School of Engineering and Technology, (SET)
 
AT72.01 : Deterministic Optimization Models  3(3-0)
 
Course objectives:

The objective of this course is to provide the students knowledge on the deterministic decision models which can facilitate the decision making process.  Modeling concepts and applications of linear, integer, nonlinear, and dynamic programming as well as network models are addressed.  Solution methodologies for each type of optimization models are discussed. The student will also learn how to use modeling and optimization software.
 
Learning Outcomes:
The students on the completion of this course would be able to
•      Formulate mathematical programs for practical optimization problems
•      Apply appropriate mathematical programs to solve real world problems
•      Formulate solutions for network flow problems
 
Pre-requisite(s):

None
 
Course Outline:
I.       Introduction
1.      Operations Research and Management Science
2.      Basic Modeling Concepts
3.      Standard Models (LP, IP, MIP, DP, NP, Combinatorial)
4.      Examples and Applications

II.    Linear Programming
1.      The Graphical Method
2.      Simplex and Revised Simplex Methods
3.      Duality and Dual Simplex Method
4.      Sensitivity Analysis
5.      Column Generation and Dantzig-Wolfe Decomposition

III. Integer Programming and Combinatorial Optimization
1.      Standard IP, MIP, and Combinatorial Problems and Applications
2.      Cutting Plane Methods
3.      Branch and Bound Approach
4.      Heuristic Approach
IV. Network Flow Problems
1.      Transportation and Assignment Models
2.      Network Flow Models and Applications

V.    Dynamic Programming
1.      Principle of Optimality
2.      Backward & Forward Recursive Techniques
3.      Applications of DP


VI. Nonlinear Programming
1.      Optimality Conditions for Unconstrained Optimization
2.      Optimality Conditions for Constrained Optimization
3.      Numerical Search Algorithms
 
 
Learning Resources:

Textbook:
W.L. Winston: Operations Research Applications and Algorithms, 4th edition, Cengage Learning,2003.   
 
Reference Books:
1.     F.S. Hillier and G.J. Lieberman: Introduction to Operations Research, 9th edition, McGraw-Hill, 2009.  
2.     K.G. Murty: Operations Research Deterministic Optimization Models, 1st edition, Prentice Hall, 1995.   
3.     R.L. Rardin: Optimization in Operations Research, 1st edition, Prentice Hall, 1998.
4.     H.A. Taha: Operations Research: An Introduction, 9th edition, Prentice Hall, 2010.
5.     H.P. Williams: Model Building in Mathematical Programming, 5th edition, John Wiley & Sons, 2013.
6.     L.A. Wolsey: Integer Programming, 1st edition, Wiley-Interscience, 1998.
 
Journals and Magazines:
1.     European Journal of Operational Research, Elsevier
2.     International Journal of Production Research, Taylor and Francis
3.     International Journal of Production Economics, Elsevier
4.     Journal of the Operational Research Society, Palgrave Macmillan
5.     Management Science, Informs

Others: Lecture Notes
 
Time Distribution and Study Load:
Lecture hours      : 45 hours
Tutorials               : 15 hours
Assignments       : 45 hours
Self-study             :  90 hours
 
Teaching and Learning Methods:
The teaching is done via lectures by the instructor. The learning method includes tutorials on using optimization software packages, and individual assignments.
 
Evaluation Scheme:
Mid-semester examination 30%, home assignments 20%, and final examination 50%. The examinations are open-book.

An “A” would be awarded if a student shows a deep understanding of all techniques discussed in this course and can apply those techniques to deal with theoretical as well as practical problems. A “B” would be awarded if a student shows the ability to apply the techniques provided to deal with practical problems. A “C” would be given if a student possesses understanding on basic techniques and can apply the acquired knowledge to some practical problems. A “D” would be given if a student does not meet expectations in understanding and application of basic techniques.
 
Instructor(s):
SECTION NAME