In this paper, we study revenue maximization assortment and pricing problems under the threshold-based choice model, in which, a product is placed into a consumer's consideration set if its utility to the consumer exceeds the utility of a specified threshold. We consider two cases: when the random shock is logistically distributed or Gumbelly distributed. For both these two cases, the revenue-maximizing assortment problem is NP-hard. Although in the two cases, the best revenue-ordered assortment and the same-price policy can not achieve the optimal profit for the assortment problem and the pricing problem, respectively, we show that, they can guarantee a good bound on the optimal revenue. Finally, we show that when the random shock is logistically distributed, our policies can be asymptotically optimal if the search cost of consumers is sufficiently small. When the random shock is Gumbelly distributed, the best revenue-ordered assortment can asymptotically admit a 0.77 approximation of the optimal revenue for the assortment problem; the same-price policy can be asymptotically optimal for the pricing problem. These suggest that our policies share some robustness to achieve a good performance guarantee for the optimal revenue.
{"title":"Assortment Optimization and Pricing Under the Threshold-Based Choice Models","authors":"Xu Tian, Anran Li, R. Steinberg","doi":"10.2139/ssrn.3694222","DOIUrl":"https://doi.org/10.2139/ssrn.3694222","url":null,"abstract":"In this paper, we study revenue maximization assortment and pricing problems under the threshold-based choice model, in which, a product is placed into a consumer's consideration set if its utility to the consumer exceeds the utility of a specified threshold. We consider two cases: when the random shock is logistically distributed or Gumbelly distributed. For both these two cases, the revenue-maximizing assortment problem is NP-hard. Although in the two cases, the best revenue-ordered assortment and the same-price policy can not achieve the optimal profit for the assortment problem and the pricing problem, respectively, we show that, they can guarantee a good bound on the optimal revenue. Finally, we show that when the random shock is logistically distributed, our policies can be asymptotically optimal if the search cost of consumers is sufficiently small. When the random shock is Gumbelly distributed, the best revenue-ordered assortment can asymptotically admit a 0.77 approximation of the optimal revenue for the assortment problem; the same-price policy can be asymptotically optimal for the pricing problem. These suggest that our policies share some robustness to achieve a good performance guarantee for the optimal revenue.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130354480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Standard regression technique uses Ordinary Least Square estimator (OLS) for model fitting. In the presence of outliers OLS fits the model vary sharply with respect to actual regression curve. For model fitting, this paper applies robust estimation approach as a substitute for OLS. This approach reduces the ill effect of outliers and learns the representation of data. Various robust regression techniques, namely, L estimators, M estimators, S estimator and MM estimator have been used which works on the principle of order statistics and weighting techniques to reduce the weight of distant observations. These estimators are applied on four data set out of which 3 are taken from UCI repository and one is taken from NASA Surface meteorology and Solar energy. When comparing the methods on the basis of bias and variance parameters MM estimator performs well in majority of the data set while in some cases M estimator also exhibited promising results.
{"title":"Robust Techniques to Estimate Parameters of Linear Models","authors":"Neel Pandey","doi":"10.2139/ssrn.3694906","DOIUrl":"https://doi.org/10.2139/ssrn.3694906","url":null,"abstract":"Standard regression technique uses Ordinary Least Square estimator (OLS) for model fitting. In the presence of outliers OLS fits the model vary sharply with respect to actual regression curve. For model fitting, this paper applies robust estimation approach as a substitute for OLS. This approach reduces the ill effect of outliers and learns the representation of data. Various robust regression techniques, namely, L estimators, M estimators, S estimator and MM estimator have been used which works on the principle of order statistics and weighting techniques to reduce the weight of distant observations. These estimators are applied on four data set out of which 3 are taken from UCI repository and one is taken from NASA Surface meteorology and Solar energy. When comparing the methods on the basis of bias and variance parameters MM estimator performs well in majority of the data set while in some cases M estimator also exhibited promising results.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115691559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides nonparametric identification results for random coefficient distributions in perturbed utility models. We cover discrete and continuous choice models. We establish identification using variation in mean quantities, and the results apply when an analyst observes aggregate demands but not whether goods are chosen together. We require exclusion restrictions and independence between random slope coefficients and random intercepts. We do not require regressors to have large supports or parametric assumptions.
