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Customer Choice Models And Assortment Optimization
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Book Synopsis Customer Choice Models and Assortment Optimization by : James Mario Davis
Download or read book Customer Choice Models and Assortment Optimization written by James Mario Davis and published by . This book was released on 2015 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis handles a fundamental problem in retail: given an enormous variety of products which does the retailer display to its customers? This is the assortment planning problem. We solve this problem by developing algorithms that, given input parameters for products, can efficiently return the set of products that should be displayed. To develop these algorithms we use a mathematical model of how customers react to displayed items, a customer choice model. Below we consider two classic customer choice models, the Multinomial Logit model and Nested Logit model. Under each of these customer choice models we develop algorithms that solve the assortment planning problem. Additionally, we consider the constrained assortment planning problem where the retailer must display products to customers but must also satisfy operational constraints.
Book Synopsis Customer Choice Modeling for Retail Category Assortment Planning and Product-line Extension by : Elham Nosratmirshekarlou
Download or read book Customer Choice Modeling for Retail Category Assortment Planning and Product-line Extension written by Elham Nosratmirshekarlou and published by . This book was released on 2020 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing competitiveness and increasing availability of data is generating great interest in data-driven analytics across industries. One of the areas that has gained a lot of attention is Customer choice modeling, which aims to explain the choices individual customers make in choosing from a set of products based on their preferences. While effective customer choice modeling is essential to a wide variety of application domains, including retail, it is challenging in practice due to limitations around the quality of the data available for modeling and potentially complex choice behaviors. This dissertation presents a hybrid modeling approach that relies on both parametric and non-parametric methods to derive effective recommendations for product development and assortment planning. A generic non-parametric ranking-based choice model is first derived using random utility maximization to best model revealed product-level preferences from sales transactions and inventory records. The resulting product-level ranking-based choice model is utilized to establish customer segments and derive more actionable product attribute-based parametric models that can be employed for product assortment optimization as well as product-line extension. Then, in order to leverage from the correlatedness of customers' preferences toward similar attributes across multiple categories of products, we use cross category customer choice models to make the base predictions more accurate. The proposed modeling approach is validated using data from a leading global apparel retailer as well as synthetic experiments.
Book Synopsis Assortment and Inventory Optimization by : Mohammed Ali Aouad
Download or read book Assortment and Inventory Optimization written by Mohammed Ali Aouad and published by . This book was released on 2017 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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%.
Book Synopsis On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and Its Application to Assortment Optimization by : Hakjin Chung
Download or read book On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and Its Application to Assortment Optimization written by Hakjin Chung and published by . This book was released on 2016 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.
Book Synopsis Operations Management Under Consumer Choice Models with Multiple Purchases by : Shujie Luan
Download or read book Operations Management Under Consumer Choice Models with Multiple Purchases written by Shujie Luan and published by . This book was released on 2020 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the effects of multiple purchases that arise in the retailing of consumer goods, in which the product choice and consumer surplus depend not only on what to purchase but also on how many units to purchase. We incorporate the multiple purchases into consumer choice behavior and study a series of associated operational problems. Most of the discrete choice models in the current literature often assume that a customer chooses exactly one unit of a product. The assumption of “one purchase” is too restrictive in some practical scenarios (e.g., consumer goods) because customers often purchase multiple units of a product. We take the widely-used multinomial logit (MNL) model as a showcase and incorporate the effects of multiple purchases into the classic discrete choice model. In the new choice framework, consumers first form a consideration set, then select one product from consideration set and determine the purchase quantity of the selected product. In the absence of fixed cost, we characterize the structure of the optimal policy for the assortment optimization problem; whereas in the presence of product-differentiated fixed costs, the assortment problem becomes NP-complete, so we propose an efficient heuristic. We further develop a polynomial time algorithm for the assortment problem with identical fixed cost for each product. For the joint assortment and pricing problem, we show it can be decoupled into multiple multi-product pricing problems with different assortment sizes, each of which can be transformed into a single-variable problem. For the price competition problem, we characterize the existence and uniqueness of the Nash equilibrium. We combine the alternating optimization algorithm with the expectation maximization algorithm to overcome the non-concavity and missing data issues in estimation. An empirical study on JD.com data shows that incorporating the effects of multiple purchases into discrete choice models can improve model fitting and prediction accuracy, while ignoring the effects of multiple purchases may lead substantial losses.
Book Synopsis Assortment Optimization and Pricing Under the Threshold-Based Choice Models by : Xu Tian
Download or read book Assortment Optimization and Pricing Under the Threshold-Based Choice Models written by Xu Tian and published by . This book was released on 2020 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study revenue maximization assortment and pricing problems under threshold-based choice models, where a product is placed in a consumer's consideration set if its utility to the consumer exceeds the utility of an outside option by a specified threshold. We discuss two such models: the relative utility and absolute utility threshold-based choice models. For both models, the best revenue-ordered assortment and same-price policy can not achieve the optimal profit for the assortment problem or the pricing problem. Further, the revenue-maximizing assortment problem is NP-complete or NP-hard. However, we show that a performance guarantee relative to the optimal policy can be found for each model: for the relative utility model, by employing the best revenue-ordered assortment and same-price policy; for the absolute utility model, via a dynamic-program-based algorithm and a same-price policy. Finally, we show that our algorithms can be asymptotically optimal if the search cost of consumers is sufficiently small.
