Download or read book Bayesian Dynamic Pricing Policies written by J. Michael Harrison and published by . This book was released on 2018 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by applications in financial services, we consider a seller who offers prices sequentially to a stream of potential customers, observing either success or failure in each sales attempt. The parameters of the underlying demand model are initially unknown, so each price decision involves a trade-off between learning and earning. Attention is restricted to the simplest kind of model uncertainty, where one of two demand models is known to apply, and we focus initially on performance of the myopic Bayesian policy (MBP), variants of which are commonly used in practice. Because learning is passive under the MBP (that is, learning only takes place as a by-product of actions that have a different purpose), it can lead to incomplete learning and poor profit performance. However, under one additional assumption, a constrained variant of the myopic policy is shown to have the following strong theoretical virtue: the expected performance gap relative to a clairvoyant who knows the underlying demand model is bounded by a constant as the number of sales attempts becomes large.

Download or read book Bayesian Dynamic Pricing and Subscription Period Selection with Unknown Customer Utility written by Yuan-Mao Kao and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a service provider offering a subscription service to customers over a multi-period planning horizon. The customers decide whether to subscribe according to a utility model that represents their preferences for the service. The provider has a prior belief about the customer utility model, and updates its belief based on the transaction data of new customers and the usage data of existing subscribers. The provider aims to minimize its regret, namely the expected profit loss relative to a clairvoyant who knows the customer utility model. To analyze regret, we first study the clairvoyant's full-information problem. The resulting dynamic program, however, suffers from the curse of dimensionality. We develop a customer-centric approach to resolve this issue and obtain the optimal policy for the full-information problem. This approach balances the provider's immediate and future profits from an individual customer. When the provider does not have full information, we find that the simple and commonly used certainty-equivalence policy, which learns only passively, exhibits poor performance. We illustrate that this can be due to incomplete or slow learning, but can also occur because of offering a suboptimal contract with a long subscription period at the beginning. We propose a two-phase learning policy that first focuses on information accumulation and then profit maximization. We show that our policy achieves asymptotically optimal performance with its regret growing logarithmically in the planning horizon. Our results indicate that the provider should be cautious about offering a long subscription period when it is uncertain about customer preferences.

Download or read book Optimal Bayesian Demand Learning Over Short Horizons written by Jue Wang and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, i.e., 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.

Download or read book Operationalizing Dynamic Pricing Models written by Steffen Christ and published by Springer Science & Business Media. This book was released on 2011-04-02 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steffen Christ shows how theoretic optimization models can be operationalized by employing self-learning strategies to construct relevant input variables, such as latent demand and customer price sensitivity.

Download or read book Bayesian Dynamic Pricing with Unknown Customer Willingness to Pay and Limited Inventory written by Li Chen and published by . This book was released on 2019 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a dynamic pricing problem in which the seller sells a limited amount of inventory over a short time horizon. The distribution of customer willingness-to-pay is unknown, and the seller learns about the distribution from observing customer purchase decisions. Such a problem arises in practice when certain unique assets are put for sale (e.g., selling a house), but the problem is known to be both analytically and computationally challenging. In this paper, we seek to derive new insights, solution bounds, and heuristics for the problem. We formulate the problem as a Bayesian dynamic program and transform it with an unnormalized prior. Based on the unnormalized prior, we first show that the optimal price for this problem is always finite, which motivates us to search for the optimal solution via the first-order condition. To this end, we prove a generalized envelope theorem for the Bayesian dynamic program, and derive an explicit expression of the first-order derivative of the dynamic program objective function. This derivative expression reveals new insights about the intertwined effects of left censoring, right censoring, and limited inventory in the problem. It also enables us to derive new, easy-to-compute solution bounds and two derivative-based heuristics for the problem. The first heuristic approximates the derivative by a weighted average of its upper and lower bounds, and the second heuristic uses an easy-to-compute open-loop policy as a surrogate for the approximate evaluation of the derivative function. Numerical studies show that both heuristics perform well, with the second heuristic consistently outperforming existing heuristics in the literature. Overall, our paper prescribes a new, derivative-based approach to tackle the dynamic pricing problem with unknown customer willingness-to-pay, limited inventory, and short horizon. Our proposed solutions can help managers to achieve near optimal revenue performance for this challenging problem.

