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We consider a firm (e.g., retailer) selling a single nonperishable product over a finite-period planning horizon. Demand in each period is stochastic and price-dependent, and unsatisfied demands are backlogged. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity, but it knows neither the form of demand dependency on selling price nor the distribution of demand uncertainty a priori, hence it has to make pricing and ordering decisions based on historical demand data. We propose a nonparametric data-driven policy that learns about the demand on the fly and, concurrently, applies learned information to determine replenishment and pricing decisions. The policy integrates learning and action in a sense that the firm actively experiments on pricing and inventory levels to collect demand information with the least possible profit loss. Besides convergence of optimal policies, we show that the regret, defined as the average profit loss compared with that of the optimal solution when the firm has complete information about the underlying demand, vanishes at the fastest possible rate as the planning horizon increases.

Coordinating Pricing and Inventory Replenishment with Nonparametric Demand Learning