Optimal Control, Differential Variational Inequalities, and Their Application to Traffic Science, Revenue Management and Supply Chain

Optimal control problems and differential Nash games have been employed by many scholars in the study of dynamic pricing, supply chain management and transportation network flow problems. This dissertation emphasizes the extension of frequently employed deterministic, open-loop modeling paradigms into feedback and stochastic cases respectively with a focus on the computational perspective.;For the feedback differential Nash games, this dissertation briefly reviews the classical theory of Hamilton-Jacobi-Bellman equation and the general technique to synthesis feedback optimal control from its solution. Such techniques are then applied to the investigation of a dynamic competitive pricing problem of perishable products with fixed initial inventories (DPFI). Other qualitative analysis and numerical extensions of the DPFI model are also provided.;In the study of differential Nash games with Ito-type of stochastic dynamics, this dissertation starts from reviewing the stochastic maximum principle. It then proposes stochastic differential variational inequality (S-DVI) as the necessary condition for stochastic differential Nash games. As an application, this dissertation provides formulation, qualitative analysis and algorithm for a stochastic differential oligopsony problem where multiple agents compete in the procurement of key raw material which follows Ito-type of stochastic price dynamics.