Huseyin Topaloglu

Incorporating Discrete Choice Models into Revenue Management Decisions

Over the last couple of decades, there has been enormous progress in using discrete choice models to understand how customers choose and substitute among products and incorporating this understanding into operational models to decide which assortment of products to offer to customers or what prices to charge. We owe some of this progress to increase in the computational power so that we can build and solve more detailed operational models, but perhaps, most of this progress is due to the fact that online sales channels started providing fine-grained data on how customers browse the products. In this talk, we will go over fundamental discrete choice models that have been used in building operational assortment optimization and pricing models, overview the main algorithmic approaches that have been developed to solve the operational models, and identify research prospects. The focus will be on both static models that make one-shot assortment optimization or pricing decisions, as well as dynamic models that explicitly capture the evolution of demand and inventories over time.

Enrique Zuazua

enrique.zuazua@fau.de
https://dcn.nat.fau.eu/enrique-zuazua/

[1] Friedrich Alexander Universität Erlangen Nürnberg - Alexander von Humboldt Professorship, Germany
[2] Fundación Deusto, Bilbao
[3] Universidad Autónoma de Madrid

Control and Machine Learning

Systems control, or cybernetics—a term first coined by Ampère and later popularized by Norbert Wiener—refers to the science of control and communication in animals and machines. The pursuit of this field dates back to antiquity, driven by the desire to create machines that autonomously perform human tasks, thereby enhancing freedom and efficiency.

The objectives of control systems closely parallel those of modern Artificial Intelligence (AI), illustrating both the profound unity within Mathematics and its extraordinary capacity to describe natural phenomena and drive technological innovation.

In this lecture, we will explore the connections between these mathematical disciplines and their broader implications. We will also discuss our recent work addressing two fundamental questions: Why does Machine Learning perform so effectively? And how can data-driven insights be integrated into the classical applied mathematics framework, particularly in the context of Partial Differential Equations (PDE) and numerical methods?