Mathematical Programming

Applied Mathematics Honours Course (2007)

Introduction
Course content
Administrative Information

Textbook and Class notes
Course format and Assessment method
Course timetable for 2007
2007 Course lecturer

Assignments and Marks
The Operations Research Society of South Africa

Introduction

This course is suitable for graduate students on honours level in applied mathematics and engineering who have a background in elementary optimisation techniques and basic linear algebra (although most of the necessary background will be recapped at the start of the course). Computer programming skills are not essential, but are helpful.

Course content

This course builds on the foundation laid in Applied Mathematics 344 within the field of optimisation. Topics studied include:

Linear programming: The simplex algorithm and tableau; introduction to Lindo and Excel; matrix formulation of LP; complexity of the simplex algorithm; sensitivity analysis and duality.
Integer programming: Problem formulation; branch-and-bound method; implicit enumeration; cutting plane algorithm.
Multiple-objective programming: Goal programming; complexity of multiple-objective approaches; sensitivity analysis within goal programming.
Dynamic programming: Backward recursion; network problems; inventory control and resource allocation; formulation of recursions; forward recursion.

Emphasis is placed on using these techniques to model real world applications, solving the resulting models and interpreting solutions in very real and practical terms. Examples of problems include transport problems; knapsack problems; travelling salesman problem; network problems; resource allocation problems.

Outcomes of the course thus far.

Administrative Information

Textbook and Class notes

The official textbook for the course is WL Winston, Operations Research: Applications & Algorithms, 3rd edition [4th edition], Duxbury Press, Belmont, California, 1994 [2004]. Class notes will also be provided for certain topics such as complexity theory and multi-objective programming.

Course format and Assessment method for 2007

The course consists of one 2-hour and one 1-hour lecture per week. Students are expected to hand in homework assignments regularly at the start of the 2-hour lecture. There is a written tests during the course and at the end of the course. Marks for homework assignments together with those for tests make up the candidate's final mark for the course.

Course timetable for 2007

The honours timetable will be finalized on Monday, 5 February 2007 at 08:30 in room A308.

Assignments and Marks

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2007 marks

	The Operations Research Society of South Africa (ORSSA)

Mathematical Programming fall within the field of Operations Research, also know as Management Science. Management problems occur when a conflict exist between the different resources available and goals that one wishes to achieve.

Formally, Operations Research (OR) and the Management Sciences (MS) are the professional disciplines that deal with the application of information technology for informed decision-making. OR/MS Professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behaviour and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

Today thousands of individuals pursue careers in operations research, the management sciences and closely related professions. Their work has achieved an increasingly important role in both the public and private sectors. OR/MS professionals inform public officials on such topics as energy policy; design and operation of urban emergency systems; defense; health care; water resource planning; and criminal justice. They also address a wide variety of issues in communication systems; computer operations, design, and networking; transportation; marketing; finance; inventory planning; manufacturing; and many other topics that aim to improve business productivity. In addition, recently some OR/MS professionals have contributed to the physical sciences (in biology, chemistry, and physics).

The Operations Research Society of South Africa (ORRSA) [Die Operasionele Navorsingsvereniging van Suid Afrika(ONSA)] exists primarily to further the interests of those engaged in, or interested in, OR activities. The student membership fee is only R20 annually. The newsletters also contain job advertisements in the field of OR/MS. Furthermore, students with membership can also publish their CV's in the newsletter if they are looking for a career in OR/MS.

Click here to visit the ORRSA web page.