Technical Note—Data-Based Dynamic Pricing and Inventory Control with Censored Demand and Limited Price Changes

AbstractPricing and inventory replenishment are important operations decisions for firms such as retailers. To make these decisions effectively, a firm needs to know the demand distribution and its dependency on selling price, which is usually estimated using sales data at various testing price levels. Although more testing prices can lead to a better estimation of the demand–price relationship, frequent price changes are costly and come with adverse effect such as customers’ negative perception. In this article, data-driven algorithms are developed that learn the demand structure with constraints on the number of price changes. These algorithms are shown to converge to the optimal clairvoyant solution, and the convergence rates are the best possible in terms of profit loss.A firm makes pricing and inventory replenishment decisions for a product over T periods to maximize its expected total profit. Demand is random and price sensitive, and unsatisfied demands are lost and unobservable (censored demand). The firm knows the demand process up to some parameters and needs to learn them through pricing and inventory experimentation. However, because of business constraints, the firm is prevented from making frequent price changes, leading to correlated and dependent sales data. We develop data-driven algorithms by actively experimenting inventory and pricing decisions and construct maximum likelihood estimator with censored and correlated samples for parameter estimation. We analyze the algorithms using the T-period regret, defined as the profit loss of the algorithms over T periods compared with the clairvoyant optimal policy that knew the parameters a priori. For a so-called well-separated case, we show that the regret of our algorithm is O(T1/(m+1)) when the number of price changes is limited by m≥1 and is O(logT) when limited by βlogT for some positive constant β>0, whereas for a more general case, the regret is O(T1/2) when the underlying demand is bounded and O(T1/2⁡logT) when the underlying demand is unbounded. We further prove that our algorithm for each case is the best possible in the sense that its regret rate matches with the theoretical lower bound.