COURSE OBJECTIVES

Handle the discrete aspects of a decision problem with the help of Integer Programming (IP).

TARGET AUDIENCE

Engineers, economists, scientists and developers interested in modeling decision problems and implementing optimization algorithms.

Integer Linear Programming (ILP)
• A brief reminder of Linear Programming.
• Formulations: What is an Integer Program? Formulation of an Integer Linear Program. Combinatorial explosion. IP Formulations. Alternatives Formulations.
• Optimality, relaxation and bounds: optimality and relaxation, linear relaxations, combinatorial relaxations, lagrangian relaxation, duality, primal bounds.
• Modeling techniques and illustrations.
• Solving Integer Linear Programs with Branch-and-Bound.
• Principles of cutting methods and Branch- and-Cut. Numerical examples.

Application
• Introducing, modeling and solving a Travelling Salesman Problem with the FICO® Xpress solver.
• Introducing, modeling and solving an industrial problem with FICO® Xpress.
• Comparison between a naive formulation of the problem and a formulation including cuts.

Introduction to decomposition techniques
• Introduction to decomposition techniques: illustration of the interest of column generation.
• Principles and practical interest of column generation techniques.
• Presentation of an industrial application.