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Price Optimization Under The Finite Mixture Logit Model
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Book Synopsis Price Optimization Under the Finite-Mixture Logit Model by : Ruben van de Geer
Download or read book Price Optimization Under the Finite-Mixture Logit Model written by Ruben van de Geer and published by . This book was released on 2019 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider price optimization under the finite-mixture logit model. This model assumes that customers belong to one of a number of customer segments, where each customer segment chooses according to a multinomial logit model with segment-specific parameters. We reformulate the corresponding price optimization problem and develop a novel characterization. Leveraging this new characterization, we construct an algorithm that obtains prices at which the revenue is guaranteed to be at least (1-epsilon) times the maximum attainable revenue for any prespecified epsilon>0. Existing global optimization methods require exponential time in the number of products to obtain such a result, which practically means that the prices of only a handful of products can be optimized. The running time of our algorithm, however, is exponential in the number of customer segments and only polynomial in the number of products. This is of great practical value, since in applications the number of products can be very large, while it is has been found in various contexts that a low number of segments is sufficient to capture customer heterogeneity appropriately. The results of our numerical study show that our algorithm runs fast on a broad range of problem instances.
Book Synopsis Assortment and Price Optimization Under an Endogenous Context-Dependent Multinomial Logit Model by : Yicheng Bai
Download or read book Assortment and Price Optimization Under an Endogenous Context-Dependent Multinomial Logit Model written by Yicheng Bai and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by empirical evidence that the utility of each product depends on the assortment of products offered along with it, we propose an endogenous context-dependent multinomial logit model (Context-MNL) under which the utility of each product depends on both the product's intrinsic value and the deviation of the intrinsic value from the expected maximum utility among all the products in the offered assortment. Under the Context-MNL model, an assortment provides a context in which customers evaluate the utility of each product. Our model generalizes the standard multinomial logit model and allows the utility of each product to depend on the offered assortment. The model is parsimonious, requires only one parameter more than the standard multinomial logit model, captures the assortment-dependent effect endogenously, and does~not require the decision-maker to determine in advance the relevant attributes of the assortment that might affect the product utility. The Context-MNL model also admits tractable maximum likelihood estimation and is operationally tractable, with efficient solution methods for solving assortment and price optimization problems. Our numerical study, which is based on data from Expedia, shows that compared to the standard multinomial logit model, the Context-MNL model substantially improves out-of-sample goodness of fit and prediction accuracy.
Book Synopsis Multiproduct Price Optimization Under the Multilevel Nested Logit Model by : Hai Jiang
Download or read book Multiproduct Price Optimization Under the Multilevel Nested Logit Model written by Hai Jiang and published by . This book was released on 2014 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce this multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.
Book Synopsis Capacitated Assortment and Price Optimization Under the Multinomial Logit Model by : Ruxian Wang
Download or read book Capacitated Assortment and Price Optimization Under the Multinomial Logit Model written by Ruxian Wang and published by . This book was released on 2014 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an assortment and price optimization problem where a retailer chooses an assortment of competing products and determines their prices to maximize the total expected profit subject to a capacity constraint. Customers' purchase behavior follows the multinomial logit choice model with general utility functions. This paper simplifies it to a problem of finding a unique fixed point of a single-dimensional function and visualizes the assortment optimization process. An efficient algorithm to find the optimal assortment and prices is provided.
Book Synopsis Assortment and Price Optimization Under MNL Model with Price Range Effect by : Stefanus Jasin
Download or read book Assortment and Price Optimization Under MNL Model with Price Range Effect written by Stefanus Jasin and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the assortment and price optimization problems under Multinomial Logit (MNL) model with price range effect, where the utility of a product is affected by the relative position of its price with respect to the highest and the lowest prices in the offer set. This model is motivated by the so-called Range Theory popularized in the behavioral economics and psychology literature. It addresses the limitation of a single-point interpretation of reference price, which ignores the impact of all other distributional information. We investigate the pure assortment problem, the pure pricing problem, and the joint assortment and pricing problem under the MNL model with price range effect. For each model, we first identify the structure of the optimal policy, and then we propose tractable algorithms that either output the optimal solution in polynomial time or admit an Fully Polynomial-Time Approximation Scheme (FPTAS).
Book Synopsis The Elements of Joint Learning and Optimization in Operations Management by : Xi Chen
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.
Book Synopsis Discrete Choice Methods with Simulation by : Kenneth Train
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Book Synopsis Multi-Product Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities by : Guillermo Gallego
Download or read book Multi-Product Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities written by Guillermo Gallego and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study firms that sell multiple substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multi-product pricing problem under the general Nested Logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest-invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and show that similar techniques can be used to significantly simplify the corresponding pricing problems.
Book Synopsis Optimal Pricing of Correlated Product Options Under the Paired Combinatorial Logit Model by : Hongmin Li
Download or read book Optimal Pricing of Correlated Product Options Under the Paired Combinatorial Logit Model written by Hongmin Li and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study price optimization with price-demand relationships captured by the paired combinatorial logit (PCL) model which overcomes restrictions of the well-studied multinomial logit (MNL) and nested logit (NL) models. The PCL model allows for choice-correlation and, like the NL model, includes the MNL model as a special case. Compared to the NL models, the PCL model does not restrict the sequence of the choice structure and allows for different covariances among all pairs of choices. This additional flexibility in structure enables a more accurate representation of some choice settings and broadens its empirical applications. Hence, it is of both theoretical and practical interests to extend the normative studies on the MNL and NL models to the PCL model and examine the pricing problem under this model. Due to cross-nesting of choice alternatives, the pricing problem under the PCL model poses a greater challenge than the MNL and NL models. However, using the concept of P-matrix, we are able to identify conditions for a unique optimal price solution and develop an efficient and theoretically sound approach for finding the optimal prices. We show that the analysis and solution approach are generalizable to other GEV family models with cross-nested alternatives.
