Download or read book On the Surprising Sufficiency of Linear Models for Dynamic Pricing with Demand Learning written by Omar Besbes and published by . This book was released on 2014 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a multi-period single product pricing problem with an unknown demand curve. The seller's objective is to adjust prices in each period so as to maximize cumulative expected revenues over a given finite time horizon; in doing so, the seller needs to resolve the tension between learning the unknown demand curve and maximizing earned revenues. The main question that we investigate is the following: how large of a revenue loss is incurred if the seller uses a simple parametric model which differs significantly (i.e., is misspecified) relative to the underlying demand curve. This "price of misspecification'' is expected to be significant if the parametric model is overly restrictive. Somewhat surprisingly, we show (under reasonably general conditions) that this may not be the case.

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 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 Behavioral Consequences of Dynamic Pricing written by David Prakash and published by BoD – Books on Demand. This book was released on 2022-08-19 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Digital technologies are driving the application of dynamic pricing. Today, this pricing strategy is used not only for perishable products such as flights or hotel rooms, but for almost any product or service category. With dynamic pricing, retailers frequently adjust their prices over time to respond to factors such as demand, their supply and that of competitors, or the time of sale. Additionally, dynamic pricing allows retailers to take advantage of a large share of consumers' willingness to pay while avoiding losses from unsold products. Ultimately, this can lead to an increase in revenue and profit. However, the application of dynamic pricing comes with great challenges. In addition to the technological implementation, companies have to take into account that dynamic pricing can cause complex and unintended behavioral consequences on the consumer side. The key objective of this dissertation is to provide a deeper understanding of the impact of dynamic pricing on consumer behavior. To this end, this dissertation presents insights from four perspectives. First, how reference prices as a critical component in purchase decisions are operationalized. Second, how customers search for products priced dynamically, differentiated by business and private customers, as well as by different devices used for the search. Third, whether and how dynamic pricing influences the impact of internal reference prices on purchase decisions. Finally, this dissertation demonstrates that consumers perceive price changes as personalized in different purchase contexts, leading to reduced perceptions of fairness and undesirable behavioral consequences.

Download or read book Revenue Management and Pricing Analytics written by Guillermo Gallego and published by Springer. This book was released on 2019-08-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: “There is no strategic investment that has a higher return than investing in good pricing, and the text by Gallego and Topaloghu provides the best technical treatment of pricing strategy and tactics available.” Preston McAfee, the J. Stanley Johnson Professor, California Institute of Technology and Chief Economist and Corp VP, Microsoft. “The book by Gallego and Topaloglu provides a fresh, up-to-date and in depth treatment of revenue management and pricing. It fills an important gap as it covers not only traditional revenue management topics also new and important topics such as revenue management under customer choice as well as pricing under competition and online learning. The book can be used for different audiences that range from advanced undergraduate students to masters and PhD students. It provides an in-depth treatment covering recent state of the art topics in an interesting and innovative way. I highly recommend it." Professor Georgia Perakis, the William F. Pounds Professor of Operations Research and Operations Management at the Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts. “This book is an important and timely addition to the pricing analytics literature by two authors who have made major contributions to the field. It covers traditional revenue management as well as assortment optimization and dynamic pricing. The comprehensive treatment of choice models in each application is particularly welcome. It is mathematically rigorous but accessible to students at the advanced undergraduate or graduate levels with a rich set of exercises at the end of each chapter. This book is highly recommended for Masters or PhD level courses on the topic and is a necessity for researchers with an interest in the field.” Robert L. Phillips, Director of Pricing Research at Amazon “At last, a serious and comprehensive treatment of modern revenue management and assortment optimization integrated with choice modeling. In this book, Gallego and Topaloglu provide the underlying model derivations together with a wide range of applications and examples; all of these facets will better equip students for handling real-world problems. For mathematically inclined researchers and practitioners, it will doubtless prove to be thought-provoking and an invaluable reference.” Richard Ratliff, Research Scientist at Sabre “This book, written by two of the leading researchers in the area, brings together in one place most of the recent research on revenue management and pricing analytics. New industries (ride sharing, cloud computing, restaurants) and new developments in the airline and hotel industries make this book very timely and relevant, and will serve as a critical reference for researchers.” Professor Kalyan Talluri, the Munjal Chair in Global Business and Operations, Imperial College, London, UK.

