QUANTITATIVE METHODS AND OPTIMIZATION
Learning outcomes of the course unit
The two main Learning Goals that are targeted by this course are: “Achieving analytical excellence” and “Complex Problem Solving”. The specific learning goals of the course are the ability to: analyze and model a decision problem presented as a case study; communicate with decision-aid experts and consultants; use computing tools (e.g. CPLEX) for solving decision problems; write a two-level report, with i) an Executive Summary addressed to an Executive
Committee and presenting conclusions, decisions and evaluation, and ii) a Technical Appendix addressed to experts presenting models and methods.
Course contents summary
The course is provided with a first part in which the basic concepts of Linear and Integer Programming are discussed. In particular, the course will present: Basic linear algebra and discrete mathematics concepts; linear programming and duality theory; integer linear programming and exact solution algorithm; complexity of the algorithms and the basics of graphs theory. Different families of exact method will be presented in details with a special attention to branch-and-cut and branch-and-price algorithms. The second part of the course is on the modeling, starting from the integer linear programming models for basic NP-complete problems with special emphasis on the discussion of the quality of their continuous relaxation. Finally, some more complex applications involving models with an exponential number of variables and/or constraints are discussed. The third and final part is devoted to Optimization for Data Science. In this part the techniques developed in the first two parts of the course will be used to effectively takle several Data Science Optimization problems, like clustering, classification and Support Vector Machine.
Optimization is a very powerful tool for modeling and solving decision problems arising in different areas, like engineering, finance, logistic, management, production and many others. The first part of the course covers the modeling aspects of the field, providing the tools for constructing effective mathematical models, i.e., models that can be solved in practice. The second part is devoted to the algorithmic aspects: basic algorithms are reviewed and more sophisticated ones, useful for those models characterized by a large number of variables and/or constraints, are presented in detail. Finally, the third part of the course present several real-world applications. The ability to analyze, model and structure a decision problem will be stressed and emphasized as well as the proper solving techniques and algorithms. Several sessions will be devoted to discussing and solving case studies.
Laurence A. Wolsey: ‘Integer Programming. Editore: Wiley-Interscience. Dispense fornite dal docente. G. Cornuejols, M.Trick: Quantitative Methods for the Management Sciences, Course Notes at the Carnegie Mellon University, USA ( http://mat.gsia.cmu.edu/classes/QUANT/notes/notes.html)
Free download: http://mat.gsia.cmu.edu/classes/QUANT/NOTES/notes.pdf
L. Lovász and K. Vesztergombi: Discrete Mathematics
Lecture Notes, Yale University, Spring 1999
In the course, special attention is devoted to the development of the theory and its
applications. The course is also focused on the developent of case studies of concrete applications. Several practical courses on machine will illustrate the use of the algorithms studied to solve optimization models on real-world datasets.
Assessment methods and criteria
Written exam plus project.