Course IntPM: Integer Programming Methods

Time:	Monday 11.00–12.45
Period:	17 November 2025 – 15 December 2025 and 19 January 2026 – 16 February 2026
Location:	All LNMB courses take place on the Campus Utrecht Science Park. Room HFG 611, Hans-Freudenthal building, Budapestlaan 6, 3584 CD Utrecht
Lecturers:	Dr. R. Spliet (Erasmus University Rotterdam) and Dr. M. Walter (University of Twente)

Course description

The vast majority of problems in combinatorial optimization can be formulated as an integer linear program (ILP): Maximize or minimize a linear objective function subject to linear constraints and the additional restriction that the decision variables can take only integer values (typically only 0/1). This makes ILPs a perfect tool for formulating problems in combinatorial optimization; many software packages are available for this. The drawback is that solving ILPs is generally a computationally demanding task; it is NP-hard. Nevertheless, in practice, also these problems have to be solved. In this course we focus on techniques for solving ILPs.

The following topics will be treated:

the expressive power of ILPs in combinatorial optimisation
geometry of integer linear programmes
easy and difficult ILPs
geometric techniques based on cutting planes
decomposition techniques

More information can be found on this website.

Literature

Conforti, Cornuejols, and Zambelli, Integer programming, Springer 2014 (available online via springerlink)

Prerequisites

Knowledge of linear algebra and linear programming.

Examination

Take home problems.

Address of the lecturers

Dr. Remy Spliet
Erasmus Universiteit Rotterdam
Department of Economics
Postbus 1738, 3000 DR Rotterdam
Phone: 010 4081342
E-mail: spliet@ese.eur.nl

Dr. Matthias Walter
University of Twente,
Faculty of Electrical Engineering, Mathematics & Computer Science
P.O. Box 217
7500 AE Enschede
Phone: 053 4898744
E-mail: m.walter@utwente.nl,