Download or read book Information Processing and Management of Uncertainty in Knowledge Based Systems written by Marie-Jeanne Lesot and published by Springer Nature. This book was released on 2020-06-05 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three volume set (CCIS 1237-1239) constitutes the proceedings of the 18th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2020, in June 2020. The conference was scheduled to take place in Lisbon, Portugal, at University of Lisbon, but due to COVID-19 pandemic it was held virtually. The 173 papers were carefully reviewed and selected from 213 submissions. The papers are organized in topical sections: homage to Enrique Ruspini; invited talks; foundations and mathematics; decision making, preferences and votes; optimization and uncertainty; games; real world applications; knowledge processing and creation; machine learning I; machine learning II; XAI; image processing; temporal data processing; text analysis and processing; fuzzy interval analysis; theoretical and applied aspects of imprecise probabilities; similarities in artificial intelligence; belief function theory and its applications; aggregation: theory and practice; aggregation: pre-aggregation functions and other generalizations of monotonicity; aggregation: aggregation of different data structures; fuzzy methods in data mining and knowledge discovery; computational intelligence for logistics and transportation problems; fuzzy implication functions; soft methods in statistics and data analysis; image understanding and explainable AI; fuzzy and generalized quantifier theory; mathematical methods towards dealing with uncertainty in applied sciences; statistical image processing and analysis, with applications in neuroimaging; interval uncertainty; discrete models and computational intelligence; current techniques to model, process and describe time series; mathematical fuzzy logic and graded reasoning models; formal concept analysis, rough sets, general operators and related topics; computational intelligence methods in information modelling, representation and processing.

Download or read book Dynamic Pricing with an Unknown Demand Model written by N. Bora Keskin and published by . This book was released on 2018 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a monopolist who sells a set of products over a time horizon of T periods. The seller initially does not know the parameters of the products' linear demand curve, but can estimate them based on demand observations. We first assume that the seller knows nothing about the parameters of the demand curve, and then consider the case where the seller knows the expected demand under an incumbent price. It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order √T in the former case and of order logT in the latter case. To derive pricing policies that are practically implementable, we take as our point of departure the widely used policy called greedy iterated least squares (ILS), which combines sequential estimation and myopic price optimization. It is known that the greedy ILS policy itself suffers from incomplete learning, but we show that certain variants of greedy ILS achieve the minimum asymptotic loss rate. To highlight the essential features of well-performing pricing policies, we derive sufficient conditions for asymptotic optimality.

Download or read book Digital Era and Fuzzy Applications in Management and Economy written by Martha del Pilar Rodríguez García and published by Springer Nature. This book was released on 2022-03-31 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to contribute to the discussion about the implications of fuzzy logic, neural networks, digital era, and other intelligent techniques on organizations. This book will be very useful for academic researchers and postgraduate students aiming to introduce themselves to the field of quantitative techniques for overcoming uncertain environments and developing models to make decisions. Developments in other theories and socioeconomic and computational changes have shed light on the importance of fuzzy applications in social sciences. The treatment of uncertainty in the economic and business analysis is fundamental and requires instruments compatible with the uncertain environment of economics and business, because most of the traditional models have been overtaken by this reality when trying to make decisions with uncertain information. In the face of information technology, digitization, and uncertainty, organizations confront new opportunities and challenges. In order to take advantage of these opportunities and overcome current and future challenges, it is needed to understand the evolution of these phenomenon.

