Coordinating Pricing and Inventory Replenishment with Nonparametric Demand Learning

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 sensitive, and unsatisfied demands are backlogged. At the beginning of each period, the firm determines its selling price and inventory replenishment quantity with the objective of maximizing total profit, but it knows neither the average demand (as a function of price) nor the distribution of demand uncertainty a priori; hence, it has to make pricing and ordering decisions based on observed demand data. We propose a nonparametric, data-driven algorithm that learns about the demand on the fly and, concurrently, applies learned information to make replenishment and pricing decisions. The algorithm integrates learning and action in a sense that the firm actively experiments on pricing and inventory levels to collect demand information with minimum profit loss. Besides convergence of optimal policies, we show that the regret of the algorithm, defined as the average profit loss compared with that of the optimal solution had the firm known the underlying demand information, vanishes at the fastest possible rate as the planning horizon increases.