Parametric Demand Learning with Limited Price Explorations in a Backlog Stochastic Inventory System

In this paper we study a multi-period stochastic inventory system with backlogs. Demand in each period is random and price sensitive, but the firm has little or no prior knowledge about demand distribution and how each customer responds to the selling price, so the firm needs to make periodic pricing and inventory replenishment decisions to maximize expected total profit. We consider the scenario where the firm is faced with the business constraint that prevents it from conducting extensive price exploration, and develop parametric data-driven algorithms for pricing and inventory decisions. We measure the performances of the algorithms by regret, which is the profit loss compared to a clairvoyant who has complete information about the demand distribution. We analyze the cases where the number of price changes is restricted to a given number or a small number relative to the planning horizon, and show that the regrets for the corresponding learning algorithms converge at the best possible rates in the sense that they reach the theoretical lower bounds. Numerical results indicate that these algorithms empirically perform very well. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transaction, datasets, additional tables, detailed proofs, etc