Download or read book Dynamic Pricing with Demand Model Uncertainty written by Mr. Nuri Bora Keskin and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Pricing decisions often involve a tradeoff between learning about customer behavior to increase long-term revenues, and earning short-term revenues. In this thesis we examine that tradeoff. Whenever a firm is not certain about how its customers will respond to price changes, there is an opportunity to use price as a tool for learning about a demand curve. Most firms try to solve the tradeoff between learning and earning by managing these two goals separately. A common practice is to first estimate the parameters of the demand curve, and then choose the optimal price, assuming the parameter estimates are accurate. In this thesis we show that this conventional approach is far from being optimal, running the risk of incomplete learning--a negative statistical outcome in which the decision maker stops learning prematurely. We also propose several remedies to avoid the incomplete learning problem, and guard against poor performance. In Chapter 1, we model a learn-and-earn problem using a theoretical framework in which a seller has a prior belief about the demand curve for its product, and updates his belief upon observing customer responses to successive sales attempts. We assume that the seller's prior is a binary distribution, i.e. one of two demand curves is known to apply, although our analysis can be extended to any finite prior. In this setting, we first analyze the myopic Bayesian policy (MBP), which is a stylized representative of the estimate-and-then-optimize policies described above. Our analysis makes three contributions to the literature: first, we show that under the MBP the seller's beliefs can get stuck at a confounding value, leading to poor revenue performance. This result elucidates incomplete learning as a consequence of myopic pricing. Our second contribution is the development of a constrained variant of the MBP as a way to tweak the MBP in the binary-prior setting. By forbidding prices that are not sufficiently informative, constrained MBP (CMBP) avoids the incomplete learning problem entirely, and moreover, its expected performance gap relative to a clairvoyant who iv knows the underlying demand curve is bounded by a constant independent of the sales horizon. Finally, we generalize the CMBP family to obtain more flexible pricing policies that are suitable in case the seller has an arbitrary prior on model parameters. The incomplete learning result and the pricing policies we design have a practical significance. Because firms have no means to check whether they are suffering from incomplete learning, the myopic policies used in practice need to be modified with some kind of forced price experimentation, and our policies provide guidelines on how price experimentation can be employed to prevent incomplete learning. In Chapter 2, we consider several research questions: for example, when a seller has been charging an incumbent price for a very long time, how can he make use of the information contained in that incumbent price? Or, when a seller offers multiple products with substitutable demand, can he safely employ an independent price experimentation strategy for each product? More importantly, what if the particular pricing policies in literature are not feasible in a given business setting? To handles such cases, can we derive general principles that identify the essential ingredient of successful price experimentation policies? We address these questions using a fairly general dynamic pricing model, where a monopolist sells a set of products over a given time horizon. The expected demand for products is given by a linear curve, the parameters of which are not known by the seller. The seller's goal is to learn the parameters of the demand curve as he keeps trying to earn revenues. This chapter makes four main contributions to the learning-and-earning literature. First, we formulate an incumbent-price problem, where the seller starts out knowing one point on its demand curve, and show that the value of information contained in the incumbent price is substantial. Second, unlike previous studies that focus on a particular form of price experimentation, we derive general sufficient conditions for accumulating information in a near-optimal manner. We believe that practitioners can use these conditions as guidelines to design successful pricing policies in various settings. Third, we develop a unifying theme to obtain performance bounds in operations management problems with model uncertainty. We employ (i) the concept of Fisher information to derive natural lower bounds on regret, and (ii) martingale theory to analyze the estimation errors and generate well-performing policies. Finally, we analyze the pricing of multiple products with substitutable demand. Our analysis shows that multi-product pricing is not a straightforward repetition of single-product pricing. Learning in a high dimensional price space essentially requires sufficient "variation" in the directions of successive price vectors, which brings forth the idea of orthogonal pricing. In Chapter 3, we extend our analysis to the case where information can become obsolete. The particular dynamic pricing problem we consider includes a seller who tries to simultaneously learn about a time-varying demand curve, and earn sales revenues. We conduct a simulation study to evaluate the revenue performance of several pricing policies in this setting. Our results suggest that policies designed for static demand settings do not perform well in time-varying demand settings. Moreover, if the demand environment is not very noisy and the changes are not very frequent, a simple modification of the estimate-and-then-optimize approach, which is based on a moving time window, performs reasonably well in changing demand environments.

Download or read book A Logit Model Analysis of Dynamic Pricing Policies written by Pradeep K. Chintagunta and published by . This book was released on 1992 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Elements of Joint Learning and Optimization in Operations Management written by Xi Chen and published by Springer Nature. This book was released on 2022-09-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bayesian Forecasting and Dynamic Models written by Mike West and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.

Download or read book Optimization and Learning written by Bernabé Dorronsoro and published by Springer Nature. This book was released on 2021-08-16 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the refereed proceedings of the 4th International Conference on Optimization and Learning, OLA 2021, held in Catania, Italy, in June 2021. Due to the COVID-19 pandemic the conference was held online. The 27 full papers were carefully reviewed and selected from 62 submissions. The papers presented in the volume are organized in topical sections on ​synergies between optimization and learning; learning for optimization; machine learning and deep learning; transportation and logistics; optimization; applications of learning and optimization methods.

