Objective
The course aims at familiarizing the students with fundamental modeling techniques and analytic methods, for the support of decision making in operational business environments. The covered methodologies constitute invaluable tools in optimizing decision making, in all modern business environments. The expected learning outcome includes the ability of development and analysis of optimization models and the accumulation of experience in implementing and using solving methods. Moreover, it includes the knowledge of decision optimization and forecasting methods, that constitute fundamental analytical tools of decision theory. It is expected that the students will develop the critical ability of choosing the appropriate methodology for each operational decision making problem, and build awareness of each methodology’s advantages and constraints.
Course Contents
- Introduction to Linear Programming. Linear Programming Examples, Feasible and Optimum Solutions, Graphical Solving.
- Optimization of Linear Programs. Standard Form, Algebraic Simplex Method, Simplex Tableau, Alternative Methods.
- Duality Theory. Primal-Dual Linear Programs, Fundamental Theorems, Economic Interpretation, Sensitivity Analysis.
- The ΑMPL/GMPL Languages for Linear Programming. Syntax, Development of Models for Linear Optimization, Applications.
- Network Optimization Problems. The Transportation and Assignment Problems, Minimum Cost Flows, Properties, Optimization, Heuristic Methods.
- Integer Linear Programming. Modeling Aspects, Examples, Global Optimization (Branch and Bound Method), Local Optimization Methods (Hill Climbing, Simulated Annealing).
- Matlab/Octave Software. Basic Operations, Control Flow Statements, Visualization, Examples and Applications.
- Forecasting Methods. Regression Methods, Least-Squares Method, Gradient Descent, Elements of Time Series.
- Decision Analysis. Maximum Likelihood Rule, Bayes Rule, Decision Making with Experimentation, Decision Trees.
- Matlab/Octave Applications. Programming Forecasting and Decision Analysis Methods, Experimentation.
- F. S. Hillier, G. J. Liebermann. Introduction to Operations Research, McGraw Hill, 10th Edition, 2014.
- R. J. Vanderbei. Linear Programming: Foundations and Extensions, Springer, 3rd Edition, 2008.
- W. Michiels. Theoretical Aspects of Local Search, Springer, 2010.
- T. Hastie, R. Tibshirani, J. Friedman. The Elements of Statistical Learning, Springer, 2nd edition, 2013