97271 - Mathematical Programming

Learning outcomes

Students are expected to acquire knowledge of theoretical and algorithmic tools to formulate and analyze mathematical optimization models using Mixed Integer Linear Programming (MILP), as well as design solution methods.

Course contents

The course aims to present both the theoretical and algorithmic aspects as well as some software tools for mathematical optimization problems formulated as Mixed Integer Linear Programs (MILP).

The course aims to simultaneously stimulate creativity and rigor during all phases of the realization of a decision support system based on mathematical optimization techniques.

• Linear Programming (LP)
• LP vs MILP formulations and "classical" problems
• Some notes on computational complexity theory to classify the "difficulty" of a MILP problem
• "Basic" algorithms for solving MILP problems
• Some notes on polyhedral combinatorics for describing the convex envelopes of the solutions
• "Advanced" algorithms to solve MILP with an exponential number of variables and/or constraints (column generation and separation)
• Decomposition techniques and relaxations for "structured" MILP problems
• Software tools to solve MILP models
• Real applications related to resource optimization

Readings/Bibliography

• Integer Programming by Laurence A. Wolsey
  John Wiley & Sons Inc., 2020.
• Integer and Combinatorial Optimization by George Nemhauser and Laurence A. Wolsey 
  John Wiley & Sons, Inc., 1999.

Teaching methods

Face-to-face lectures and exercises.

Assessment methods

Submission of a final project followed by an oral exam consistsing of  a presentation of the project with a critical discussion of the results obtained, possible variations/extensions, as well as theoretical questions on the entire program of the course. It will be required to submit the project reasonably in advance (to be agreed) with respect to the oral presentation. The evaluation of the project contributes substantially to forming the final grade.

Teaching tools

The teaching material will be available on the University of Bologna e-learning platform (https://virtuale.unibo.it ).

Office hours

See the website of Laura Galli