Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information

• 成果类型: Article
• 署名作者: Chen, Boxiao; Simchi-Levi, David; Wang, Yining; Zhou, Yuan
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Massachusetts Institute of Technology (MIT); State University System of Florida; University of Florida; University of Illinois System; University of Illinois Urbana-Champaign; Yanqi Lake Beijing Institute of Mathematical Sciences & Applications
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2021.4171
• 发表日期: 2022
• 页码: 5684-5703
• 关键词: Dynamic pricing; INVENTORY CONTROL; Fixed Ordering Cost; online learning; asymptotic analysis

摘要

We consider the periodic review dynamic pricing and inventory control problemwith fixed ordering cost. Demand is randomand price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated (s, S, p) policy is proved to be optimal, where s and S are the reorder point and order-up-to level for ordering strategy, and p, a function of on-hand inventory level, characterizes the pricing strategy. In this paper, we consider incomplete demand information and develop online learning algorithms whose average profit approaches that of the optimal (s, S, p) with a tight (O) over tilde (root T) regret rate. A number of salient features differentiate our work from the existing online learning researches in the operations management (OM) literature. First, computing the optimal (s, S, p) policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in OMthat only require solving single-period optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profit-to-go function. The necessity of analyzing action-dependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult than existing bandit learning algorithms. Second, the pricing function p is of infinite dimension, and approaching it is much more challenging than approaching a finite number of parameters as seen in existing researches. The demand-price relationship is estimated based on upper confidence bound, but the confidence interval cannot be explicitly calculated due to the complexity of the DP recursion. Finally, because of the multiperiod nature of (s, S, p) policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy p, which is unknown to the learner a priori. In this paper, the demand randomness is approximated by an empirical distribution constructed using dependent samples, and a novelWassersteinmetric-based argument is employed to prove convergence of the empirical distribution.