Department of
Mathematical Sciences
CARNEGIE MELLON UNIVERSITY
OPERATIONS RESEARCH II 21-393
Professor A.M.Frieze,
Wean Hall 7202, x8476,
alanatrandomdotmathdotcmudotedu
1. COURSE OBJECTIVES
(i) To develop and extend the students knowledge of mathematical
techniques underlying the application of Operations Research.
(ii) To give experience of working in a group on a project.
2. COURSE TEXT
There is no required book for the course. There are a number of books
which cover much of the material, none of which are recommended.
1. Introduction to Operations Research,
by F.S.Hillier and G.J.Liebermann, (published by McGraw-Hill).
2. Operations Research: Applications and Algorithms,
by W.L.Winston, (published by P.W.S. Kent).
3. Principles of Operations Research,
by H.M.Wagner, (published by Prentice-Hall).
3. TOPICS
I will make a selection from the following:
1. Linear Programming
Duality and Dual Simplex, Sensitivity Analysis and Parametric
Programming,
Simple Upper Bounds,
Interior Point methods, Two-Person Zero-Sum Games.
2. Integer Linear
Programming
Formulations, 0-1 Programming, Cutting Planes and Branch and Bound.
3. Combinatorial
Optimisation
Shortest Paths, Assignment, Minimum Spanning Trees, Network Flows,
PERT/CPM, Machine Scheduling, NP-Completeness, Heuristics.
4. Non-Linear Programming
Karush, Kuhn-Tucker Conditions, Quadratic Programming.
5. Inventory Theory
6. Dynamic
Programming
Markov Decision Processes
7. Markowicz Model in
Mathematical Finance
4. THE PROJECT
The class will be partitioned into working groups of three/four
students. These groups should be formed voluntarily. If necessary, I
will make assignments. Each group will work together on a short project
which it will research, write a paper on and make a presentation to the
class near the end of the semester. Examples of previous projects are
obtainable from Dr. Walker. It will be your responsibility to think
of a project. I will vet your ideas for suitability and practicality.
The evaluation of the project will be based on the following factors:
The degree to which the project
demonstrates the group's ability to abstract a problem into
mathematical form and to employ the
appropriate solution techniques.
The degree to which the group
demonstrates professional writing and presentation skills.
Suggested schedule for carrying out project:
Activity
|
Target
Date for Completion |
Form small group 3/4 students
|
September 3. |
| Settle on idea for project |
September 28. |
| Finish research |
November 30 |
| Finish write-up |
December 17. |
5. GRADING SYSTEM
There will be an initial set of homeworks, amounting to approxmately
one quarter the normal load for a one semester course. There will also
be two tests.
| Project |
50% |
| 2 Tests |
20% each |
| Homework |
10% |
There will be no written final. The tests will be open book and notes.
6. CLASS SCHEDULE
Lectures MWF 1.30 - 2.20PM in WEH6423.
Tests: September 28, November 2.
7. OFFICE HOURS
Wed,Thu 11.00 - 12.00AM in WEH7202.
8. HOMEWORK
9. OLD
TESTS
10. SCHEDULE
Curriculum Goals: The aim of this course is to increase the
student's knowledge of the techniques and applicability of mathematical
ideas in the solution of organisational problems. The project is an
important component in increasaing the student's
confidence in applying these ideas.