Context Dependent Discrete Choice Models and Assortment Optimization for Online Retail PDF Download
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Author: Uzma Mushtaque
Publisher:
ISBN:
Category :
Languages : en
Pages : 420
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Book Description
Author: Uzma Mushtaque
Publisher:
ISBN:
Category :
Languages : en
Pages : 420
Get Book Here
Book Description
Author: Yicheng Bai
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Wang Chi Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
Motivated by online retail applications, we study the online personalized assortment optimization problem. A seller conducts sales by offering assortments of products to a stream of arriving customers. The customers' purchase behavior follows their respective personalized Multinomial Logit choice models, which vary according to their individual attributes. The seller aims to maximize his revenue by offering personalized assortments to the customers, notwithstanding his uncertainty about the customers' choice models. We propose a Thompson Sampling based policy, policy Pao-Ts, where surrogate models for the latent choice models are constructed using samples from a progressively updated posterior distribution. We derive bounds on the revenue loss, namely Bayesian regret, incurred by policy Pao-Ts, in comparison to the optimal policy which is provided with the latent models. The regret bounds hold even when the customers' attributes vary arbitrarily, but not independently and identically distributed.
Author: David A. Hensher
Publisher: Routledge
ISBN: 1351140752
Category : Business & Economics
Languages : en
Pages : 485
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Book Description
Originally published in 1981. Discrete-choice modelling is an area of econometrics where significant advances have been made at the research level. This book presents an overview of these advances, explaining the theory underlying the model, and explores its various applications. It shows how operational choice models can be used, and how they are particularly useful for a better understanding of consumer demand theory. It discusses particular problems connected with the model and its use, and reports on the authors’ own empirical research. This is a comprehensive survey of research developments in discrete choice modelling and its applications.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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Book Description
In this paper, we consider the yet-uncharted assortment optimization problem under the Exponomial choice model, where the objective is to determine the revenue maximizing set of products that should be offered to customers. Our main algorithmic contribution comes in the form of a fully polynomial-time approximation scheme (FPTAS), showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. This result is obtained through a synthesis of ideas related to approximate dynamic programming, that enable us to derive a compact discretization of the continuous state space by keeping track of several key statistics in "rounded" form throughout the overall computation. Consequently, we obtain the first provably-good algorithm for assortment optimization under the Exponomial choice model, which is complemented by a number of hardness results for natural extensions. We show in computational experiments that our solution method admits an efficient implementation, based on additional pruning criteria.Furthermore, we conduct empirical evaluations of the Exponomial choice model. We present a number of case studies using real-world data sets, spanning retail, online platforms, and transportation. We focus on a comparison with the popular Multinomial Logit choice model (MNL), which is largely dominant in the choice modeling practice, as both models share a simple parametric structure with desirable statistical and computational properties. We identify several settings where the Exponomial choice model has better predictive accuracy than MNL and leads to more profitable assortment decisions. We provide implementation guidelines and insights about the performance of the Exponomial choice model relative to MNL.
Author: Mohammed Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 256
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Book Description
Finding optimal product offerings is a fundamental operational issue in modern retailing, exemplified by the development of recommendation systems and decision support tools. The challenge is that designing an accurate predictive choice model generally comes at the detriment of efficient algorithms, which can prescribe near-optimal decisions. This thesis attempts to resolve this disconnect in the context of assortment and inventory optimization, through theoretical and empirical investigation. First, we tightly characterize the complexity of general nonparametric assortment optimization problems. We reveal connections to maximum independent set and combinatorial pricing problems, allowing to derive strong inapproximability bounds. We devise simple algorithms that achieve essentially best-possible factors with respect to the price ratio, size of customers' consideration sets, etc. Second, we develop a novel tractable approach to choice modeling, in the vein of nonparametric models, by leveraging documented assumptions on the customers' consider-then-choose behavior. We show that the assortment optimization problem can be cast as a dynamic program, that exploits the properties of a bi-partite graph representation to perform a state space collapse. Surprisingly, this exact algorithm is provably and practically efficient under common consider-then-choose assumptions. On the estimation front, we show that a critical step of standard nonparametric estimation methods (rank aggregation) can be solved in polynomial time in settings of interest, contrary to general nonparametric models. Predictive experiments on a large purchase panel dataset show significant improvements against common benchmarks. Third, we turn our attention to joint assortment optimization and inventory management problems under dynamic customer choice substitution. Prior to our work, little was known about these optimization models, which are intractable using modern discrete optimization solvers. Using probabilistic analysis, we unravel hidden structural properties, such as weak notions of submodularity. Building on these findings, we develop efficient and yet conceptually-simple approximation algorithms for common parametric and nonparametric choice models. Among notable results, we provide best-possible approximations under general nonparametric choice models (up to lower-order terms), and develop the first constant-factor approximation under the popular Multinomial Logit model. In synthetic experiments vis-a-vis existing heuristics, our approach is an order of magnitude faster in several cases and increases revenue by 6% to 16%.
