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Author: James Mario Davis
Publisher:
ISBN:
Category :
Languages : en
Pages : 424
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Book Description
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.
Author: James Mario Davis
Publisher:
ISBN:
Category :
Languages : en
Pages : 424
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Book Description
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.
Author: Elham Nosratmirshekarlou
Publisher:
ISBN:
Category : Industrial engineering
Languages : en
Pages : 71
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Book Description
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.
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: Hakjin Chung
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
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.
Author: Xu Tian
Publisher:
ISBN:
Category :
Languages : en
Pages : 42
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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.
Author: Shujie Luan
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
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.
Author: Uzma Mushtaque
Publisher:
ISBN:
Category :
Languages : en
Pages : 420
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Author: Ruxian Wang
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ISBN:
Category :
Languages : en
Pages : 0
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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.
Author: Jacob Feldman
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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Book Description
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.
Author: Ruxian Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
