Optimization Models for Dynamic Pricing and Inventory Control under Uncertainty and Competition

1. Optimization Models for Dynamic Pricing and Inventory Control under Uncertainty and Competition Investigator: ElodieAdida, Mechanical and Industrial Engineering • A small improvement in pricing and revenue management strategy may yield significant profits. • What are the optimal prices and production levels over time? How to allocate capacity among multiple products? • What is the impact of demand uncertainty? • What is the impact of competition? Can we predict the state of equilibrium? • Is there a realistic and yet computationally tractable way to model the dynamic problem? • Modeling the optimal decision-making problem as a nonlinear, constrained, dynamic program • Robust optimization technique incorporates the presence of uncertainty with limited probabilistic information • Dynamic aspect with feedback (closed-loop) or without feedback (open-loop) • Game theoretical framework and determination of Nash equilibria encompasses competitors’ interactions • Price of anarchy: loss of efficiency due to competition in the system • Heuristic algorithm to determine the optimal pricing and allocation of available production capacity among products • Under data uncertainty, equivalent robust formulation is of the same order of complexity; involves safety stock levels • In a duopoly with uncertain demand, a relaxation algorithm converges to a particular unique Nash equilibrium • A good trade-off between performance (closed-loop) and tractability (open-loop) is to let controls be linearly dependent with the uncertain data realizations • Design of incentives (such as a contract) to reduce the loss of efficiency when suppliers compete on prices.