Joint Pricing and Inventory Management with Strategic Customers

Abstract

We consider a joint pricing and inventory management problem wherein a seller sells a single product over an infinite horizon via dynamically determining anonymous posted prices and inventory replenishment quantities. Customers arrive over time with a deterministic arrival rate but heterogeneous product valuations. Unlike typical inventory models, we assume that customers are forward-looking, who can strategize their times of purchases. A customer incurs waiting and monitoring cost if he delays his time of purchase anticipating a lower future price. The seller incurs fixed ordering cost and inventory holding cost. The seller seeks a joint pricing and inventory policy that maximizes her long-run average profit. We show that the optimal policy is cyclic, i.e., the seller repeats the pricing and ordering decisions over cycles of the same length. Under this optimal policy, strategic customer equilibrium behaviors are proven to be myopic. The seller's optimal long-run average profit in the presence of strategic customers is the same as her optimal profit in an auxiliary classical backlogging model wherein customers are myopic that they make their purchasing decisions immediately upon their arrivals. Remarkably, this implies that solving the (seemingly very hard) model with strategic customers is as easy and tractable as solving the above auxiliary model with myopic customers. Our results settle the open debate whether incorporating strategic customer behaviors significantly complicates the model. The answer is surprisingly appealing. Our results allow firms to incorporate strategic customer behaviors with little modeling and computational overhead. We develop a novel approach to prove the optimality of our proposed policy in the presence of strategic customers. In particular, we establish a benchmark profit that is the seller's optimal profit in the joint mechanism design and inventory control problem. We show that this benchmark serves as an upper bound of all joint pricing and inventory policies. We then show that this benchmark is upper bounded by the seller's profit under our proposed policy, which then implies the optimality of our policy.