Book Synopsis Context Dependent Discrete Choice Models and Assortment Optimization for Online Retail by : Uzma Mushtaque
Download or read book Context Dependent Discrete Choice Models and Assortment Optimization for Online Retail written by Uzma Mushtaque and published by . This book was released on 2017 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling Consumer Choice and Optimizing Assortment Under the Threshold Multinomial Logit Model by : Ruxian Wang
Download or read book Modeling Consumer Choice and Optimizing Assortment Under the Threshold Multinomial Logit Model written by Ruxian Wang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper incorporates heterogeneous threshold effects into the classical multinomial logit (MNL) model, and studies the associated operations problems such as estimation and assortment optimization. The derived model is referred to as the threshold multinomial logit (TMNL) model and incorporates the recently proposed threshold Luce (T-Luce) model as a limiting case. Under the TMNL model, consumers first form their (heterogeneous) consideration set: If an alternative with significantly low utility is dominated by another one, it will not be included in the consideration set. The TMNL model can alleviate the restricted substitution patterns of MNL due to the independence of irrelevant alternatives (IIA) property, and therefore can model more flexible choice behavior. We develop a maximum likelihood based estimation to calibrate the proposed threshold model and further establish its statistical properties such as consistency and asymptotic normality under mild conditions. An efficient EM algorithm is also developed to handle the scenario with incomplete sales data. Our extensive numerical studies on synthetic and real datasets show that the new model can improve the goodness of fit and prediction accuracy of consumer choice behavior. In addition, we characterize the optimal strategies and provide efficient solutions for the associated assortment optimization problems under the TMNL model. Our theoretical and empirical results suggest that the threshold effects should be taken into account in firms' decision making such as demand estimation and operations management, and ignoring these effects could lead to sub-optimal solutions or even substantial losses for firms.
Book Synopsis Customer Choice Models Versus Machine Learning by : Jacob Feldman
Download or read book Customer Choice Models Versus Machine Learning written by Jacob Feldman and published by . This book was released on 2019 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Consumer Choice Models with Endogenous Network Effects by : Ruxian Wang
Download or read book Consumer Choice Models with Endogenous Network Effects written by Ruxian Wang and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network externality arises when the utility of a product depends not only on its attributes, but also on the number of consumers who purchase the same product. In this paper, we propose and analyze consumer choice models that endogenize such network externality. We first characterize the choice probabilities under such models and conduct studies on comparative statics. Then we investigate the assortment optimization problem under such choice models. Although the problem is generally NP-hard, we show that a new class of assortments, called quasi-revenue-ordered assortments, which consist of a revenue-ordered assortment plus at most one additional item, are optimal under mild conditions. We also propose an iterative estimation method to calibrate such choice models, for both uncensored and censored data cases. An empirical study on a mobile game dataset shows that our proposed model can provide better fits for the data, increase the prediction accuracy for consumer choices and potentially increase revenue.
Book Synopsis Assortment Optimization Under Multiple-Discrete Customer Choices by : Heng Zhang
Download or read book Assortment Optimization Under Multiple-Discrete Customer Choices written by Heng Zhang and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an assortment optimization problem where the customer may purchase multiple products and possibly more than one unit of each product purchased. We adopt the customer consumption model based on the Multiple-Discrete-Choice (MDC) model proposed by Huh and Li (2021). We identify conditions under which the profit-ordered sets are optimal. Without these conditions, we show that assortment optimization is NP-hard. Furthermore, we prove that a generalization of the profit-ordered sets achieves an approximation guarantee of 1/2. We also present an algorithm that computes an epsilon-optimal solution to the assortment problem in running time polynomial in 1/epsilon and the problem input size, once we impose the mild technical assumption that model parameters are bounded.
