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Author: Ningyuan Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.
Author: Ningyuan Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.
Author: Maxime C. Cohen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Following the increasing popularity of personalized pricing, there is a growing concern from customers and policy makers regarding fairness considerations. This paper studies the problem of dynamic pricing with unknown demand under two types of fairness constraints: price fairness and demand fairness. For price fairness, the retailer is required to (i) set similar prices for different customer groups (called group fairness) and (ii) ensure that the prices over time for each customer group are relatively stable (called time fairness). We propose an algorithm based on an infrequently-changed upper-confidence-bound (UCB) method, which is proved to yield a near-optimal regret performance. In particular, we show that imposing group fairness does not affect the demand learning problem, in contrast to imposing time fairness. On the flip side, we show that imposing time fairness does not impact the clairvoyant optimal revenue, in contrast to imposing group fairness. For demand fairness, the retailer is required to satisfy that the resulting demand from different customer groups is relatively similar (e.g., the retailer offers a lower price to students to increase their demand to a similar level as non-students). In this case, we design an algorithm adapted from a primal-dual learning framework and prove that our algorithm also achieves a near-optimal performance.
Author: Guillermo Gallego
Publisher: Springer
ISBN: 1493996061
Category : Business & Economics
Languages : en
Pages : 336
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Book Description
“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.
Author: Xiaocheng Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
A merchant sells a product over a selling season of T time periods in presence of a limited inventory. The merchant observes new external information at the beginning of each time period and then sets a price for that time period. Initially, the merchant does not know the distribution of the external information and the demand function, i.e., how the external information and price jointly impact the demand distribution in a single time period. The seller's decision, setting price dynamically, serves dual roles to learn the unknown demand function and to balance inventory, with an ultimate goal to maximize the expected revenue over the selling season. We characterize and prove a full spectrum of relations between the optimal revenue achieved in three decision-making regimes: the merchant's online decision-making regime, a clairvoyant regime with complete knowledge about the demand function and all the external information in advance, and a deterministic regime in which the demand function and all the uncertainties are revealed at the beginning. In the analyses, we derive an unconstrained representation of the optimality gap for generic constrained online learning problems, which renders tractable lower and upper bounds for the expected revenue achieved by dynamic pricing algorithms between different regimes. This analytical framework also inspires the design of two dual-based history-dependent dynamic pricing algorithms for the clairvoyant regime and the online regime. Numerical experiments are conducted to demonstrate the performances of our algorithms.
Author: Gah-Yi Ban
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
We consider a seller who can dynamically adjust the price of a product at the individual customer level, by utilizing information about customers' characteristics encoded as a d-dimensional feature vector. We assume a personalized demand model, parameters of which depend on s out of the d features. The seller initially does not know the relationship between the customer features and the product demand, but learns this through sales observations over a selling horizon of T periods. We prove that the seller's expected regret, i.e., the revenue loss against a clairvoyant who knows the underlying demand relationship, is at least of order s √T under any admissible policy. We then design a near-optimal pricing policy for a “semi-clairvoyant” seller (who knows which s of the d features are in the demand model) that achieves an expected regret of order s √Tlog T. We extend this policy to a more realistic setting where the seller does not know the true demand predictors, and show that this policy has an expected regret of order s √T(log d+logT), which is also near-optimal. Finally, we test our theory on simulated data and on a data set from an online auto loan company in the United States. On both data sets, our experimentation-based pricing policy is superior to intuitive and/or widely-practiced customized pricing methods such as myopic pricing and segment-then- optimize policies. Furthermore, our policy improves upon the loan company's historical pricing decisions by 47% in expected revenue over a six-month period.
Author: Chen, Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Yanzhe (Murray) Lei
Publisher:
ISBN:
Category :
Languages : en
Pages : 38
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Book Description
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 novel 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 relative revenue loss compared to the optimal dynamic pricing solution 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.
Author: Aleksandrs Slivkins
Publisher:
ISBN: 9781680836202
Category : Computers
Languages : en
Pages : 306
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Book Description
Multi-armed bandits is a rich, multi-disciplinary area that has been studied since 1933, with a surge of activity in the past 10-15 years. This is the first book to provide a textbook like treatment of the subject.
Author: Guy Desaulniers
Publisher: Springer Science & Business Media
ISBN: 0387254862
Category : Business & Economics
Languages : en
Pages : 369
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Book Description
Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
Author: Warren B. Powell
Publisher: John Wiley & Sons
ISBN: 0470182954
Category : Mathematics
Languages : en
Pages : 487
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Book Description
A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.
