Monopoly pricing with limited demand information

Eren, Serkan; Maglaras, Costis

doi:10.1057/rpm.2009.41

Cited by 59 publications

(35 citation statements)

References 22 publications

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“…They use a conservative max-min formulation that does not involve real-time demand learning and bears no closed form solution in general. Eren and Maglaras [20] also study the robust setting and use a competitive ratio formulation. However, they only deal with the setting without inventory constraint and assume deterministic demand.…”

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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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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“…The [15] proposes a polynomial time algorithm for the two stage dynamic pricing model under minimizing the maximal regret value. [28] studies the problem of robust pricing under limited information or different learning ability, and establishes a model with the objective of minimizing the competition ratio (competitive ratio). For each situation, the optimal solution in the form of closed-form is…”

Section: Robust Pricing Controlmentioning

confidence: 99%

Robust Capacity Control in Revenue Management: A Literature Review

Jiang¹

2018

OJBM

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Revenue management is one of the classical topics in operations research. In recent 10 years, robust optimization methodology motivated a rapid growing amount of literature on robust revenue management. This stream of research does not rely on strict prior assumptions on distribution of random demand in classical revenue management theory but is capable to maintain tractable and to derive interesting structural properties of optimal solution. In this paper, we first briefly introduce theoretical basis of revenue management and then provide detailed review of literature on robust revenue management. Then potential directions of future research are identified.

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“…Robust or nonparametric approaches do not assume a known parametric functional form of the demand, and generally investigate how to maximize revenue in worstcase scenarios. Such approaches can be found in Kleinberg and Leighton (2003), Cope (2007), Lim and Shanthikumar (2007), Eren and Maglaras (2010), and Besbes and Zeevi (2009)…”

Section: Parametric Approaches With Bayesianmentioning

confidence: 99%

Simultaneously Learning and Optimizing Using Controlled Variance Pricing

2014

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P rice experimentation is an important tool for firms to find the optimal selling price of their products. It should be conducted properly, since experimenting with selling prices can be costly. A firm, therefore, needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue. In this paper, we propose such a pricing policy, called controlled variance pricing (CVP). The key idea of the policy is to enhance the certainty equivalent pricing policy with a taboo interval around the average of previously chosen prices. The width of the taboo interval shrinks at an appropriate rate as the amount of data gathered gets large; this guarantees sufficient price dispersion. For a large class of demand models, we show that this procedure is strongly consistent, which means that eventually the value of the optimal price will be learned, and derive upper bounds on the regret, which is the expected amount of money lost due to not using the optimal price. Numerical tests indicate that CVP performs well on different demand models and time scales.

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Monopoly pricing with limited demand information

Cited by 59 publications

References 22 publications

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

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

Robust Capacity Control in Revenue Management: A Literature Review

Simultaneously Learning and Optimizing Using Controlled Variance Pricing

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