Author: Clark Charles Pixton
Publisher:
ISBN:
Category :
Languages : en
Pages : 120
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Book Description
We study multi-product revenue management problems, focusing on the role of uncertainty in both the seller and the customer decision processes. We begin by considering a logit model framework for personalized revenue management problems where utilities are functions of customer attributes, so that data for any one customer can be generalized to others via regression. We establish finite-sample convergence guarantees on the model parameters. The parameter convergence guarantees are then extended to out-of-sample performance guarantees in terms of revenue, in the form of a high-probability bound on the gap between the expected revenue of the best action taken under the estimated parameters and the revenue generated by a decision-maker with full knowledge of the choice model. In the second chapter, we study the static assortment optimization problem under weakly rational choice. This setting applies to most choice models studied and used in practice. We give a mixed-integer linear optimization formulation and present two branch-and-bound algorithms for solving this optimization problem. The formulation and algorithms require only black-box access to purchase probabilities, and thus provide exact solution methods for a general class of discrete choice models, in particular those models without closed-form choice probabilities. We give approximation results for our algorithms in two special cases, and test the performance of our algorithms with heuristic stopping criteria. The third section, motivated by data from an online retailer, describes sales of durable goods online, focusing on the effects of uncertainty about product quality and learning from customer reviews. We describe the nature of the tradeoff between learning product quality over time and substitution effects between products offered in the same category on the same website. Specifically, small differences in product release tines can be magnified substantially over time. The learning process takes longer in markets with more products. The process also takes longer in markets with higher price because customers take more risk in these markets when purchasing under uncertainty. This results in both smaller demand for new products in high-priced markets and more market concentration around fewer, well-established products. We discuss operational implications and show application to a break-even analysis.
Author: Gerardo Berbeglia
Publisher:
ISBN:
Category :
Languages : en
Pages : 67
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Book Description
Demand estimation is a fundamental task in retail operations and revenue management, providing the necessary input data for inventory control, assortment and price optimization models. The task is particularly difficult in operational contexts when product availability varies over time and customers may substitute. In addition to the classical multinomial logit (MNL) model and its variants (e.g., nested logit, mixed MNL), new demand models have been proposed (e.g., the Markov chain model) and others have been revisited (e.g., the rank-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column generation, EM algorithms). In this paper, we conduct a systematic, empirical study of different demand models and estimation algorithms, spanning both maximum likelihood and least squares criteria. Through an exhaustive set of numerical experiments on synthetic and real data, we provide comparative statistics of the quality of the different choice models and estimation methods, and characterize operational environments suitable for different model/estimation implementations.
Author: Xue Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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Book Description
In this research, we consider an online assortment optimization problem, where a decision-maker needs to sequentially offer assortments to users instantaneously upon their arrivals and users select products from offered assortments according to the contextual multinomial logit choice model. We propose a computationally efficient Lasso-RP-MNL algorithm for the online assortment optimization problem under the cardinality constraint in high-dimensional settings. The Lasso-RP-MNL algorithm combines the Lasso and random projection as dimension reduction techniques to alleviate the computational complexity and improve the learning and estimation accuracy under high-dimensional data with limited samples. For each arriving user, the Lasso-RP-MNL algorithm constructs an upper-confidence bound for each individual product's attraction parameter, based on which the optimistic assortment can be identified by solving a reformulated linear programming problem. We demonstrate that for the feature dimension $d$ and the sample size dimension $T$, the expected cumulative regret under the Lasso-RP-MNL algorithm is upper bounded by $ tilde{ mathcal{O}}( sqrt{T} log d)$ asymptotically, where $ tilde{ mathcal{O}}$ suppresses the logarithmic dependence on $T$. Furthermore, we show that even when available samples are extremely limited, the Lasso-RP-MNL algorithm continues to perform well with a regret upper bound of $ tilde{ mathcal{O}}( T^{ frac{2}{3}} log d)$. Finally, through synthetic-data-based experiments and a high-dimensional XianYu assortment recommendation experiment, we show that the Lasso-RP-MNL algorithm is computationally efficient and outperforms other benchmarks in terms of the expected cumulative regret.
Author: Öykü Naz Attila
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In several application domains, discrete choice models have become a popular tool to accurately predict complex choice behavior within the classical predict-then-optimize paradigm. Due to a variety of possible error sources, however, estimated choice models may be subject to ambiguity, which may induce different optimal decisions of highly varying quality. While previous studies focused on reducing the uncertainty within a nominal choice model, this study approaches the issue of ambiguity from a different angle by directly mitigating choice model ambiguity associated with a given set of predictive models in terms of their ability to yield optimal decisions. To this end, we propose a framework and a set of performance metrics that aim at gauging the reliability of choice models and their induced decisions, therefore enabling the decision-maker to identify choice models that are likely to produce high quality decisions.