Download or read book The Oxford Handbook of Pricing Management written by Özalp Özer and published by Oxford University Press (UK). This book was released on 2012-06-07 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: A definitive reference to the theory and practice of pricing across industries, environments, and methodologies. It covers all major areas of pricing including, pricing fundamentals, pricing tactics, and pricing management.

Download or read book The Oxford Handbook of Pricing Management written by Özalp Özer and published by OUP Oxford. This book was released on 2012-06-07 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of Pricing Management is a comprehensive guide to the theory and practice of pricing across industries, environments, and methodologies. The Handbook illustrates the wide variety of pricing approaches that are used in different industries. It also covers the diverse range of methodologies that are needed to support pricing decisions across these different industries. It includes more than 30 chapters written by pricing leaders from industry, consulting, and academia. It explains how pricing is actually performed in a range of industries, from airlines and internet advertising to electric power and health care. The volume covers the fundamental principles of pricing, such as price theory in economics, models of consumer demand, game theory, and behavioural issues in pricing, as well as specific pricing tactics such as customized pricing, nonlinear pricing, dynamic pricing, sales promotions, markdown management, revenue management, and auction pricing. In addition, there are articles on the key issues involved in structuring and managing a pricing organization, setting a global pricing strategy, and pricing in business-to-business settings.

Download or read book Bayesian Forecasting and Dynamic Models written by Mike West and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with Bayesian learning, inference and forecasting in dynamic environments. We describe the structure and theory of classes of dynamic models and their uses in forecasting and time series analysis. The principles, models and methods of Bayesian forecasting and time - ries analysis have been developed extensively during the last thirty years. Thisdevelopmenthasinvolvedthoroughinvestigationofmathematicaland statistical aspects of forecasting models and related techniques. With this has come experience with applications in a variety of areas in commercial, industrial, scienti?c, and socio-economic ?elds. Much of the technical - velopment has been driven by the needs of forecasting practitioners and applied researchers. As a result, there now exists a relatively complete statistical and mathematical framework, presented and illustrated here. In writing and revising this book, our primary goals have been to present a reasonably comprehensive view of Bayesian ideas and methods in m- elling and forecasting, particularly to provide a solid reference source for advanced university students and research workers.

Download or read book Handbook of the Economics of Marketing written by and published by North Holland. This book was released on 2019-09-15 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Economics of Marketing, Volume One: Marketing and Economics mixes empirical work in industrial organization with quantitative marketing tools, presenting tactics that help researchers tackle problems with a balance of intuition and skepticism. It offers critical perspectives on theoretical work within economics, delivering a comprehensive, critical, up-to-date, and accessible review of the field that has always been missing. This literature summary of research at the intersection of economics and marketing is written by, and for, economists, and the book's authors share a belief in analytical and integrated approaches to marketing, emphasizing data-driven, result-oriented, pragmatic strategies. Helps academic and non-academic economists understand recent, rapid changes in the economics of marketing Designed for economists already convinced of the benefits of applying economics tools to marketing Written for those who wish to become quickly acquainted with the integration of marketing and economics

Download or read book Optimal Advertising and Pricing Policies in a Mature Market written by Sheng C. Hu and published by . This book was released on 1989 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Evolutionary Multi Criterion Optimization written by Michael Emmerich and published by Springer Nature. This book was released on 2023-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2022 held in Leiden, The Netherlands, during March 20-24, 2023. The 44 regular papers presented in this book were carefully reviewed and selected from 65 submissions. The papers are divided into the following topical sections: Algorithm Design and Engineering; Machine Learning and Multi-criterion Optimization; Benchmarking and Performance Assessment; Indicator Design and Complexity Analysis; Applications in Real World Domains; and Multi-Criteria Decision Making and Interactive Algorithms..

Download or read book Learning Customers Price Sensitivity Through Bayesian Updating written by Nafiseh Ghorbaniyan and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a seller who sells a product over T discrete period in the season. The arrival rate of customers is known but the parameter of customer sensitivity to price is unknown. We assume that the seller has a prior belief in this parameter, which is updated using the Bayesian rule. The seller's objective is to maximize total expected revenue by determining the product price at the beginning of each period. We use a stochastic discrete-time dynamic programming model for both optimal dynamic pricing and demand learning. We show that in periods with high sales, using sales information to learn the demand parameter may result in an unacceptable value for this parameter. We conclude that ignoring sales information in this period is the best policy. Furthermore, we investigate the factors that intensify this situation.