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Author: Yiwei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 60
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Book Description
We consider a firm that sells a single type product on multiple local markets over a finite horizon via dynamically adjusted prices. To prevent price discrimination, prices posted on different local markets at the same time are the same. The entire horizon consists of one or multiple change-points. Each local market's demand function linearly evolves over time between any two consecutive change-points. Each change-point is classified as either a zero-order or a first-order change-point in terms of how smooth the demand function changes at this point. At a zero-order change-point, at least one local market's demand function has an abrupt change. At a first-order change-point, all local markets' demand functions continuously evolve over time, but at least one local market's demand evolution speed has an abrupt change. The firm has no information about any parameter that modulates the demand evolution process before the start of the horizon. The firm aims at finding a pricing policy that yields as much revenue as possible. We show that the regret under any pricing policy is lower bounded by CT^{1/2} with C>0, and the lower bound becomes as worse as CT^{2/3} if at least one change-point is a first-order change-point.We propose a Joint Change-Point Detection and Time-adjusted Upper Confidence Bound (CU) algorithm. This algorithm consists of two components: the change-point detection component and the exploration-exploitation component. In the change-point detection component, the firm uniformly samples each price for one time in each batch of the time interval with the same length. She uses sales data collected at the times that she uniformly samples prices to both detect whether a change occurs and judge whether it is a zero-order or a first-order change if it occurs. In the exploration-exploitation component, the firm implements a time-adjusted upper confidence bound (UCB) algorithm between two consecutive detected change-points. Because demand dynamically evolves between two consecutive change-points, we introduce a time factor into the classical UCB algorithm to correct the bias of using historic sales data to estimate demand at present. We show that the CU algorithm achieves the regret lower bounds (up to logarithmic factors).
Author: Yiwei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 60
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Book Description
We consider a firm that sells a single type product on multiple local markets over a finite horizon via dynamically adjusted prices. To prevent price discrimination, prices posted on different local markets at the same time are the same. The entire horizon consists of one or multiple change-points. Each local market's demand function linearly evolves over time between any two consecutive change-points. Each change-point is classified as either a zero-order or a first-order change-point in terms of how smooth the demand function changes at this point. At a zero-order change-point, at least one local market's demand function has an abrupt change. At a first-order change-point, all local markets' demand functions continuously evolve over time, but at least one local market's demand evolution speed has an abrupt change. The firm has no information about any parameter that modulates the demand evolution process before the start of the horizon. The firm aims at finding a pricing policy that yields as much revenue as possible. We show that the regret under any pricing policy is lower bounded by CT^{1/2} with C>0, and the lower bound becomes as worse as CT^{2/3} if at least one change-point is a first-order change-point.We propose a Joint Change-Point Detection and Time-adjusted Upper Confidence Bound (CU) algorithm. This algorithm consists of two components: the change-point detection component and the exploration-exploitation component. In the change-point detection component, the firm uniformly samples each price for one time in each batch of the time interval with the same length. She uses sales data collected at the times that she uniformly samples prices to both detect whether a change occurs and judge whether it is a zero-order or a first-order change if it occurs. In the exploration-exploitation component, the firm implements a time-adjusted upper confidence bound (UCB) algorithm between two consecutive detected change-points. Because demand dynamically evolves between two consecutive change-points, we introduce a time factor into the classical UCB algorithm to correct the bias of using historic sales data to estimate demand at present. We show that the CU algorithm achieves the regret lower bounds (up to logarithmic factors).
Author: Xi Chen
Publisher: Springer Nature
ISBN: 3031019261
Category : Business & Economics
Languages : en
Pages : 444
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Book Description
This book examines recent developments in Operations Management, and focuses on four major application areas: dynamic pricing, assortment optimization, supply chain and inventory management, and healthcare operations. Data-driven optimization in which real-time input of data is being used to simultaneously learn the (true) underlying model of a system and optimize its performance, is becoming increasingly important in the last few years, especially with the rise of Big Data.