Download or read book Dynamic Pricing with Demand Learning and Reference Effects written by Arnoud den Boer and published by . This book was released on 2020 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Linear Models written by Debasis Sengupta and published by World Scientific. This book was released on 2003 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Models: An Integrated Approach aims to provide a clearand deep understanding of the general linear model using simplestatistical ideas. Elegant geometric arguments are also invoked asneeded and a review of vector spaces and matrices is provided to makethe treatment self-contained.

Download or read book Linear Models written by Brenton R. Clarke and published by John Wiley & Sons. This book was released on 2008-09-19 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful approach to the analysis of variance in the study of linear models Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. The author begins with a presentation of the classic fixed-effects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of least-squares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical two-way and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include: Vector space theory The theory of least squares estimation Gauss-Markov theorem Kronecker products Diagnostic and robust methods for linear models Likelihood approaches to estimation A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.

Download or read book Context Based Dynamic Pricing with Separable Demand Models written by Jinzhi Bu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Dynamic Pricing with Demand Model Uncertainty written by N. Bora Keskin and published by . This book was released on 2014 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a price-setting firm that sells a product over a continuous time horizon. The firm is uncertain about the sensitivity of demand to price adjustments, and continuously updates its prior belief on an unobservable sensitivity parameter by observing the demand responses to prices. The firm's objective is to minimize the infinite-horizon discounted loss, relative to a clairvoyant that knows the unobservable sensitivity parameter. Using partial differential equations theory, we characterize the optimal pricing policy, and then derive a formula for the optimal learning premium that projects the value of learning onto prices. We compare and contrast the optimal pricing policy with the myopic pricing policy, and quantify the cost of myopically neglecting to charge a learning premium in prices. We show that the optimal learning premium for a firm that looks far into the future is the squared coefficient of variation (SCV) in the firm's posterior belief. Based on this principle, we design a simple variant of the myopic policy, namely the SCV rule, and prove that this policy is long-run average optimal.

Download or read book Linear Model Methodology written by Andre I. Khuri and published by CRC Press. This book was released on 2009-10-21 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given the importance of linear models in statistical theory and experimental research, a good understanding of their fundamental principles and theory is essential. Supported by a large number of examples, Linear Model Methodology provides a strong foundation in the theory of linear models and explores the latest developments in data analysis.After

Download or read book Dynamic Pricing with Demand Learning Under Competition written by Carine Anne Marie Simon and published by . This book was released on 2007 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: (cont.) Finally, we consider closed-loop strategies in a duopoly market when demand is stochastic. Unlike open-loop policies (such policies are computed once and for all at the beginning of the time horizon), closed loop policies are computed at each time period, so that the firm can take advantage of having observed the past random disturbances in the market. In a closed-loop setting, subgame perfect equilibrium is the relevant notion of equilibrium. We investigate the existence and uniqueness of a subgame perfect equilibrium strategy, as well as approximations of the problem in order to be able to compute such policies more efficiently.

Download or read book Plane Answers to Complex Questions written by Ronald Christensen and published by Springer Nature. This book was released on 2020-03-13 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: estimation including biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.

Download or read book Dynamic Learning and Pricing with Model Misspecification written by Mila Nambiar and published by . This book was released on 2020 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a multi-period dynamic pricing problem with contextual information where the seller uses a misspecified demand model. The seller sequentially observes past demand, updates model parameters, and then chooses the price for the next period based on time-varying features. We show that model misspecification leads to correlation between price and prediction error of demand per period, which in turn leads to inconsistent price elasticity estimate and hence suboptimal pricing decisions. We propose a ``random price shock'' (RPS) algorithm that dynamically generates randomized price shocks to estimate price elasticity while maximizing revenue. We show that the RPS algorithm has strong theoretical performance guarantees, that it is robust to model misspecification, and that it can be adapted to a number of business settings, including (1) when the feasible price set is a price ladder, and (2) when the contextual information is not IID. We also perform offline simulations gauging the performance of RPS on a large fashion retail dataset, and find that is expected to earn 8~20% more revenue on average than competing algorithms that do not account for price endogeneity.