Stochastic Control Through a Modern Lens: Applications in Supply Chain Analytics and Logistical Systems

Abstract

The thesis investigates classical multi-period stochastic control problems through a modern lens, including stochastic inventory control, dynamic pricing and vehicle routing. A brief history of the academic works on stochastic control is presented in Chapter 1, where the relevance of papers on stochastic processes, dynamic programming and reinforcement learning is also discussed. This thesis then focuses on revisiting inventory control, dynamic pricing and vehicle routing i) in a data-driven fashion; ii) with flexible architectures. Chapters 2-3 present several state-of-the-art results on data-driven inventory control. In Chapter 2, the following question is revisited: how much data is needed in order to obtain a (nearly) optimal policy for inventory control? To resolve this long-standing open question, a novel sample-based algorithm is proposed for the backlog setting and a matching (up to a logarithmic factor) lower-bound is also given. In Chapter 3, the same question for the joint pricing and inventory control problem is studied and the first sample-efficient solution is proposed. Chapter 4 is dedicated to the vehicle routing problem with stochastic demands (VRPSD). By combining ideas from vehicle routing and manufacturing process flexibility, a new approach to VRPSD is proposed, that uses overlapped routing with customer sharing in route determination, whose performance is close to the theoretical lower-bound, and significantly improves upon the routing strategy without overlapped routes. Chapter 5 concludes the thesis, and points out several future research directions.