Talk Abstract: Many real world decision problems are dynamic and affected by uncertainty. Stochastic Programming provides a powerful approach to handle this uncertainty within a multi-period decision framework. However, as the number of stages
increases, these problems become challenging to solve due to their rapid growth in complexity. To tackle this, approximation techniques are often used to simplify the original problem, providing useful upper and lower bounds for the objective function’s optimal
value.
This tutorial explores several methods for generating bounds in multistage optimization problems under uncertainty. We begin by reviewing bounds based on distribution and function approximations, drawing from established literature, and illustrating their
connection to the "generalized moment problem". Next, we discuss bounds based on scenario grouping under the assumption that a sufficiently large scenario tree is given but is unsolvable, both in the context of stochastic programming and distributionally robust
optimization. Finally, guaranteed bounds based on the concepts of first order and convex order stochastic dominance are presented. These approximations are versatile, applying to a wide range of problems without requiring specific conditions like linearity,
convexity, or stagewise independence. Our tutorial aims to highlight current research gaps and inspire further investigation into promising directions within this field.
Speaker Bio: Francesca Maggioni is Professor of Operations Research at the Department of Management, Information and Production Engineering (DIGIP) of the University of Bergamo (Italy). She graduated summa con laude in 2003 in Mathematics at the
“Università Cattolica del Sacro Cuore” of Brescia (Italy) and completed her PhD in Pure and Applied Mathematics at University of Milano Bicocca (Italy), in 2006. Her research interests concern both methodological and applicative aspects for optimization under
uncertainty. From a methodological point of view, she has developed different types of bounds and approximations for stochastic, robust and distributionally robust multistage optimization problems. She applies these methods to solve problems in logistics,
transportation, energy and machine learning. On these topics she has published more than 60 scientific articles featured in peer-reviewed operations research journals. In 2021 her research has been supported as principal investigator by a grant from the Italian
Ministry of Education for the project “ULTRA OPTYMAL Urban Logistics and sustainable TRAnsportation: OPtimization under uncertainTY and MAchine Learning”. She currently chairs the EURO Working Group on Stochastic Optimization and the AIRO Thematic Section
of Stochastic Programming. She has been secretary and treasurer of the Stochastic Programming Society. She is Associate Editor of the journals Transportation Science, Computational Management Science (CMS), EURO Journal on Computational Optimization (EJCO),
TOP, International Transactions in Operational Research (ITOR), Networks and guest editor of several special issues in Operations Research and Applied Mathematics journals.
The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.