2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
WA9 - Applications of distributionally robust optimization
May 18, 2022 10:30 AM – 12:10 PM
Location: Groupe Cholette (yellow)
Chaired by Chun Peng
10:30 AM - 10:55 AM
Network Flow Models for Two-Stage Robust Binary Optimization
In this talk, we examine two-stage robust binary optimization (RBO) problems with objective uncertainty. We describe a new set of reformulation techniques inspired by decision diagrams which enable the transformation of the infinite-dimensional two-stage RBO problem into a single constrained network flow model. We show that the network flow model is easy to implement and performs well computationally compared to existing solution methods.
10:55 AM - 11:20 AM
Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning
Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. We propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable generation expansion planning problem, called R-ETEM, in which demand responses of EV users are uncertain. Then, we employ a linear-quadratic game to simulate the average charging behavior of EV users. The two models are coupled through a dynamic price signal broadcasted by the utility. Mean-field game theory is used to solve the linear-quadratic game model. Finally, we develop a new coupling algorithm between R-ETEM and the linear-quadratic game with the purpose of adjusting in R-ETEM the uncertainty level of EV demand responses.
11:20 AM - 11:45 AM
Distributional Robustness and Inequity Mitigation in Disaster Preparedness of Humanitarian Operations
In this paper, we study a predisaster relief network design problem with uncertain demands. The aim is to determine the prepositioning and reallocation of relief supplies. Motivated by the call of the International Federation of Red Cross and Red Crescent Societies (IFRC) to leave no one behind, we consider three important practical aspects of humanitarian operations: shortages, equity, and uncertainty. Numerical studies on the 2010 Yushu earthquake positively demonstrate the value of our methodology in alleviating geographical inequities and reducing shortages. Our case study also provides several other interesting insights that may be useful for humanitarian organizations for disaster preparedness.
11:45 AM - 12:10 PM
Distributionally robust optimization for multi-item lot sizing problem under yield uncertainty
This research investigates a distributionally robust optimization approach to the lot-sizing problem with backorder and yield uncertainty under event-wise ambiguity sets. We rely on the Moment-based, Wasserstein and K-Means clustering ambiguity sets to represent the yield distribution. We also consider static and static-dynamic decision strategies to calculate a solution. In this talk, we will present the performance of different sets of ambiguity to determine a production plan that is satisfactorily robust to changes in the environment. The numerical experiment shows that the model remains tractable for all ambiguity sets considered and the production plans obtained remain efficient for different strategies and decision contexts.