A
first learning objective is to introduce some discrete linear and non-linear
models using systems of finite difference equations. Students will learn to analyse solutions both quantitatively and
qualitatively. In particular, 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.
A
second learning objective is to present integer, nonlinear and stochastic
linear programming and genetic algorithms, including their applications to the
Beer Game and to the Long Wave model for optimising ordering policies. The Matlab Optimization Toolbox and Genetic Algorithm and
Direct Search Toolbox software programs will be used.
The course also equips students with the tools for
solving operational research problems, with particular emphasis on industrial
operational decisions. The elements of Decision Theory in the presence of
uncertainty and multiple objectives are presented. The resolution of problems
concerning management decisions in situations with and without operational risk
are discussed, through use of Influence Diagrams and Decision Trees. Reliability
problems are then addressed, with special emphasis on building Probabilistic
Risk Assessment models for optimising maintenance and stochastic optimisation
problems with coherent risk measures. The course will alternate lectures on the theory
with the analysis of examples and case studies encountered in industrial
practice.
None
Syllabus
1
- Discrete dynamical systems and finite difference equations
2-
Linear systems of the 1st and 2nd order: stability and examples.