Dynamic pricing and inventory control with no backorders under uncertainty and competition

Abstract

Recently, revenue management has become popular in many industries such as the airline, the supply chain, and the transportation industry. Decision makers realize that even small improvements in their operations can have a significant impact on their profits. Nevertheless, determining pricing and inventory optimal policies in more realistic settings may not be a tractable task. Ignoring the potential inaccuracy of parameters may lead to a solution that actually performs poorly, or even that violates some constraints. Finally, competitors impact a supplier's best strategy by influencing her demand, revenues, and field of possible actions. Taking a game theoretic approach and determining the equilibrium of the system can help understand its state in the long run. This thesis presents a continuous time optimal control model for studying a dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting. We introduce a demand-based model with convex costs. A key part of the model is that no backorders are allowed, as this introduces a constraint on the state variables. We first study the deterministic version of this problem.

(cont.) We introduce and study a solution method that enables to compute the optimal solution on a finite time horizon in a monopoly setting. Our results illustrate the role of capacity and the effects of the dynamic nature of demand. We then introduce an additive model of demand uncertainty. We use a robust optimization approach to protect the solution against data uncertainty in a tractable manner, and without imposing stringent assumptions on available information. We show that the robust formulation is of the same order of complexity as the deterministic problem and demonstrate how to adapt solution method. Finally, we consider a duopoly setting and use a more general model of additive and multiplicative demand uncertainty. We formulate the robust problem as a coupled constraint differential game. Using a quasi-variational inequality reformulation, we prove the existence of Nash equilibria in continuous time and study issues of uniqueness. Finally, we introduce a relaxation-type algorithm and prove its convergence to a particular Nash equilibrium (normalized Nash equilibrium) in discrete time.