Lecture 20 Review of ISM 206 Optimization Theory and Applications

Class Schedule LectureTopic 1Introduction and Modeling 2Intro to Linear Programming 3The simplex method 4Duality and Sensitivity Analysis 5Other LP Methods. Transportation, Assignment and Network Optimization Problems 6Unconstrained Nonlinear Optimization 7Nonlinear Programming

Class Schedule LectureTopic 8Nonlinear Programming 2 9Nonlinear Programming 3 10Dynamic Programming 11Integer Programming 13Metaheuristics 14Game Theory

Class Schedule LectureTopic 15Decision Analysis 16Markov Chains 17Queueing Theory 18Inventory theory THANKSGIVING 19Simulation 20Review FINAL EXAMFinal Exam

Topics covered Linear Programming –Models –Simplex Method –Duality –Sensitivity –Interior Point Methods Special Integer LP problems –Networks, flows, transportation, assignment Nonlinear Programming –Single vs. multivariable –Constrained and unconstrained –With linear constraints –Quadratic objective –KKT Conditions –The Lagrangian function –Gradient search, bisection, Newton’s method –Sequential LP methods for nonlinear (Frank-Wolfe)

Topics Covered Dynamic Programming –Deterministic problems –Shortest path algorithms –Cost to go –Problem of Dimensionality Integer Programming –Integer and binary constraints –Formulating ‘or’ statements as binary constraints –Branch and bound algorithm Branching Fathoming –Extending to integer variables –Simplifying integer programming by Tightening constraints Eliminating Redundant constraints Fixing variables

Topics Covered Metaheuristics –Large scale (NP-hard) problems –Neighborhood structure of problems –Simulated Annealing Searching without strict descent –Genetic Algorithms Combining features of good solutions –Tabu search Keeping list of previously tried solutions Game Theory –Two player, zero sum games –Mixed strategies –Dominating strategies –Finding equilibrium points Graphical method With LP

Topics Covered Decision Analysis –Dealing with large uncertainties –Bayes’ decision rule –Bayes’ theorem –Decision Trees –Calculating expectations from experts –Value of experimentation –Value of information Markov Chains –Stochastic processes –The Markov property –Stationary transition probabilities –Steady state distribution –Absorbing states

Topics Covered Queueing Theory –Models for communication systems, manufacturing, customer service –Notation././. –Little’s Law –Exponential arrivals, poisson processes –M/M/s system analysis Inventory Theory –Single commodity inventory control –EOQ Model Fixed costs, deterministic demand optimal policy –Extension to uncertain demand case Simulation –Generating uniform rv –Converting uniform rv to other types of rv –Monte-carlo analysis