Assortment of Optimization and Pricing Problems Under Multi-stage Multinomial Logit Models PDF Download
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Author: Yuhang Ma
Publisher:
ISBN:
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Languages : en
Pages : 163
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Book Description
In most E-commerce scenarios such as hotel booking and online shopping, products are not offered to customers simultaneously. Instead, they are divided into different webpages and presented to customers sequentially. In this thesis, we focus on solving a common problem faced by online retailers: when products are revealed to customers sequentially, which products should the retailers display at each stage and what prices should the retailers charge for each product so that the expected revenue can be maximized? To solve those problems, we generalize the classical multinomial logit model to capture the customer's choice behavior under the sequential setting and present efficient algorithms for different generalized choice models and different operational constraints.
Author: Yuhang Ma
Publisher:
ISBN:
Category :
Languages : en
Pages : 163
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Book Description
In most E-commerce scenarios such as hotel booking and online shopping, products are not offered to customers simultaneously. Instead, they are divided into different webpages and presented to customers sequentially. In this thesis, we focus on solving a common problem faced by online retailers: when products are revealed to customers sequentially, which products should the retailers display at each stage and what prices should the retailers charge for each product so that the expected revenue can be maximized? To solve those problems, we generalize the classical multinomial logit model to capture the customer's choice behavior under the sequential setting and present efficient algorithms for different generalized choice models and different operational constraints.
Author: Yicheng Bai
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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: Qingwei Jin
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ISBN:
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Languages : en
Pages : 54
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Book Description
With increasing availability of consumer data and rapid advancement and applications of technologies, online retailers are gaining better knowledge of shopping behavior and preferences of their customers. Thus more and more retailers are providing customized product assortment to better match the needs of customers and generate more sales. In this paper, we study a two-stage revenue management model where a retailer decides non-customized price discounts at stage one due to fairness consideration and customized product assortment at stage two (upon the arrival of customers) under the multinomial logit choice model. We employ a robust approach for the joint discounts and customized assortment optimization problem to handle data uncertainty for estimating customer preferences and distribution of different customer segments. We analyze the structural properties of the problems and propose efficient computational methods to solve the problems with/without cardinality constraint on the assortment. In certain cases, our algorithm converges at a superlinear rate. When there is a cardinality constraint on the assortment, we find the retailer should offer deeper discounts as the constraint becomes more restrictive. We also provide some discussion on the value of our robust solution and the extension when the customer discount sensitivity function is also uncertain. Finally, our extensive numerical study shows that the solutions under the robust approach perform very well compared to the one assuming accurate information and has robustness when there is uncertainty.
Author: Ruxian Wang
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Languages : en
Pages : 7
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Book Description
We consider an assortment and price optimization problem where a retailer chooses an assortment of competing products and determines their prices to maximize the total expected profit subject to a capacity constraint. Customers' purchase behavior follows the multinomial logit choice model with general utility functions. This paper simplifies it to a problem of finding a unique fixed point of a single-dimensional function and visualizes the assortment optimization process. An efficient algorithm to find the optimal assortment and prices is provided.
Author: Hai Jiang
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Languages : en
Pages : 34
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Book Description
We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce this multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.