{"title":"Identification of Random Coefficient Latent Utility Models","authors":"R. Allen, John Rehbeck","doi":"10.2139/ssrn.3545696","DOIUrl":"https://doi.org/10.2139/ssrn.3545696","url":null,"abstract":"This paper provides nonparametric identification results for random coefficient distributions in perturbed utility models. We cover discrete and continuous choice models. We establish identification using variation in mean quantities, and the results apply when an analyst observes aggregate demands but not whether goods are chosen together. We require exclusion restrictions and independence between random slope coefficients and random intercepts. We do not require regressors to have large supports or parametric assumptions.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131192516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a parametric choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The literature on constrained assortment optimization lacks a practically efficient method which that is general to deal with different types of parametric choice models (e.g., the multinomial logit, mixed logit or general multivariate extreme value models). In this paper, we propose a new approach that allows to address this issue. The idea is that, under a general parametric choice model, we formulate the problem into a binary nonlinear programming model, and use an iterative algorithm to find a binary solution. At each iteration, we propose a way to approximate the objective (expected revenue) by a linear function, and a polynomial-time algorithm to find a candidate solution using this approximate function. We also develop a greedy local search algorithm to further improve the solutions. We test our algorithm on instances of different sizes under various parametric choice model structures and show that our algorithm dominates existing exact and heuristic approaches in the literature, in terms of solution quality and computing cost.
{"title":"An Algorithm for Assortment Optimization Under Parametric Discrete Choice Models","authors":"Tien Mai, Andrea Lodi","doi":"10.2139/ssrn.3370776","DOIUrl":"https://doi.org/10.2139/ssrn.3370776","url":null,"abstract":"This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a parametric choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The literature on constrained assortment optimization lacks a practically efficient method which that is general to deal with different types of parametric choice models (e.g., the multinomial logit, mixed logit or general multivariate extreme value models). In this paper, we propose a new approach that allows to address this issue. The idea is that, under a general parametric choice model, we formulate the problem into a binary nonlinear programming model, and use an iterative algorithm to find a binary solution. At each iteration, we propose a way to approximate the objective (expected revenue) by a linear function, and a polynomial-time algorithm to find a candidate solution using this approximate function. We also develop a greedy local search algorithm to further improve the solutions. We test our algorithm on instances of different sizes under various parametric choice model structures and show that our algorithm dominates existing exact and heuristic approaches in the literature, in terms of solution quality and computing cost.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115699036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism. Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds.
{"title":"Equivalent Choice Functions and Stable Mechanisms","authors":"Jan Christoph Schlegel","doi":"10.2139/ssrn.3306009","DOIUrl":"https://doi.org/10.2139/ssrn.3306009","url":null,"abstract":"We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that \"equivalence\", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism. \u0000Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121583607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We exploit the discontinuous jump in criminal sanctions at the age of majority in conjunction with administrative data from California to generate regression discontinuity estimates of the deterrent effect. Estimates show that the greater severity imposed upon adolescents at age 18 deters violent crime by 10-12%. Results are robust to multiple techniques and specifications. Using these results, we estimate an elasticity of crime with respect to sanction intensity that ranges from -0.145 to -0.174. We extend our results to demographic sub-populations and find female offenders, as well as white and Asian offenders, are relatively more responsive to sanctions.
{"title":"Do Greater Sanctions Deter Youth Crime? Evidence from a Regression Discontinuity Design","authors":"N. Lovett, Yuhan Xue","doi":"10.2139/ssrn.3116414","DOIUrl":"https://doi.org/10.2139/ssrn.3116414","url":null,"abstract":"We exploit the discontinuous jump in criminal sanctions at the age of majority in conjunction with administrative data from California to generate regression discontinuity estimates of the deterrent effect. Estimates show that the greater severity imposed upon adolescents at age 18 deters violent crime by 10-12%. Results are robust to multiple techniques and specifications. Using these results, we estimate an elasticity of crime with respect to sanction intensity that ranges from -0.145 to -0.174. We extend our results to demographic sub-populations and find female offenders, as well as white and Asian offenders, are relatively more responsive to sanctions.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131628311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the BLP-LASSO model, which augments the classic BLP (Berry, Levinsohn, and Pakes, 1995) random-coefficients logit model to allow for data-driven selection among a high- dimensional set of control variables. Economists often study consumers’ aggregate behavior across markets choosing from a menu of differentiated products. In this analysis, local demo- graphic characteristics can serve as controls for market-specific preference heterogeneity. Given rich demographic data, implementing these models requires specifying which variables to include in the analysis, an ad hoc process typically guided primarily by a researcher’s intuition. We pro- pose a data-driven approach to estimate these models applying penalized estimation algorithms imported from the machine learning literature that are known to be valid for uniform inferences with respect to variable selection. Our application explores the effect of campaign spending on vote shares in data from Mexican elections.
