We consider the periodic review dynamic pricing and inventory control problem with fixed ordering cost. Demand is random and price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated [Formula: see text] policy is proved to be optimal, where s and S are the reorder point and order-up-to level for ordering strategy, and [Formula: see text], 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 [Formula: see text] with a tight [Formula: see text] 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 [Formula: see text] policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in OM that 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 [Formula: see text] 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 [Formula: see text] policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy [Formula: see text], 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 novel Wasserstein metric-based argument is employed to prove convergence of the empirical distribution. This paper was accepted by J. George Shanthikumar, big data analytics.
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Cost Based Nonlinear Pricing
The arrival of digital commerce has lead to an increasing use of personalization and differentiation strategies. With differentiated products along the quality dimension and/or the quantity dimension comes the need for nonlinear pricing policies or second degree price discrimination. The optimal pricing strategies for quality and quantity differentiated products were first investigated by Mussa and Rosen (1978) and Maskin and Riley (1984), respectively. The optimal pricing strategies were shown to depend heavily on the prior distribution of the private information regarding the types, and ultimately the willingness-to-pay of the buyers. Yet, frequently the sellers possess only weak and incomplete information about the distribution of demand. This paper aims to develop robust pricing policies that are independent of specific demand distributions and provide revenue guarantees across all possible distributions.
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- Award ID(s):
- 2049754
- NSF-PAR ID:
- 10529579
- Editor(s):
- Hartline, Jason
- Publisher / Repository:
- ACM
- Date Published:
- Edition / Version:
- 1
- Volume:
- 24th
- Issue:
- 1
- ISBN:
- 9798400701047
- Page Range / eLocation ID:
- 272 to 272
- Subject(s) / Keyword(s):
- Nonlinear Pricing
- Format(s):
- Medium: X Size: 1mb Other: xls
- Size(s):
- 1mb
- Location:
- London United Kingdom
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3580507.3597697
