Combinatorial Optimization I: Integer Programming
— The discrete nature of many decision problems can lead to a so-called combinatorial explosion. Whenever avoiding such phenomena (e.g. by relaxing integrity constraints) proves to be impossible, Integer Programming (IP) allows to tackle a great number of Combinatorial Optimization problems such as those found in the domain of logistics, production management or scheduling.


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


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


Artelys consultants specialized in modeling and solving large size optimization models applied to the domains of energy, transport and logistics.


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.

• 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.


Practical information

Next session
06-21-2022 – 06-22-2022
Special session available
(minimum of 4 participants, on-site or online)

Training Duration
2 days

Training cost per person: 
1 400 € excluding taxes.
This includes the materials, meals, coffee and handouts. Computers are provided.

Entire Catalog
Available on this link

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