Seminar: Bounds and Approximations in Stochastic Programming

Contact Name: Alberto Santini

Live-streaming of the seminar will be available at the following URL:

https://webconference.unibo.it/or-seminar

Abstract

Stochastic programming deals with optimization problems involving uncertain data. Such a kind of problems occur in almost all areas of science and engineering, from transportation, energy to finance. However, stochastic programs are usually hard to solve in realistically sized problems. Providing bounds for their optimal solution, may help in evaluating whether it is worth the additional computations for the stochastic program versus simplified approaches. In this seminar, after introducing basic properties and solution techniques of two-stage and multistage stochastic programming, approximation methods both in the linear and non-linear cases will be evaluated.

The approximation methods are based on different level of information gained from deterministic, sub-problems solutions and rolling-horizon approaches. The idea behind is that in case the solution of a large stochastic program is quite demanding, one may try to solve simpler problems for finding lower and upper bounds and proceed to find tighter and tighter bounds, if the difference between the first two is quite large. The described relationships applies also to the integer case. Structural similarities between the stochastic solution and its deterministic counterpart are also analyzed. The aim of the methods is to find out, even when the value of stochastic solution VSS is large, if the deterministic solution carries useful information for the stochastic case. It turns out that a large VSS does not necessarily imply that the deterministic solution is useless for the stochastic setting.

Measures of the structure of the deterministic solution which generalize the loss using the skeleton solution by taking into account the information on reduced costs associated to the out-of-basic variables in the expected value solution, will be introduced and inequalities in relation to the standard VSS are presented. Numerical results on a multistage inventory problem and on a real case supply transportation problem provided by the primary Italian cement producer illustrate the relationships.

About the Speaker

Positions

(Oct. 2011 − now) Assistant Professor in Operations Research (Ricerca Operativa, s.s.d. 01/A6, MAT/09) at the Department of Management, Economics and Quantitative Methods, University of Bergamo (I).

(Oct. 2006 − Sept. 2011) Assistant Professor in Mathematics (Metodi matematici delle scienze attuariali e finanziarie, s.s.d. SECS−S/06) at the Department of Mathematics Statistics, Computer Science and Applications “Lorenzo Mascheroni”, Faculty of Economics, University of Bergamo (I).

(Nov. 2005 − Sept. 2006) Research Assistant at Department of Mathematics Statistic and Applications, Faculty of Economics, University of Bergamo (I). Title of research project: “Applications of stochastic programming to energy and finance”, Project supervisor: Prof. Marida Bertocchi.

Education

(Dec. 4 2006) Ph.D. in Mathematics at University of Milano-Bicocca (I). Title of the thesis: Kinematics of elastic filaments and magnetic relaxation of flux tubes. Supervisor: Professor Renzo L. Ricca.

(Sept. 18 2003) Degree in Mathematics at Università Cattolica del Sacro Cuore of Brescia (I), mark: 110/110 e lode. Title of the thesis: Relazioni fra K-loop e strutture di riflessione con l’applicazione al modello di Poicaré di piano iperbolico. Advisor: Prof. Silvia Pianta.

Awards and Merits

Merit Scholarship as one of the two best students of the Faculty of Mathematics, Physics and Natural Sciences of the Università Cattolica del Sacro Cuore of Brescia, for the academic years 2000/2001 and 2001/2002.

Ph.D. Scholarship in the years 2003-2006, Department of Mathematics and Applications of the University of Milano-Bicocca.

Poster entitled Modeling filament kinematics for proteic coding and viral spooling, selected as one of the three best posters for an oral presentation during the “Conference on Knots and other Entanglements in Biopolymers: Topological and Geometrical Aspects of DNA, RNA and Protein Structures”, Trieste, (Sept. 15−20 2008) (I).

Grant from the Italian group of mathematical physics “Progetto Giovani GNFM 2009”: “Energy of knotted DNA filaments”.

Selection of the paper: Velocity, energy and helicity of vortex knots and unknots by Maggioni, Alamri, Barenghi and Ricca, for the September 2010 issue of Virtual Journal of Atomic Quantum Fluids; Section: Topological excitations of quantum fluids.

Scientific Research Award “5 per 1000” for scientific merits in the years 2008−2010 as researcher of the Department of Mathematics, Statistics, Computer Science and Application of the University of Bergamo (I).

Second Place Winner: Interactive Poster Session, “INFORMS Conference” 13–16 Nov. 2011 Charlotte, North Carolina (USA).

Selected as a semi-finalist for the INFORMS Interactive Poster Session, “INFORMS Conference” 14-17 Oct. 2012 Phoenix, Arizona (USA).

Scientific Research Award “5 per 1000” for scientific merits in the years 2012-2013-2014 as researcher of the Department of Management, Economics and Quantitative Methods of the University of Bergamo (I).