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Department of Mathematical Sciences

{\bf CARNEGIE MELLON UNIVERSITY}

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{\bf OPERATIONS RESEARCH II 21-393}
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{\bf Professor A.M.Frieze, 

Wean Hall 7202, x8476, alan@random.math.cmu.edu}

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{\bf 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.

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{\bf 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. 

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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).

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{\bf 3. TOPICS}\\I will make a selection from the following:

1. {\bf Linear Programming}\\
Duality and Dual Simplex, Sensitivity Analysis and Parametric
Programming, 
Simple Upper Bounds, 
Interior Point methods, Two-Person Zero-Sum Games.

2. {\bf Integer Linear Programming}\\
Formulations, 0-1 Programming, Cutting Planes and Branch and Bound.

3. {\bf Combinatorial Optimisation}\\
Shortest Paths, Assignment, Minimum Spanning Trees, Network Flows, 
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PERT/CPM, Machine Scheduling, NP-Completeness, Heuristics.

4. {\bf Non-Linear Programming}\\
Karush, Kuhn-Tucker Conditions, Quadratic Programming.

5. {\bf Inventory Theory}\\
6. {\bf Markov Decision Processes}\\
7. {\bf Markowicz Model in Mathematical Finance}

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{\bf 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: 
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\item 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.
\item the degree to which the group demonstrates professional writing
and 
presentation skills.
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Suggested schedule for carrying out project:

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{\bf Activity} & {\bf Target Date for Completion}\\
Form small group 3/4 students & September 4\\
Settle on idea for project & September 29\\
Finish research & November 17\\
Finish write-up & December 1
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{\bf 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.

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Project &  50\% \\
2 Tests &  20\% each\\
Homework & 10\%
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There will be no written final. The tests will be open book and notes.

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{\bf 6. CLASS SCHEDULE}

Lectures MWF 10.30 - 11.20 in DH 1211.

{\bf Tests} September 30, October 21.

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 {\bf 7. OFFICE HOURS}

MTWThF 9.30 - 10.00 in WEH7202.
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