The Data-Driven Newsvendor Problem – Asymptotic Learning and Finite Sample Guarantees

: (Alternative Format Thesis)

Abstract

The Newsvendor Problem is a fundamental challenge in inventory management and operations research. The setting describes a retailer who needs to choose the level of inventory. Right after, customers arrive and express a random demand for the product. The retailer formulates the decision based on a history of sales data and past choices. The decision maker's objective is to learn the optimal stocking decision over time. This is a specific quantile of the demand distribution called the critical fractile. The agent learns about this quantile through repeated interactions with the environment.

In each period, the retailer can improve the quality of the immediate observation by ordering more. As a downside, this also increases the risk of having worthless products left over. Thus, a careful balance needs to be struck. This is an example of the exploration-exploitation dilemma.

Determining exactly how the agent should interact with the environment is unresolved to-date. Much of the existing research focuses on the process "from data to decisions". In this thesis we study the opposite direction: how decisions impact data. We will show that a history of sales contains a base level of knowledge about the critical fractile. It represents the worst state of belief a data-driven agent can experience. We will prove that this low-point is unavoidable and cannot be influenced by the decision maker. It will occur in finite time, and will always be experienced the same way irrespective of the agent's actions.

In addition, we examine how the base knowledge evolves over time. Our framework links the degree of exploration to the speed of learning under adverse conditions. This information-centric perspective provides a new interpretation of the decision maker's role. One where knowledge improves passively over time while the agent's actions can only affect the lead time, i.e. the time until the learning process is completed. We also provide new tools to evaluate and compare different policies during the design phase.

Date of Award	7 May 2025
Original language	English
Awarding Institution	University of Bath
Sponsors	EPSRC
Supervisor	Alex Cox (Supervisor) & Clarice Poon (Supervisor)