A bilevel framework for decision-making under uncertainty with contextual information. (April 2022)

• Record Type: Journal Article
• Authors: Muñoz, M.A.; Pineda, S.; Morales, J.M.
• Is Part Of: Omega. Volume 108(2022)
• Publication Date: 2022-04
• Subjects: Data-driven decision-making under uncertainty -- Bilevel programming -- Statistical regression -- Strategic producer -- Electricity market; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2021.102575
• Languages: English
• ISSNs: 0305-0483

Abstract

Highlights: We propose an approach for decision-making under uncertainty with contextual information. Our approach fits a parametric model to the data to maximize its decision value. Our framework translates into a bilevel program to be solved using off-the-shelf solvers. We showcase the benefits of our approach using three different classical problems. We also compare our approach with existing ones in a realistic case study. Abstract: In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically tailored to maximizing the decision value, while accounting for possible feasibility constraints. From a mathematical point of view, our framework translates into a bilevel program, for which we provide both a fast regularization procedure and a big-M-based reformulation that can be solved using off-the-shelf optimization solvers. We showcase the benefits of moving from the traditional scheme for model estimation (based on statistical quality metrics) to decision-guided prediction using three different practical problems. We also compare our approach with existing ones in a realistic case study that considers a strategic power producer that participates in the Iberian electricity market. Finally, we use these numerical simulations to analyze the conditions (in terms of the firm's cost structure and production capacity) under which our approach proves to be more advantageous to the producer.