Joint Pricing and Inventory Management with Strategic Customers
61 Pages Posted: 28 Apr 2016 Last revised: 21 Nov 2022
Date Written: June 14, 2017
Abstract
We consider a model wherein the seller sells a product to customers over an infinite horizon. At each time, the seller decides a set of purchase options offered to customers and the inventory replenishment quantity. Each purchase option specifies a price and a product delivery time. Customers are infinitesimal and arrive to the system with a constant rate. Customer product valuations are heterogenous and follow a stationary distribution. A customer's arrival time and product valuation are his private information. Customers are forward looking, i.e., they strategize their purchasing times. A customer incurs delay disutility from postponing to place an order and waiting for the product delivery. A customer's delay disutility rate is perfectly and positively correlated with his valuation. The seller has zero replenishment lead time. The seller incurs fixed ordering cost and inventory holding cost. The seller seeks a joint pricing, delivery and inventory policy that maximizes her long-run average profit. Through a tractable upper bound constructed by solving a mechanism design problem, we derive an optimal joint pricing, delivery and inventory policy, which is a simple cyclic policy. We also extend our policy to a stochastic setting and establish its asymptotic optimality.
Keywords: joint pricing and inventory control, strategic customers, optimal policy, mechanism design
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