Sabanci University
Summer 2015
Deterministic Models in Operations Research
Instructor:
Prof. Ami Arbel
Office:
Office hours:
Teaching Assistants:
Grade: TBD
Description:
This course presents deterministic modeling and solution techniques that form the
basis for an introductory course to Operations Research (OR). The course covers the
specific topics listed below and allows using the computer lab for numerical
experimentation.
Course Contents:
1
Operations Research
1.1
History
1.2
Modeling
1.3
Classes of problems
2
Linear Programming
2.1
Modeling linear programming (LP) problems
2.2
Graphical solutions of LP problems
2.3
The linear algebra of the simplex algorithm
2.4
The simplex algorithm - pivoting and tableaus
2.5
The revised simplex algorithm
2.6
Duality theory
2.7
The dual algorithm
2.8
Sensitivity and parametric analysis
3
Network Analysis
3.1
Transportation networks
3.2
Assignment problems
3.3
Maximum flow problems
3.4
Shortest path problems
3.5
Minimum spanning tree
4
Integer Programming
4.1
Modeling capabilities
4.2
The branch-and-bound and cuttring plane algorithms
Textbooks: W.L. Winston, Operations Research: Applications and Algorithms, 2003
References:
 A. Arbel, Exploring Interior-Point Linear Programming, MIT Press, 1993.
 F.S. Hillier and G.J. Lieberman, Introduction to Operations Research, McGrawHill, 2004.

R.V. Vanderbei, Linear Programming: Foundations and Extensions, Springer,
2012.
Historical background: Operations Research, Vol. 50, No. 1, January 2002
Tentative Term Schedule
Week Day
Topic
Mon. Introduction to Operations Research (3)
Modeling optimization problems (1)
1
Tue. Modeling optimization problems (4)
Mon. Modeling optimization problems + Standard form (1)
Linear Algebra, Graphical solution methods (3)
2
Tue. Preview & properties of linear programs (3)
Mon. The Simplex algorithm (4)
3 Tue. The Simplex algorithm (4)
Mon. Midterm
Discussion
4
Tue. The revised simplex(4)
Mon. Duality (4)
5 Tue. Dual algorithm and sensitivity analysis (4)
Mon. Parametric analysis. Additional topics (time permitting)
6 Tue. Transportation Networks + Assignment
Mon. Network Flows
7 Tue. Integer programming modeling and algorithms
Chapter