Dynamic Pricing and Learning: Historical Origins, Current Research, and New Directions

Boer, Alexander

doi:10.2139/ssrn.2334429

Cited by 17 publications

(8 citation statements)

References 321 publications

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“…Other related papers in this context are Chakraborty et al. () and den Boer (). On the other hand, our paper assumes that demand functions are estimated at an aggregate level, using historical purchase data.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

Cohen

Gupta

Kalas

et al. 2020

Production and Operations Management

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W e study a multi-period, multi-item dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing prices, while satisfying several business rules. The strength of our work lies in our graphical model reformulation, which allows us to use ideas from combinatorial optimization. We do not make any assumptions on the structure of the demand function. The complexity of our method depends linearly on the number of time periods but is exponential in the memory of the model (number of past prices that affect current demand) and in the number of items. We prove that the profit maximization problem is NP-hard by showing an approximation preserving reduction from the weighted Max-3-SAT problem. We next introduce the discrete reference price model which is a discretized version of the reference price model, accounting for an exponentially smoothed contribution of all past prices. We show that our problem can be solved efficiently under this model. We then approximate common demand functions using the discrete reference price model. To handle cross-item effects among multiple items, we propose to use a virtual reference price that assigns a reference price for each category of items (as opposed to a reference price for each item). To enhance the tractability of our approach, we cluster items into blocks and show how to adapt our method to include business constraints across blocks. Finally, we apply our solution approach using demand models calibrated with supermarket data and validate its practical performance.

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Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

Cohen

Gupta

Kalas

et al. 2020

Production and Operations Management

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“…Some firms could perform the price experimentation as a part of the market research phase before the actual business operation. For example, the companies selling their products on the internet can utilize digital price tags to gather price-demand data for online customers (den Boer 2015 ). However, other firms could have business constraints on the frequency of price changes for their products (Cheung et al.…”

Section: Introductionmentioning

confidence: 99%

“…Fast and accurate estimation of the demand curve becomes particularly important for the novel field of dynamic pricing for revenue management (Bertsimas and Perakis 2006 ; Besbes et al. 2014 ; den Boer 2012 , 2015 ). Dynamic pricing means pricing the product in a time varying way, according to the changes in demand, in order to maximize revenue (Ibrahim and Atiya 2016 ).…”

Section: Introductionmentioning

confidence: 99%

Novel pricing strategies for revenue maximization and demand learning using an exploration–exploitation framework

2021

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The price demand relation is a fundamental concept that models how price affects the sale of a product. It is critical to have an accurate estimate of its parameters, as it will impact the company's revenue. The learning has to be performed very efficiently using a small window of a few test points, because of the rapid changes in price demand parameters due to seasonality and fluctuations. However, there are conflicting goals when seeking the two objectives of revenue maximization and demand learning, known as the learn/earn trade-off. This is akin to the exploration/exploitation trade-off that we encounter in machine learning and optimization algorithms. In this paper, we consider the problem of price demand function estimation, taking into account its exploration-exploitation characteristic. We design a new objective function that combines both aspects. This objective function is essentially the revenue minus a term that measures the error in parameter estimates. Recursive algorithms that optimize this objective function are derived. The proposed method outperforms other existing approaches.

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“…Although a substantial body of literature on dynamic pricing and demand learning has been established (Aviv and Vulcano 2012, den Boer 2015), most existing works focus on heuristic policies that are asymptotically optimal, that is, near optimal in the long run. Little is known about pricing decisions over short horizons.…”

Section: Introductionmentioning

confidence: 99%

Optimal Bayesian Demand Learning over Short Horizons

Wang

2021

Production and Operations Management

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We investigate the optimal Bayesian dynamic pricing and demand learning policy over short selling horizons, where the pricing decisions are time‐sensitive. The seller fine‐tunes the price near an incumbent price in order to maximize the total revenue. The existing literature focuses on policies that are asymptotically optimal, that is, near optimal when the selling horizons are sufficiently long, but little is known about the optimal Bayesian policies, especially over short horizons. We formulate the problem as a finite‐horizon stochastic dynamic program and identify a connection between the optimality equations and the generalized Weierstrass transform (GWT). We fully characterize the structure of the Bayesian optimal policy for the linear Gaussian demand model and prove that the optimal policy adjusts the myopic price away from the incumbent price. A notable exception occurs when the two prices coincide and the precision of the posterior belief exceeds a threshold, in which case it is optimal to forgo learning and use a fixed‐price policy. Exploiting the structural results makes it possible to compute the optimal policy efficiently on an ordinary computer.

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Dynamic Pricing and Learning: Historical Origins, Current Research, and New Directions

Cited by 17 publications

References 321 publications

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

Novel pricing strategies for revenue maximization and demand learning using an exploration–exploitation framework

Optimal Bayesian Demand Learning over Short Horizons

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