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

• 成果类型: Article
• 署名作者: Chen, Boxiao; Chao, Xiuli; Wang, Yining
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Michigan System; University of Michigan; State University System of Florida; University of Florida
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.1993
• 发表日期: 2020
• 页码: 1445-1456
• 关键词: maximum-likelihood-estimation; policies; management; models

摘要

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(log T) when limited by beta log T for some positive constant beta > 0, whereas for a more general case, the regret is O(T-1/2) when the underlying demand is bounded and O(T-1/2 log T) 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.