MATU9JA - Optimisation in Theory and Practice

SCQF Level: 10
Availability: Spring, Advanced module
Course Prerequisite: MATU913
Credit Value: 20 (1 module)

Aims

Optimisation problems arise in many areas of intellectual endeavour - in both the physical and social sciences and throughout business and engineering. The objective of this module is to develop the skills necessary to first model and then to solve optimisation problems.

Learning Outcomes

Students should be able to formulate and solve sequential decision problems using dynamic programming, interpret and solve transportation problems using the stepping-stone method, solve linear programmes by the graphical and simplex methods, solve nonlinear programmes using lagrangian theory, derive the dual of a nonlinear programming problem, and solve some simple problems in optimal control theory.

Content

A1: Shortest distance problem : Dynamic Programming and the Floyd algorithm
A2: Problems on a network: transportation and assignment problems, the stepping- stone and Hungarian algorithms
A3: Applications
B1: Linear Programming, including the mixed-integer case
B2: Lagrangean theory: inequality constrained optimisation, duality
B3: Applications: Discrete Optimal Control

Transferable Skills

Managing time effectively, working methodically, competence in presentation and communication.

Bibliography

W. L. WINSTON, "Operations Research : Applications and Algorithms", 2nd edition Duxbury Press, 1991.

Teaching Format

3 one-hour lectures and a 1.5 hour workshop per week.

Assessment

1/3 Coursework (2 class tests) and 2/3 examination.

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