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# Student guide Faculty of Engineering A.Y. 2010/11

Mathematical Methods for Industrial Applications
Aim of the course
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.
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Syllabus
1 - Discrete dynamical systems and finite difference equations
2- Linear systems of the 1st and 2nd order: stability and examples.
3- Nonlinear systems: stability and examples.
4 - Logistics equation, Hénon system, Lotka-Volterra model.
5 - Qualitative study of discrete dynamical systems.
5 - Beer Game
6 - Long Wave
7 - Nonlinear programming: introduction and examples.
9 - Nonlinear programming: solution methods.
10 - Stochastic linear programming:
11 - Optimization Toolbox
12 - Genetic algorithms and the Genetic Algorithm Toolbox

13. Operational problems:
- Influence diagrams and decision trees
- The Bayesian approach
- Multiple preferences in the presence of certainty and uncertainty
- Applications to optimisation of operational and managerial decisions in industrial installations

14. Reliability applications:
- The structure function
- The energy function
- Application of Markov Chains
- Maintenance optimisation: analytical and numerical methods
Examinations
There will be a written final exam.