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. A customer's arrival time and product valuation are his private information. Customers are forward-looking, who can strategize their times of purchases. Customer unsatisfied demand is backlogged. A customer incurs disutility from delaying making the purchasing decision and incurring product delivery delay. 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 the 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. We adopt a mechanism design approach to prove the optimality of our proposed policy in the presence of strategic customers.

Index Terms

• Theory of computation

  • Design and analysis of algorithms

    • Algorithm design techniques

      • Dynamic programming

  • Theory and algorithms for application domains

    • Algorithmic game theory and mechanism design

      • Algorithmic mechanism design

      • Computational pricing and auctions