我们引入了BLP- lasso模型，它增强了经典的BLP (Berry, Levinsohn, and Pakes, 1995)随机系数logit模型，以允许在高维控制变量集中进行数据驱动的选择。经济学家经常研究消费者在不同市场中选择不同产品的总体行为。在这个分析中，当地的人口特征可以作为市场偏好异质性的控制因素。考虑到丰富的人口统计数据，实现这些模型需要指定在分析中包含哪些变量，这是一个特别的过程，通常主要由研究人员的直觉指导。我们提出了一种数据驱动的方法来估计这些模型，应用从机器学习文献中引入的惩罚估计算法，这些算法已知对变量选择的统一推断是有效的。我们的应用程序探讨了墨西哥选举数据中竞选支出对投票份额的影响。
{"title":"BLP-LASSO for Aggregate Discrete Choice Models with Rich Covariates","authors":"B. Gillen, Sergio Montero, H. Moon, M. Shum","doi":"10.2139/ssrn.2700775","DOIUrl":"https://doi.org/10.2139/ssrn.2700775","url":null,"abstract":"We introduce the BLP-LASSO model, which augments the classic BLP (Berry, Levinsohn, and Pakes, 1995) random-coefficients logit model to allow for data-driven selection among a high- dimensional set of control variables. Economists often study consumers’ aggregate behavior across markets choosing from a menu of differentiated products. In this analysis, local demo- graphic characteristics can serve as controls for market-specific preference heterogeneity. Given rich demographic data, implementing these models requires specifying which variables to include in the analysis, an ad hoc process typically guided primarily by a researcher’s intuition. We pro- pose a data-driven approach to estimate these models applying penalized estimation algorithms imported from the machine learning literature that are known to be valid for uniform inferences with respect to variable selection. Our application explores the effect of campaign spending on vote shares in data from Mexican elections.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129497431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jacob B. Feldman, Dennis J. Zhang, Xiaofei Liu, N. Zhang
We compare the performance of two approaches for finding the optimal set of products to display to customers landing on Alibaba's two online marketplaces, Tmall and Taobao. Both approaches were placed online simultaneously and tested on real customers for one week. The first approach we test is Alibaba's current practice. This procedure embeds thousands of product and customer features within a sophisticated machine learning algorithm that is used to estimate the purchase probabilities of each product for the customer at hand. The products with the largest expected revenue (revenue * predicted purchase probability) are then made available for purchase. The downside of this approach is that it does not incorporate customer substitution patterns; the estimates of the purchase probabilities are independent of the set of products that eventually are displayed. Our second approach uses a featurized multinomial logit (MNL) model to predict purchase probabilities for each arriving customer. In this way we use less sophisticated machinery to estimate purchase probabilities, but we employ a model that was built to capture customer purchasing behavior and, more specifically, substitution patterns. We use historical sales data to fit the MNL model and then, for each arriving customer, we solve the cardinality-constrained assortment optimization problem under the MNL model online to find the optimal set of products to display. Our experiments show that despite the lower prediction power of our MNL-based approach, it generates significantly higher revenue per visit compared to the current machine learning algorithm with the same set of features. We also conduct various heterogeneous-treatment-effect analyses to demonstrate that the current MNL approach performs best for sellers whose customers generally only make a single purchase.
