equations; and linear, mathematical and dynamic programming. It shows how these tools are applied in an economic and business context with applications taken from the mineral and energy industries. It requires both analytical as well as computer solutions. At the end of the course you will be able to appreciate and apply mathematics for better personal, economic and business decision making. Prerequisites: Principles of Microeconomics, MATH111; or permission of instructor.
The course focuses on creating computerized models of real or proposed complex systems for performance evaluation. Simulation provides a cost effective way of pre-testing proposed systems and answering “what-if” questions before incurring the expense of actual implementations. The professional version of a widely used commercial software package, “Arena,” is used to build models, analyze and interpret the results. Other business analysis and productivity tools that enhance the analysis capabilities of the simulation software are introduced to show how to search for practically acceptable solutions within the simulation models. Both discrete-event and continuous simulation models are covered through extensive use of applications including call centers, various manufacturing operations, production/inventory systems, bulk-material handling and mining, port operations, high-way traffic systems and computer networks. Prerequisites: MATH111, MATH530; or permission of instructor.
As an advanced course in optimization, this course will address both unconstrained and constrained nonlinear model formulation and corresponding algorithms (e.g., Gradient Search and Newton’s Method, and Lagrange Multiplier Methods and Reduced Gradient Algorithms, respectively). Applications of state-of-the-art hardware and software will emphasize solving real-world problems in areas such as mining, energy, transportation, and the military. Prerequisite: MATH111; EBGN525 or EBGN555; or permission of instructor.
This course addresses the formulation of linear programming models, examines linear programs in two dimensions, covers standard form and other basics essential to understanding the Simplex method, the Simplex method itself, duality theory, complementary slackness conditions, and sensitivity analysis. As time permits, multi-objective programming and stochastic programming are introduced. Applications of linear programming models discussed in this course include, but are not limited to, the areas of manufacturing, finance, energy, mining, transportation and logistics, and the military. Prerequisite: MATH111; MATH332 or EBGN509; or permission of instructor. 3 hours lecture; 3 semester hours.
Network models are linear programming problems that possess special mathematical structures. This course examines a variety of network models, specifically, spanning tree problems, shortest path problems, maximum flow problems, minimum cost flow problems, and transportation and assignment problems. For each class of problem, we present applications in areas such as manufacturing, finance, energy, mining, transportation and logistics, and the military. We also discuss an algorithm or two applicable to each problem class. As time permits, we explore combinatorial problems that can be depicted on graphs, e.g., the traveling salesman problem and the Chinese postman problem, and discuss the tractability issues associated with these problems in contrast to “pure” network models. Prerequisites: MATH111; EBGN525 or EBGN555; or permission of the instructor.
This course addresses the formulation of linear integer programming models, examines the standard brand-and-bound algorithm for solving such models, and covers advanced topics related to increasing the tractability of such models. These advanced topics include the application of cutting planes and strong formulations, as well as decomposition and reformulation techniques, e.g., Lagrangian relaxation, Benders decomposition, column generation. Prerequisites: MATH111; EBGN525 or EBGN555; or permission of instructor.
Introduction to the science of decision making and risk theory. Application of decision analysis and utility theory to the analysis of strategic decision problems. Focuses on the application of quantitative methods to business problems characterized by risk and uncertainty. Choice problems such as decisions concerning major capital investments, corporate acquisitions, new product introductions, and choices among alternative technologies are conceptualized and structured using the concepts introduced in this course. Prerequisite: EBGN504 or permission of instructor.
The course introduces tools of “probabilistic analysis” that are frequently used in the formal studies of management. We see methodologies that help to quantify the dynamic relationships of sequences of “random” events that evolve over time. Topics include static and dynamic Monte-Carlo simulation, discrete and continuous time Markov Chains, probabilistic dynamic programming, Markov decision processes, queuing processes and networks, Brownian motion and stochastic control. Applications from a wide range of fields will be introduced including marketing, finance, production, logistics and distribution, energy and service systems. In addition to an intuitive understanding of analytical techniques to model stochastic processes, the course emphasizes how to use related software packages for managerial decision-making. Prerequisites: MATH111, MATH530; or permission of instructor.
The use of stochastic and option pricing techniques in mineral and energy asset valuation. The Hotelling Valuation Principle. The measurement of political risk and its impact on project value. Extensive use of real cases. Prerequisites: Principles of Microeconomics, MATH111, EBGN504, EBGN505, EBGN509, EBGN510, EBGN511; or permission of instructor.
Strategic decision making is often characterized by elements of complexity and complication. Included among those elements are: (1) multiple goals and objectives, (2) numerous choice alternatives, (3) differing stakeholder interests, (4) irrevocable commitment of money or human capital; and (5) elements of risk and uncertainty. This seminar-style course expands upon the fundamentals of the introductory decision analysis course, EBGN560, provides a more in-depth understanding of DA concepts and investigates the application of risk management techniques, particularly as they relate to the petroleum industry.
As an advanced course in optimization, this course will expand upon topics in linear programming. Specific topics to be covered include advanced formulation, column generation, interior point method, stochastic optimization, and numerical stability in linear programming. Applications of state-of-the-art hardware and software will emphasize solving real-world problems in areas such as mining, energy, transportation and the military. Prerequisites: EBGN555 or consent of instructor. 3 hours lecture; 3 semester hours.