Author: Joan Morris
Publisher:
ISBN:
Category :
Languages : en
Pages : 75
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Book Description
Author: Georgia Perakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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Book Description
We consider the dynamic pricing problem of a retailer who does not have any information on the underlying demand for a product. The retailer aims to maximize cumulative revenue collected over a finite time horizon by balancing two objectives: textit{learning} demand and textit{maximizing} revenue. The retailer also seeks to reduce the amount of price experimentation because of the potential costs associated with price changes. Existing literature solves this problem in the case where the unknown demand is parametric. We consider the pricing problem when demand is non-parametric. We construct a pricing algorithm that uses piecewise linear approximations of the unknown demand function and establish when the proposed policy achieves near-optimal rate of regret, tilde{O}( sqrt{T}), while making O( log log T) price changes. Hence, we show considerable reduction in price changes from the previously known mathcal{O}( log T) rate of price change guarantee in the literature. We also perform extensive numerical experiments to show that the algorithm substantially improves over existing methods in terms of the total price changes, with comparable performance on the cumulative regret metric.
Author: Wang Chi Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
In a dynamic pricing problem where the demand function is not known a priori, price experimentation can be used as a demand learning tool. Existing literature usually assumes no constraint on price changes, but in practice sellers often face business constraints that prevent them from conducting extensive experimentation. We consider a dynamic pricing model where the demand function is unknown but belongs to a known finite set. The seller is allowed to make at most m price changes during T periods. The objective is to minimize the worst case regret, i.e., the expected total revenue loss compared to a clairvoyant who knows the demand distribution in advance. We demonstrate a pricing policy that incurs a regret of O(log^(m) T), or m iterations of the logarithm. Furthermore, we describe an implementation at Groupon, a large e-commerce marketplace for daily deals. The field study shows significant impact on revenue and bookings.
Author: Sahaj Sharda
Publisher:
ISBN: 9781641370806
Category :
Languages : en
Pages :
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Book Description
Author: Yan Zou
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Author: Hartwig Hermann Hagena
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
Author: Arnoud den Boer
Publisher:
ISBN:
Category :
Languages : en
Pages : 75
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Book Description
We consider a seller's dynamic pricing problem with demand learning and reference effects. We first study the case where customers are loss-averse: they have a reference price that can vary over time, and the demand reduction when the selling price exceeds the reference price dominates the demand increase when the selling price falls behind the reference price by the same amount. Thus, the expected demand as a function of price has a time-varying "kink" and is not differentiable everywhere. The seller neither knows the underlying demand function nor observes the time-varying reference prices. In this setting, we design and analyze a policy that (i) changes the selling price very slowly to control the evolution of the reference price, and (ii) gradually accumulates sales data to balance the tradeoff between learning and earning. We prove that, under a variety of reference-price updating mechanisms, our policy is asymptotically optimal; i.e., its T-period revenue loss relative to a clairvoyant who knows the demand function and the reference-price updating mechanism grows at the smallest possible rate in T. We also extend our analysis to the case of a fixed reference price, and show how reference effects increase the complexity of dynamic pricing with demand learning in this case. Moreover, we study the case where customers are gain-seeking and design asymptotically optimal policies for this case. Finally, we design and analyze an asymptotically optimal statistical test for detecting whether customers are loss-averse or gain-seeking.
Author: Adel Javanmard
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
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Book Description
We study the pricing problem faced by a firm that sells a large number of products, described via a wide range of features, to customers that arrive over time. Customers independently make purchasing decisions according to a general choice model that includes products features and customers' characteristics, encoded as d-dimensional numerical vectors, as well as the price offered.The parameters of the choice model are a-priori unknown to the firm, but can be learned as the (binary-valued) sales data accrues over time. The firm's objective is to minimize the regret, i.e., the expected revenue loss against a clairvoyant policy that knows the parameters of the choice model in advance, and always offers the revenue-maximizing price. This setting is motivated in part by the prevalence of online marketplaces that allow for real-time pricing.We assume a structured choice model, parameters of which depend on s out of the d product features. We propose a dynamic policy, called Regularized Maximum Likelihood Pricing (RMLP) that leverages the (sparsity) structure of the high-dimensional model and obtains a logarithmic regret in T. More specifically, the regret of our algorithm is of O(s log d log T). Furthermore, we show that no policy can obtain regret better than O(s (log d log T)).