Book Synopsis Assortment of Optimization and Pricing Problems Under Multi-stage Multinomial Logit Models by : Yuhang Ma
Download or read book Assortment of Optimization and Pricing Problems Under Multi-stage Multinomial Logit Models written by Yuhang Ma and published by . This book was released on 2019 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: In most E-commerce scenarios such as hotel booking and online shopping, products are not offered to customers simultaneously. Instead, they are divided into different webpages and presented to customers sequentially. In this thesis, we focus on solving a common problem faced by online retailers: when products are revealed to customers sequentially, which products should the retailers display at each stage and what prices should the retailers charge for each product so that the expected revenue can be maximized? To solve those problems, we generalize the classical multinomial logit model to capture the customer's choice behavior under the sequential setting and present efficient algorithms for different generalized choice models and different operational constraints.
Book Synopsis Approximate Dynamic Programming by : Warren B. Powell
Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Revenue Management and Pricing Analytics by : Guillermo Gallego
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.
Book Synopsis Multi-Product Pricing Under the Multinomial Logit Model with Local Network Effects by : Mohan Gopalakrishnan
Download or read book Multi-Product Pricing Under the Multinomial Logit Model with Local Network Effects written by Mohan Gopalakrishnan and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by direct interactions with practitioners and real-world data, we study a monopoly firm selling multiple substitute products to customers characterized by their different social network degrees. Under the multinomial logit model framework, we assume that the utility a customer with a larger network degree derives from the seller's products is subject to more impact from her neighbors and describe the customers' choice behavior by a Bayesian Nash game. We show that a unique equilibrium exists as long as these network effects are not too large. Furthermore, we study how the seller should optimally set the prices of the products in this setting. Under the homogeneous product-related parameter assumption, we show that if the seller optimally price-discriminates all customers based on their network degrees, the products' markups are the same for each customer type. Building on this, we characterize the sufficient and necessary condition for the concavity of the pricing problem, and show that when the problem is not concave, we can convert it to a single-dimensional search and solve it efficiently. We provide several further insights about the structure of optimal prices, both theoretically and numerically. Furthermore, we show that we can simultaneously relax the multinomial logit model and homogeneous product-related parameter assumptions and allow customer in- and out-degrees to be arbitrarily distributed whilemaintaining most of our conclusions robust.
Book Synopsis Price Competition Under Mixed Multinomial Logit Demand Functions by : Margaret P. Pierson
Download or read book Price Competition Under Mixed Multinomial Logit Demand Functions written by Margaret P. Pierson and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions. In these models, the market is partitioned into a finite set of market segments. We characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm. We identify a simple and very broadly satisfied condition under which a pure Nash equilibrium exists and the set of Nash equilibria coincides with the solutions of the system of first-order-condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a specific level that, under the condition, is an upper bound for a rational price choice for the firm irrespective of the competitors' prices. We show that under a somewhat stronger, but still broadly satisfied, version of the above condition, a unique equilibrium exists. We complete the picture by establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration, under sufficiently tight price bounds. We discuss how our results extend to a continuum of customer types. A discussion of the multiproduct case is included. The paper concludes with a discussion of implications for structural estimation methods.
Book Synopsis The Exponomial Choice Model by : Aydin Alptekinoglu
Download or read book The Exponomial Choice Model written by Aydin Alptekinoglu and published by . This book was released on 2015 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the use of a canonical version of a discrete choice model due to Daganzo (1979) in optimal pricing and assortment planning. In contrast to multinomial and nested logit (the prevailing choice models used for optimizing prices and assortments), this model assumes a negatively skewed distribution of consumer utilities, an assumption we motivate by conceptual arguments as well as published work. The choice probabilities in this model can be derived in closed-form as an exponomial (a linear function of exponential terms). The pricing and assortment planning insights we obtain from the Exponomial Choice (EC) model differ from the literature in two important ways. First, the EC model allows variable markups in optimal prices that increase with expected utilities. Second, when prices are exogenous, the optimal assortment may exhibit leapfrogging in prices, i.e., a product can be skipped in favor of a lower-priced one depending on the utility positions of neighboring products. These two plausible pricing and assortment patterns are ruled out by multinomial logit (and by nested logit within each nest). We provide structural results on optimal pricing for monopoly and oligopoly cases, and on the optimal assortments for both exogenous and endogenous prices. We also demonstrate how the EC model can be easily estimated--by establishing that the loglikelihood function is concave in model parameters and detailing an estimation example using real data.
Book Synopsis Econometric Models For Industrial Organization by : Matthew Shum
Download or read book Econometric Models For Industrial Organization written by Matthew Shum and published by World Scientific. This book was released on 2016-12-14 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Models for Industrial Organization focuses on the specification and estimation of econometric models for research in industrial organization. In recent decades, empirical work in industrial organization has moved towards dynamic and equilibrium models, involving econometric methods which have features distinct from those used in other areas of applied economics. These lecture notes, aimed for a first or second-year PhD course, motivate and explain these econometric methods, starting from simple models and building to models with the complexity observed in typical research papers. The covered topics include discrete-choice demand analysis, models of dynamic behavior and dynamic games, multiple equilibria in entry games and partial identification, and auction models.
Book Synopsis An exact method for assortment optimization under the nested logit model by : Laurent Alfandari
Download or read book An exact method for assortment optimization under the nested logit model written by Laurent Alfandari and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
