Information Relaxations and Duality in Stochastic Dynamic Programs: A Review and Tutorial

In this monograph, we provide an overview of the information relaxation approach for calculating performance bounds in stochastic dynamic programs (DPs). The technique involves (1) relaxing the temporal feasibility (or nonanticipativity) constraints so the decision-maker (DM) has additional information before making decisions, and (2) incorporating a penalty that punishes the DM for violating the temporal feasibility constraints. The goal of this monograph is to provide a self-contained overview of the key theoretical results of the information relaxation approach as well as a review of research that has successfully used these techniques in a broad range of applications. We illustrate the information relaxation approach on applications in inventory management, assortment planning, and portfolio optimization.