## Advanced mathematical modeling and optimizationUE-SIN.08611

 Teacher(s): Pacheco Paneque Meritxell Level: Master Type of lesson: Lecture ECTS: 5 Language(s): English Semester(s): SA-2022

This course considers modeling and optimization aspects of mixed-integer linear programming (or integer programming for short). This important subdomain of mathematical programming and extension of linear programming considers the problem of optimizing a linear function of many variables, some or all of them restricted to be integers, subject to linear constraints.

Integer programming is a thriving area of optimization. It has countless applications in production planning and scheduling, logistics, layout planning and revenue management, to name just a few. Thanks to effective and reliable software, it is widely applied in industry to improve decision-making.

In this course, we cover the theory and practice of integer programming. In the first part, we address mathematical modeling aspects. We discuss how integer variables can be used to model various practically relevant, complex decision problems. We then introduce some standard optimization problems and develop, analyze and compare different integer programming formulations for them. We also introduce powerful modeling and solving tools and test them on the optimization problems given in the course. In the second part, we address optimization aspects, in which we discuss the basic methodology applied to solve integer programs. In particular, we consider implicit enumeration techniques (branch and bound), polyhedral theory, cutting planes and primal heuristics. We also look at some advanced techniques, such as Danzig-Wolfe decomposition and column generation.

#### Training aims

With this course, the students gain the ability to formulate and solve practically relevant decision problems using integer programming, and they understand the basic methodology for solving integer programs and its implications with respect to modeling decisions.

#### Documentation

Conforti, Michele, Gérard Cornuéjols, and Giacomo Zambelli. Integer programming, Graduate Texts in Mathematics. Springer (2014).