SCQF Level: 10
Availability: Spring, Advanced module
Course Prerequisite: MATU913
Credit Value: 20 (1 module)
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.
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.
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
B1: Linear Programming, including the mixed-integer case
B2: Lagrangean theory: inequality constrained optimisation, duality
B3: Applications: Discrete Optimal Control
Managing time effectively, working methodically, competence in presentation and communication.
W. L. WINSTON, "Operations Research : Applications and Algorithms", 2nd edition Duxbury Press, 1991.
3 one-hour lectures and a 1.5 hour workshop per week.
1/3 Coursework (2 class tests) and 2/3 examination.