{"title":"Customer Choice Models versus Machine Learning: Finding Optimal Product Displays on Alibaba","authors":"Jacob B. Feldman, Dennis J. Zhang, Xiaofei Liu, N. Zhang","doi":"10.2139/ssrn.3232059","DOIUrl":"https://doi.org/10.2139/ssrn.3232059","url":null,"abstract":"We compare the performance of two approaches for finding the optimal set of products to display to customers landing on Alibaba's two online marketplaces, Tmall and Taobao. Both approaches were placed online simultaneously and tested on real customers for one week. The first approach we test is Alibaba's current practice. This procedure embeds thousands of product and customer features within a sophisticated machine learning algorithm that is used to estimate the purchase probabilities of each product for the customer at hand. The products with the largest expected revenue (revenue * predicted purchase probability) are then made available for purchase. The downside of this approach is that it does not incorporate customer substitution patterns; the estimates of the purchase probabilities are independent of the set of products that eventually are displayed. Our second approach uses a featurized multinomial logit (MNL) model to predict purchase probabilities for each arriving customer. In this way we use less sophisticated machinery to estimate purchase probabilities, but we employ a model that was built to capture customer purchasing behavior and, more specifically, substitution patterns. We use historical sales data to fit the MNL model and then, for each arriving customer, we solve the cardinality-constrained assortment optimization problem under the MNL model online to find the optimal set of products to display. Our experiments show that despite the lower prediction power of our MNL-based approach, it generates significantly higher revenue per visit compared to the current machine learning algorithm with the same set of features. We also conduct various heterogeneous-treatment-effect analyses to demonstrate that the current MNL approach performs best for sellers whose customers generally only make a single purchase.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"283 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116087960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional‐form/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality is equivalent to a pair of Slutsky‐like shape restrictions on choice‐probability functions. The forms of these restrictions differ from Slutsky inequalities for continuous goods. Unlike McFadden–Richter's stochastic revealed preference, our shape restrictions (a) are global, that is, their forms do not depend on which and how many budget sets are observed, (b) are closed form, hence easy to impose on parametric/semi/nonparametric models in practical applications, and (c) provide computationally simple, theory‐consistent bounds on demand and welfare predictions on counterfactual budge sets.
{"title":"The Empirical Content of Binary Choice Models","authors":"Debopam Bhattacharya","doi":"10.2139/ssrn.2960282","DOIUrl":"https://doi.org/10.2139/ssrn.2960282","url":null,"abstract":"An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional‐form/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality is equivalent to a pair of Slutsky‐like shape restrictions on choice‐probability functions. The forms of these restrictions differ from Slutsky inequalities for continuous goods. Unlike McFadden–Richter's stochastic revealed preference, our shape restrictions (a) are global, that is, their forms do not depend on which and how many budget sets are observed, (b) are closed form, hence easy to impose on parametric/semi/nonparametric models in practical applications, and (c) provide computationally simple, theory‐consistent bounds on demand and welfare predictions on counterfactual budge sets.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125502574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gerardo Berbeglia, Agustín Garassino, Gustavo J. Vulcano
Choice-based demand estimation is a fundamental task in retail operations and revenue management, providing necessary input data for inventory control, assortment, and price-optimization models. The task is particularly difficult in operational contexts where product availability varies over time and customers may substitute into the available options. In addition to the classical multinomial logit (MNL) model and extensions (e.g., nested logit, mixed logit, and latent-class MNL), new demand models have been proposed (e.g., the Markov chain model), and others have been recently revisited (e.g., the rank list-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column-generation and expectation-maximization (EM) algorithms). In this paper, we conduct a systematic, empirical study of different choice-based demand models and estimation algorithms, including both maximum-likelihood and least-squares criteria. Through an exhaustive set of numerical experiments on synthetic, semisynthetic, and real data, we provide comparative statistics of the predictive power and derived revenue performance of an ample collection of choice models and characterize operational environments suitable for different model/estimation implementations. We also provide a survey of all the discrete choice models evaluated and share all our estimation codes and data sets as part of the online appendix. This paper was accepted by Vishal Gaur, operations management.
{"title":"A Comparative Empirical Study of Discrete Choice Models in Retail Operations","authors":"Gerardo Berbeglia, Agustín Garassino, Gustavo J. Vulcano","doi":"10.2139/ssrn.3136816","DOIUrl":"https://doi.org/10.2139/ssrn.3136816","url":null,"abstract":"Choice-based demand estimation is a fundamental task in retail operations and revenue management, providing necessary input data for inventory control, assortment, and price-optimization models. The task is particularly difficult in operational contexts where product availability varies over time and customers may substitute into the available options. In addition to the classical multinomial logit (MNL) model and extensions (e.g., nested logit, mixed logit, and latent-class MNL), new demand models have been proposed (e.g., the Markov chain model), and others have been recently revisited (e.g., the rank list-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column-generation and expectation-maximization (EM) algorithms). In this paper, we conduct a systematic, empirical study of different choice-based demand models and estimation algorithms, including both maximum-likelihood and least-squares criteria. Through an exhaustive set of numerical experiments on synthetic, semisynthetic, and real data, we provide comparative statistics of the predictive power and derived revenue performance of an ample collection of choice models and characterize operational environments suitable for different model/estimation implementations. We also provide a survey of all the discrete choice models evaluated and share all our estimation codes and data sets as part of the online appendix. This paper was accepted by Vishal Gaur, operations management.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127972532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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