Linear Programming - 3GMA0435

Goal(s)

• This is an introductory course on the basic techniques of mathematical programming. It is a basic course in linear programming in continuous variables.
  
• At the end of the course, students will be able to model a simple problem using a linear program, including translating the constraints of the problem through a system of linear equations or inequalities. Students will also be able to solve the program using the simplex algorithm and give different economic interpretations of the output of this algorithm, using the duality theory.
  For more complex problems, students will know how to model it by a linear integer or mixed program. Resolution methods such as Branch & Bound algorithm and the quality of the models will be studied to solve these problems efficiently.
  
• Students will use linear solvers such as Excel and OPL Studio.

Content(s)

The main points are

• Modelling a problem in a linear program
• Resolution algorithms: geometrics, simplex and variants
• Duality and economic interpretation
• Sensitivity analysis
• Modelling a problem in linear programming in mixed or integer variables
• Branch & Bound algorithm
• Quality of the various modellisations
• Modelling logical constraints
• Using commercial solver

Basic courses on linear algebra and matrices.