Book Synopsis Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models by : Wang Chi Cheung
Download or read book Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models written by Wang Chi Cheung and published by . This book was released on 2017 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis When Prospect Theory Meets Consumer Choice Models by : Ruxian Wang
Download or read book When Prospect Theory Meets Consumer Choice Models written by Ruxian Wang and published by . This book was released on 2018 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problem Definition: Reference prices arise as price expectations against which consumers evaluate products in their purchase scenarios. We investigate what will happen when prospect theory (e.g., reference prices) meets consumer choice models from the perspectives of both the consumers and the firm.Academic/Practical Relevance: Consumers see multiple relevant products on a particular purchase occasion, and often compare their prices to form the willingness to pay when considering whether to purchase a particular product. Reference prices, which are not included in many choice models, may impact consumer choice behavior, so we incorporate reference prices into consumer choice models and investigate the operations management problems.Methodology: We take the widely used multi-nomial logit model as a showcase to examine the effects of reference prices through analytical and empirical study. We consider the optimization problems on assortment planning and pricing under consumer choice models with a variety of reference prices, including the lowest price and the assortment variety.Results: Our empirical study on a real data set demonstrates that incorporating reference prices into choice models can significantly improve goodness-of-fit and prediction accuracy of consumer choice behavior. Furthermore, we characterize the optimal policies for the assortment planning and pricing problems under the consumer choice models with various reference prices. In particular for the pricing problems under the reference prices defined by either the lowest price or assortment variety, we show that the optimal pricing policy has the following structure: products can be grouped into several categories based on their costs; the products in the same category charge either the same profit markup or the same price.Managerial Implications: In practice, reference prices should be taken into account in model estimation and operations management. Ignoring reference prices may lead to substantial losses.
Book Synopsis Product Line Design, Pricing and Framing Under General Choice Models by : Anran Li
Download or read book Product Line Design, Pricing and Framing Under General Choice Models written by Anran Li and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis handles fundamental problems faced by retailers everyday: how do consumers make choices from an enormous variety of products? How to design a product portfolio to maximize the expected profit given consumers’ choice behavior? How to frame products if consumers’ choices are influenced by the display location? We solve those problems by first, constructing mathematical models to describe consumers’ choice behavior from a given offer set, i.e., consumer choice models; second, by designing efficient algorithms to optimally select the product portfolio to maximize the expected profit, i.e., assortment optimization. This thesis consists of three main parts: the first part solves assortment optimization problem under a consideration set based choice model proposed by Manzini and Mariotti (2014) [Manzini, Paola, Marco Mariotti. 2014. Stochastic choice and consideration sets. Econometrica 82(3) 1153-1176.]; the second part proposes an approximation algorithm to jointly optimize products’ selection and display; the third part works on optimally designing a product line under the Logit family choice models when a product’s utility depends on attribute-level configurations.
Book Synopsis Assortment Optimization Under Consider-Then-Choose Choice Models by : Ali Aouad
Download or read book Assortment Optimization Under Consider-Then-Choose Choice Models written by Ali Aouad and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider-then-choose models, borne out by empirical literature in marketing and psychology, explain that customers choose among alternatives in two phases, by first screening products to decide which alternatives to consider, before then ranking them. In this paper, we develop a dynamic programming framework to study the computational aspects of assortment optimization models posited on consider-then-choose premises. Although ranking-based choice models generally lead to computationally intractable assortment optimization problems, we are able to show that for many practical and empirically vetted assumptions on how customers consider and choose, the resulting dynamic program is efficient. Our approach unifies and subsumes several specialized settings analyzed in previous literature. Empirically, we demonstrate the versatility and predictive power of our modeling approach on a combination of synthetic and real industry datasets, where prediction errors are significantly reduced against common parametric choice models. In synthetic experiments, our algorithms lead to practical computation schemes that outperform a state-of-the-art integer programming solver in terms of running time, in several parameter regimes of interest.
Book Synopsis Assortment Optimization Under a Single Transition Model by : Kameng Nip
Download or read book Assortment Optimization Under a Single Transition Model written by Kameng Nip and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products to the customer and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product and that each customer either purchases a product or leaves the market after one transition.We study the assortment optimization problem under this model. Particularly, we show that this problem is NP-Hard even if the customer can transition from each product to at most two products. Despite the complexity of the problem, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is at most a given number. We also provide a tight worst-case performance bound for revenue-ordered assortments. In addition, we propose a compact mixed integer program formulation for this problem, which is efficient for problems of moderate size. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.
Book Synopsis Tractable Time Slot Assortment Optimization in Attended Home Delivery Under Consider-Then-Choose Customer Choice by : Jonas Schwamberger
Download or read book Tractable Time Slot Assortment Optimization in Attended Home Delivery Under Consider-Then-Choose Customer Choice written by Jonas Schwamberger and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In attended home delivery, the delivery time slot offering problem has a significant impact on the efficiency of the retailer providing this service. Since the decision on which time slots to offer is typically made online during the customer booking process, this problem requires a real-time solution.However, solving this problem is complex since most companies offer multiple time slots over multiple days and must account for customer preferences. To adequately reflect customer choice, an appropriate customer choice model must be adopted. We employ the consider-then-choose choice model, which in the empirical literature has been shown to reflect the general underlying customer choice behavior well.We address the time slot offering problem from a customer choice perspective. In particular, we propose a time slot assortment optimization model that exploits a customer cluster structure underlying the consider-then-choose choice model to solve the time slot offering problem in real-time. In addition, we propose a method for estimating the consider-then-choose choice model with such a cluster structure from historical transaction data. We evaluate this estimation method and the proposed time slot offering model in a numerical study and demonstrate that the estimation procedure can extract the underlying choice behavior and that the time slot offering problem can be solved in real-time for realistic problem sizes of an e-grocer.
