Student guide Faculty of Engineering A.Y. 2008/09

The course is divided into two parts. The first part introduces students to discrete linear and non-linear models using systems of finite difference equations. Non linear models are of particular interest because they can give rise to chaotic dynamics and have attractors with fractal dimensions. Students will learn to analyse solutions both quantitatively and qualitatively. They will study inventory management models including the Beer Game, in which the bullwhip phenomenon emerges, and economic models including Stratagem-2, describing the Long Wave phenomenon. The solutions to the studied models will be graphically represented using Matlab.

The second part of the course presents non linear programming from an analytic and numerical perspective using the Matlab Optimisation Toolbox, in addition to linear stochastic programming and genetic algorithms, which in particular are applied to the Beer Game and to Stratagem-2 for optimising ordering policies, and showing their application to scheduling problems.

1 - Discrete dynamical systems and finite difference equations.

2- Linear systems of the 1st and 2nd order: stability and examples.

3- Non-linear systems: stability and examples.

4 - Logistics equation, Henon system, Lotka-Volterra model.

5 - Qualitative study of discrete dynamical systems.

5 - Beer Game.

6 - Long Wave.

7 - Non-linear programming: introduction and examples.

9 - Non-linear programming: solution methods.

10 - Stochastic linear programming:

11 - Optimization Toolbox

12 - Genetic algorithms.

There will be a written examination.

Study materials provided by the lecturers.

Goldberg S., Introduction to difference Equations, Dover Publications, 1986

Shone R., Economics Dynamics, Cambridge University Press, 1997

Wiston W.L., Operations Research, Duxbury Press, Belmont 1993