Dynamic Pricing and Learning with Finite Inventories

Boer, Alexander; Zwart, Bert

doi:10.1287/opre.2015.1397

Cited by 78 publications

(27 citation statements)

References 45 publications

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“…Maximum likelihood estimation is also quite commonly used (Broder and Rusmevichientong 2012, Carvalho and Puterman 2005, den , Boer and Zwart 2011, 2014. Other approaches used include linear least squares estimation (Bertsimas and Perakis 2006, Besbes and Zeevi 2014, Cooper et al 2013, Kachani et al 2007, Keskin and Zeevi 2013, 2014, and simple empirical estimation which is quite different from all other approaches and is described in detail below when we review the corresponding papers (Besbes and Zeevi 2009, 2011, Chen and Farias 2013, Wang et al 2014.…”

Section: Parametric Problemsmentioning

confidence: 99%

Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information

Chen

2015

Production and Operations Management

176

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Dynamic pricing enables a firm to increase revenue by better matching supply with demand, responding to shifting demand patterns, and achieving customer segmentation. In the last 20 years, numerous success stories of dynamic pricing applications have motivated a rapidly growing research interest in a variety of dynamic pricing problems in the academic literature. A large class of problems that arise in various revenue management applications involve selling a given amount of inventory over a finite time horizon without inventory replenishment. In this study, we identify most recent trends in dynamic pricing research involving such problems. We review existing research on three new classes of problems that have attracted a rapidly growing interest in the last several years, namely, problems with multiple products, problems with competition, and problems with limited demand information. We also identify a number of possible directions for future research.

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Section: Parametric Problemsmentioning

confidence: 99%

Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information

Chen

2015

Production and Operations Management

176

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“…Some popular estimation procedures that have been studied in the literature include Bayesian method (Araman and Caldentey [2]; Farias and van Roy [21]; Harrison et al [23]), Maximum Likelihood estimation (Broder and Rusmevichientong [11]; den Boer [17]; den Boer and Zwart [19]; den Boer and Zwart [18]; Chen et al [13]), and Least Squares approach (Bertsimas and Perakis [4]; Keskin and Zeevi [27]). In contrast to parametric model, nonparametric model does not assume that the firms know the functional form of the demand function; instead, it only assumes a certain set of mild regularity conditions such as the decreasing property of demand as a function of price, the boundedness of the first and second derivatives of the demand function, and the unimodality of the revenue function.…”

Section: Ross School Of Business University Of Michigan 2014mentioning

confidence: 99%

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

2014

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We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.3 revenue loss? It turns out that it is possible: If we use Stochastic Approximation algorithms (i.e., Kiefer-Wolfowitz and Robbins-Monro, see Broadie et al. [10]) during the exploitation phase instead of another bisection search, then the resulting revenue loss is exactly Θ( √ θ). Thus, we have provided an "optimal" nonparametric pricing heuristic for the setting of a single-product problem with inventory constraint. (In the case where the firms know the functional form of the demand function, i.e., parametric model, the Ω( √ θ) lower bound has been repeatedly shown to be tight. For example, in the setting without inventory constraints, Keskin and Zeevi [27], den Boer and Zwart [19], and Broder and Rusmevichientong [11], each proposes a parametric pricing heuristic that guarantees a revenue loss of the order of O( √ θ) . As for the setting with inventory constraints, recently Chen et al. [13] propose a heuristic that exactly matches this lower bound. Their result holds for a general parametric model with an arbitrary set of inventory constraints. Thus, they have resolved the parametric dynamic pricing problem with inventory constraints.)

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“…This phenomenon has been named incomplete learning, and it has been demonstrated theoretically that, to avoid incomplete learning while maximizing revenue, the system must follow a policy that accumulates information about the demand behavior at an adequate rate without deviating too much from the greedy policy [24]. Several heuristic methods combining this principle with a classical parametric demand model [4,8,20,31,32] have been studied, in which controlled variance pricing (CVP) [2] has arguably been the most influential method. The CVP algorithm imposes a constraint on the greedy pricing policy that requires the selected prices not be too close to the average of previously selected prices.…”

Section: Heuristic Methods For Earning While Learningmentioning

confidence: 99%

Outsmarting Human Design in Airline Revenue Management

Pinheiro¹,

Defoin-Platel²,

Régin³

2022

Algorithms

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The accurate estimation of how future demand will react to prices is central to the optimization of pricing decisions. The systems responsible for demand prediction and pricing optimization are called revenue management (RM) systems, and, in the airline industry, they play an important role in the company’s profitability. As airlines’ current pricing decisions impact future knowledge of the demand behavior, the RM systems may have to compromise immediate revenue by efficiently performing price experiments with the expectation that the information gained about the demand behavior will lead to better future pricing decisions. This earning while learning (EWL) problem has captured the attention of both the industry and academia in recent years, resulting in many proposed solutions based on heuristic optimization. We take a different approach that does not depend on human-designed heuristics. We present the EWL problem to a reinforcement learning agent, and the agent’s goal is to maximize long-term revenue without explicitly considering the optimal way to perform price experimentation. The agent discovers through experience that “myopic” revenue-maximizing policies may lead to a decrease in the demand model quality (which it relies on to take decisions). We show that the agent finds novel pricing policies that balance revenue maximization and demand model quality in a surprisingly effective way, generating more revenue over the long run than current practices.

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Dynamic Pricing and Learning with Finite Inventories

Cited by 78 publications

References 45 publications

Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information

Recent Developments in Dynamic Pricing Research: Multiple Products, Competition, and Limited Demand Information

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

Outsmarting Human Design in Airline Revenue Management

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