The lectures will cover basic topics in Operations Research. Emphasis will be on Linear Programming.
Lecturer: Olariu E. Florentin- C212, C building,
phone: 0232 20 15 46, olariu at info dot uaic dot ro
Office Hours: weekly, better by e-mail appointment
- First Part. There will be a number of three homeworks (25 points each) and a reading project (25 points) - giving a total of 100 points. (Reading projects may require a survey of a scientific papers on a designated topic.)
- Second Part. A final written exam will give another 100 points.
- Both parts worth 50% of the total grade, but 50 points is the minimum required on each of both parts.
Prerequisites: Knowledge of basics matrix algebra and some combinatorics optimization would be required.
- Bertsimas, D., J. N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, Belmont, Massachusetts, 1997.
- Chekuri, C., Topics in Research Combinatorial, University of Illinois Urbana-Champaign, Lecture Notes, 2010.
- Conforti, M., G. Cornuejols, G. Zambelli, Integer Programming, Graduate Texts in Mathematics, Springer, 2004.
- Griva, F. S., G. J. Lieberman, , Intorduction to Operations Research, McGraw Hill, 7th edition, 2001.
- Hillier, I., S. G. Nash, A. Sofer, Linear and Nonlinear Optimization, 2nd edition, SIAM, 2009.
- Kolman, B., R. E. Deck, Elementary Linear Programming with Applications, Elsevier Science and Technology Books, 1995.
- Schrijver, A., Theory of Linear and Integer Programming, Wiley & Sons, New York, 1999.
- Schrijver, A., A Course in Combinatorial Optimization, Electronic Edition, 2013.
- Taha, H. A., Operations Research: An Introduction, Prentice Hall
International, 8th edition, 2007.
- Vanderbei, R. J., Linear Programming - Foundations and Extensions, International Series in Operations Research & Management Science, Springer Science, 4th edition, 2014.
- Yang, X.-S., Introduction to Mathematical Optimization - From
Linear Programming to Metaheuristics, Cambridge International
Science Publishing, 2008.
List of Topics:
- Introduction, Motivation, and Examples.
- Geometric Linear Programming.
- Basic Feasible Solutions and Extreme Points.
- Algebra of Simplex and Simplex Algorithm.
- Degeneracy, Unboundedness, Anticycling.
- Finding an Initial Basic Feasible Solution.
- Dual Problem. Weak and Strong Duality, Complementary Slackness.
- Algebra of Dual Simplex and Dual Simplex Algorithm.
- Integer Programming Models (ILP, MILP, BILP). Examples.
- Totally Unimodular Matrices, Examples.
- Branch and Bound Algorithm for ILP.
- Cutting Plane Method for ILP.
- Lecture 1 on October 2, 2019: Introduction, Motivation, Examples, Geometric Linear Programming.
- Lecture 2 on October 9, 2019: Algebraic Approach, Basic Feasible Solutions, Extreme Points.
- Lecture 3 on October 16, 2019: Algebra of Simplex, Simplex Algorithm, Tableau Implementation.
- Lecture 4 on October 23, 2019: Simplex Special Situations, Two Phase Method, Big M Method.
- Lecture 5 on October 30, 2019: Dual Problem, Duality Theory, Dual Simplex Algorithm.
- Lecture 6 on November 6, 2018: Integer Programming, Models. Totally Unimodular Matrices.
- Lecture 7 on November 13, 2018: Branch and Bound Algorithm. Cutting Plane Method.