As an advanced course in optimization, this course will expand upon topics in integer programming. Specific topics to be covered include advanced formulation, strong integer programming formulations, Benders Decomposition, mixed integer programming cuts, constraint programming, rounding heuristics, and persistence. Applications of state-of-the-art hardware and software will emphasize solving real-world problems in areas such as mining, energy, transportation and the military. Prerequisites: EBGN557 or consent of instructor. 3 hours lecture; 3 semester hours.
Introduce advanced mathematical and numerical methods used to solve engineering problems. Analytic methods include series solutions, special functions, Sturm-Liouville theory, separation of variables, and integral transforms. Numerical methods for initial and boundary value problems include boundary, domain, and mixed methods, finite difference approaches for elliptic, parabolic, and hyperbolic equations, Crank-Nicolson methods, and strategies for nonlinear problems. The approaches are applied to solve typical engineering problems. Prerequisite: This is an introductory graduate class. The student must have a solid understanding of linear algebra, calculus, ordinary differential equations, and Fourier theory. 3 hours lecture; 1 hour lab
This course will introduce and study the theory and design of multivariable and nonlinear control systems. Students will learn to design multivariable controllers that are both optimal and robust, using tools such as state space and transfer matrix models, nonlinear analysis, optimal estimator and controller design, and multi-loop controller synthesis Prerequisite: EGGN417 or consent of instructor. 3 hours lecture; 3 semester hours. Spring semester.
The application of gradient, stochastic and heuristic optimization algorithms to linear and nonlinear optimization problems in constrained and unconstrained design spaces. Students will consider problems with continuous, integer and mixed-integer variables, problems with single or multiple objectives and the task modeling design spaces and constraints. Design optimization methods are becoming of increasing importance in engineering design and offer the potential to reduce design cycle times while improving design quality by leveraging simulation and historical design data. Prerequisites: Experience with computer programming languages, Graduate or Senior Standing or consent of the instructor. 3 hours lecture; 3 semester hours. Spring, even numbered years.
CSCI/ MATH406 ALGORITHMS (F/S)
Divide-and-conquer: splitting problems into subproblems of a finite number. Greedy: considering each problem piece one at a time for optimality. Dynamic programming: considering a sequence of decisions in problem solution. Searches and traversals: determination of the vertex in the given data set that satisfies a given property. Techniques of backtracking, branch-and-bound techniques, techniques in lower bound theory. Prerequisite: CSCI262, MATH213, MATH223 or MATH224, MATH/CSCI358. 3 hours lecture; 3 semester hours.
Advanced study of simulation techniques, random number, and variate generation. Monte Carlo techniques, simulation languages, simulation experimental design, variance reduction, and other methods of increasing efficiency, practice on actual problems. Offered every other year. Prerequisite: CSCI 262 (or equivalent), CSCI 323 (or MATH 530 or equivalent), or permission of instructor. 3 hours lecture; 3 semester hours.
Industry competitiveness in certain areas is often based on the use of better algorithms and data structures. The objective of this class is to survey some interesting application areas and to understand the core algorithms and data structures that support these applications. Application areas could change with each offering of the class, but would include some of the following: VLSI design automation, computational biology, mobile computing, computer security, data compression, web search engines, geographical information systems. Prerequisite: MATH/CSCI406, or consent of instructor. 3 hours lecture; 3 semester hours.
An introduction to stochastic models applicable to problems in engineering, physical science, economics, and operations research. Markov chains in discrete and continuous time, Poisson processes, and topics in queuing, reliability, and renewal theory. Prerequisite: MATH334. 3 hours lecture, 3 semester hours.
Introduction to probability, random variables, and discrete and continuous probability models. Elementary simulation and bootstrapping. Data summarization and analysis. Confidence intervals and hypothesis testing for means and variances. Distribution-free (i.e., nonparametric) techniques. Prerequisite: MATH213 or equivalent. 3 hours lecture; 3 semester hours.
Continuation of MATH530. Multiple regression and trend surface analysis. Analysis of variance. Experimental design (Latin squares, factorial designs, confounding, fractional replication, etc.) Nonparametric analysis of variance. Topics selected from multivariate analysis, sequential analysis or time series analysis. Prerequisite: MATH323 or MATH530 or MATH535. 3 hours lecture; 3 semester hours.
Introduction to statistical process control, process capability analysis and experimental design techniques. Statistical process control theory and techniques developed and applied to control charts for variables and attributes involved in process control and evaluation. Process capability concepts developed and applied to the evaluation of manufacturing processes. Theory of designed experiments developed and applied to full factorial experiments, fractional factorial experiments, screening experiments, multilevel experiments and mixture experiments. Analysis of designed experiments by graphical and statistical techniques. Introduction to computer software for statistical process control and for the design and analysis of experiments. Prerequisite: Consent of Instructor. 3 hours lecture, 3 semester hours.
Analysis of exploration, mining, and metallurgy systems using statistical analysis. Monte Carlo methods, simulation, linear programming, and computer methods. Prerequisite: MNGN433 or consent of instructor. 2 hours lecture, 3 hours lab; 3 semester hours. Offered in even years.
Introduction to the application and theory of geostatistics in the mining industry. Review of elementary statistics and traditional ore reserve calculation techniques. Presentation of fundamental geostatistical concepts, including: variogram, estimation variance, block variance, kriging, geostatistical simulation. Emphasis on the practical aspects of geostatistical modeling in mining. Prerequisite: MATH323 or equivalent course in statistics; graduate or senior status. 3 hours lecture; 3 semester hours.
XXX598/698 SPECIAL XTOPICS IN ____________Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once. Repeatable for credit under different titles. Requires Approval of the Advisor and ORE Program Director.