As its name implies, operations research (OR) involve "research on operations", which is applied to problems that concern how to conduct and coordinate the operations (i.e., the activities) within an organization. OR has been applied extensively in such diverse areas as financial planning, logistics and supply management, public service, health care, manufacturing, telecommunication and military, to name just a few. It has had an impressive impact on improving the efficiency of numerous organizations around the world.
In this course, we study the basic OR models relevant to business decision-making in the areas such as finance, operations management and supply chain management. The emphasis in this course is on model building, solution methods, and interpretation of results. Topics covered in this course may include: linear and non-linear programming, dynamic programming, integer programming, heuristic problem-solving methods and topics in OR modelling. Computer packages for OR modelling may be used.
Modest. Some basic knowledge on linear algebra would help. In particular, you will need to solve systems of linear equations and to obtain inverse matrix. Students with little may very quickly warm up by reviewing undergraduate text.
- Lecture notes.
- Vanderbei, Robert J., Linear Programming: Foundations and Extensions. Kluwer Academic Publishers, 2001. Available http://www.princeton.edu/~rvdb/LPbook/
- Chvatal, Linear Programming, Freeman, 1983.
4. F.S. Hillier and G.J. Lieberman, Introduction to Operations Research, Seventh (or earlier) edition, McGraw Hill, New York, 2001. (Available in university library.)
- Luenberge D.G., Linear and Nonlinear Programming, 2rd edition, Addison Wesley, 1984.
- Wayne L. Winston, Operations Research: Applications and Algorithms, 3rd edition, 1997.
1. Linear Programming Models.
- Real-world problems to motive and vaguely define the subject (LP).
2. Simplex Method.
- A general procedure for solving LP problems.
- Revised simplex method. Efficiency.
3. Duality and Sensitivity Analysis, Dual Simplex Method.
- Duality theory: The relationship between LP problem and primal (original) LP problem.
- Use of Duality theory in the interpretation and implementation of sensitive analysis when LP parameters vary.
4. Transportation, Assignment and Network Models.
- How to optimally transport goods? How to assign people to tasks? All these problems can be modelled as LP problems and streamlined simplex methods are developed for these problems.
5. Project Management with PERT/CPM.
- Techniques for coordinating numerous activities in a large-scale project.
6. Dynamic Programming.
- How to make a sequence of interrelated decisions involving many time stages.
7. Integer Programming.
- Looking for the best solution when decision variables are integers.
8. Nonlinear Programming.
- Examples and types of nonlinear programming problems, and some solution techniques.
9. Selected OR topics.
- Introduction to some OR models of common interests.