Operations Research. Overview of Areas of Faculty Research. Graduate Orientation Fall Department of Mathematical and Statistical Sciences
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1 Operations Research Overview of Areas of Faculty Research Department of Mathematical and Statistical Sciences Graduate Orientation Fall 2011
2 What is Operations Research? Agent-based modeling Airline scheduling Arrival process Assignment problem Birthdeath process Black-box optimization Blending problem Branch-and-bound Capital budgeting Cargo loading Combinatorial optimization Computational biology Critical path Data envelopment analysis Data mining Decision analysis Derivative-free optimization Deviation theory Diet problem Discrete event simulation Dynamic program Economic order problem Evolutionary game Facility location Fibonacci search Financial engineering First passage time Floor planning Forecasting Fuzziness Game theory Genetic algorithm Global optimization Golden-section search Graph theory Greedy heuristic Integer programming Inventory control Knapsack problem Linear programming Logistics Machine servicing Management science Managerial economics Manufacturing Markov chain Matrix game Matroid Maximum cut Mean return time Mean-variance model Metaheuristic Minimum cost Mixed-strategy game Monte-Carlo simulation Nash equilibrium Nearest neighbor Network flow Newsvendor problem Nonlinear program Operations management Optimization P = NP? Pareto frontier Perfect matching Policy modeling Population dynamics Pricing Prisoners dilemma Probability Production planning Project management Prospect theory Queueing Random walk Renewal process Resource allocation Revenue management Risk analysis Routing Scheduling Set covering Shadow price Shortest path Simulated annealing Simulation Spanning tree Staffing Statistical analysis Stochastic process Supply chain management System engineering Tabu search Transition probability Transportation Traveling salesman Two-person game Uncertainty Utility theory Wargaming Water flow management Work scheduling Zero-sum game
3 What can we do with Operations Research?
4 What do we do with Operations Research? O.R. and Biomedicine Computational Biology: data-intensive numerical methods Medicine/Healthcare: intensity modulated radiation therapy Bioinformatics: genomic alignment by hidden Markov models Super Simulation! uses random, probabilistic experiments to model uncertainty powerful to model stochastic and highly complex phenomena analyzes arrival, service, and departure of customers in queues Solving Puzzling Problems create and solve Sudoku puzzles using integer programming compute optimal matchings, tours, paths, and flows in graphs invent new theory and determine winning strategies of games
5 What can you do with Operations Research? (Cont.) Minimize the convex quadratic function f (x, y) = x 2 + y 2 The global minimum is (x, y) = (0, 0). Minimize the highly-nonconvex Rastrigin function Ras(x, y) = 20 + x 2 + y 2 10(cos 2πx + cos 2πy)
6 O.R. Faculty and Research Areas Stephen Billups Alexander Engau Weldon Lodwick Antolii Puhalskii Burton Simon Gary Kochenberger (Business School) Optimization, Global/Nonlinear programming, Numerical algorithms, Computational biology Optimization, Convex/Conic programming, Decision analysis, Management sciences Optimization, Fuzzy sets and systems, Interval analysis, Medical applications Probability theory, Stochastic Processes, Queueing theory, Large deviation theory Probability, Queueing, Simulation Models, Population dynamics, Evolutionary games Optimization, Discrete/Integer programming, Heuristic algorithms, Business applications
7 O.R. Course Rotation Fall 2011 Math 5310 Probability (TR 11:00-12:15 pm, Tolya) Math 5350 Mathematical Theory of Interest (TR 2:00-3:15 pm, Tolya) Math 5593 Linear Programming (MW 3:30-4:45 pm, Alex) Math 5779 Math Clinic: Simulation Optimization (TR 3:30-4:45 pm, Steve) Math 5792 Probabilistic Modeling (TR 12:30-1:45 pm, Burt) Spring 2012 Math 5490 Network Flows Math 5779 Math Clinic Math 7384 Mathematical Probability Math 7825 Topics in Optimization Fall 2012 Math 6380 Stochastic Processes Math 6595 Computational Methods in Nonlinear Programming Spring 2013 Math 5794 Optimization Modeling Math 7593/7594/7595 Advanced (Non)Linear/Integer Programming
8 Anything you like to know? Today is Pierre de Fermat s 410th birthday! Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. Welcome to our Department and to UC Denver!
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