Bounding and Sampling Methods for Multi-Stage Optimization Problems Under Uncertainty

ABSTRACT

Many real-world decision problems are dynamic and affected by uncertainty. Stochastic Programming provides a powerful approach to handling this uncertainty within a multi-period decision framework. However, as the number of stages increases, the computational complexity of these problems grows exponentially, posing significant challenges. 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 talk explores methods for generating bounds and approximations for a wide variety of problem structures affected by uncertainty. We begin by reviewing bounds based on scenario grouping in the context of stochastic programming. Next, we extend these techniques to address more complex problems such as multi-stage distributionally robust optimization and multi-horizon stochastic optimization. Finally, probabilistic guarantees for constraint sampling in multi-stage convex robust optimization problems are presented and a chain of lower bounds is provided. Numerical results on inventory management and on power generation and transmission expansion planning show the efficiency of the proposed approaches.

BIOGRAPHY

Francesca Maggioni is a Professor of Operations Research at the Department of Management, Information and Production Engineering (DIGIP) of the University of Bergamo, Italy. 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. She has published more than 60 scientific articles featured in peer-reviewed operations research journals. 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. Professor Maggioni 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, RAIRO Operations Research and guest editor of several special issues in Operations Research and Applied Mathematics journals.