Author: Lei Guan
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Languages : en
Pages : 0
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{Problem Definition:} This paper considers the operational management problems under a newly proposed choice model that captures the effect of focality. The offered assortment is separated into the focal set and the non-focal set under this new model due to the bias of focality, which is identified by the focal sets and an assortment-dependent focal parameter. A prospective consumer is more likely to choose a product from the focal set, while she may still choose one from the non-focal set for a variety of reasons such as previous purchase experience or brand loyalty. This focal multinomial logit model generalizes the famous multinomial logit model and several well-studied consideration-set choice models. In addition, it has the capability to describe and explain a variety of irrational choice behaviors often observed in practice, such as the context effect, halo effect, and choice overload. {Methodology/results:} In this paper, we primarily focus on the threshold focal set and various focal parameter settings, including the constant, cardinality, and linear focal multinomial logit models, as well as a broader model that satisfies certain regularity conditions and subsumes the above models. We analyze the computational complexity and propose polynomial-time exact or approximation algorithms to solve the assortment optimization problems under different focal parameters. We then characterize the optimal strategy for the joint price and assortment optimization problem. Additionally, we develop a mixed integer conic programming reformulation method that converges to a global optimal estimator for the model calibration problem. {Managerial Implications:} We use these methods to conduct numerical experiments on both synthetic and real data sets. The results demonstrate the efficiency of our proposed algorithms, the predictive power, and the increase in revenue for the focal multinomial logit model. Our extensive analysis implies that in practice retailers may take into account the effect of focality in consumer purchase behavior because it could increase the accuracy of demand estimation and therefore improve operational performance.
Author: Stefanus Jasin
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Languages : en
Pages : 0
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In this paper, we study the assortment and price optimization problems under Multinomial Logit (MNL) model with price range effect, where the utility of a product is affected by the relative position of its price with respect to the highest and the lowest prices in the offer set. This model is motivated by the so-called Range Theory popularized in the behavioral economics and psychology literature. It addresses the limitation of a single-point interpretation of reference price, which ignores the impact of all other distributional information. We investigate the pure assortment problem, the pure pricing problem, and the joint assortment and pricing problem under the MNL model with price range effect. For each model, we first identify the structure of the optimal policy, and then we propose tractable algorithms that either output the optimal solution in polynomial time or admit an Fully Polynomial-Time Approximation Scheme (FPTAS).
Author: Guillermo Gallego
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ISBN:
Category :
Languages : en
Pages : 26
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We study firms that sell multiple substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multi-product pricing problem under the general Nested Logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest-invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and show that similar techniques can be used to significantly simplify the corresponding pricing problems.
Author: Qingwei Jin
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Languages : en
Pages : 0
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Book Description
We study assortment optimization problems under multinomial logit choice model with two tree structured consideration set models, i.e., the subtree model and the induced paths model. In each model, there are multiple customer types and each customer type has a different consideration set. A customer of a particular type only purchases product within his consideration set. The tree structure means all products form a tree with each node representing one product and all consideration sets are induced from this tree. In the subtree model, each consideration set consists of products in a subtree and in the induced paths model, each consideration set consists of products on the path from one node to the root. All customers make purchase decisions following the same multinomial logit choice model except that different customer types have different consideration sets. The goal of the assortment optimization is to determine a set of products offered to customers such that the expected revenue is maximized. We consider both unconstrained problem and capacitated problem. We show that these problems are all NP-hard problems and propose a unified framework, which captures the tree structure in both models, to design fully polynomial time approximation schemes (FPTAS) for all these problems. Besides, we identify a special case under the induced paths model, showing that it can be solved in $O(n)$ operations.
Author: Mohan Gopalakrishnan
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ISBN:
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Languages : en
Pages : 0
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Motivated by direct interactions with practitioners and real-world data, we study a monopoly firm selling multiple substitute products to customers characterized by their different social network degrees. Under the multinomial logit model framework, we assume that the utility a customer with a larger network degree derives from the seller's products is subject to more impact from her neighbors and describe the customers' choice behavior by a Bayesian Nash game. We show that a unique equilibrium exists as long as these network effects are not too large. Furthermore, we study how the seller should optimally set the prices of the products in this setting. Under the homogeneous product-related parameter assumption, we show that if the seller optimally price-discriminates all customers based on their network degrees, the products' markups are the same for each customer type. Building on this, we characterize the sufficient and necessary condition for the concavity of the pricing problem, and show that when the problem is not concave, we can convert it to a single-dimensional search and solve it efficiently. We provide several further insights about the structure of optimal prices, both theoretically and numerically. Furthermore, we show that we can simultaneously relax the multinomial logit model and homogeneous product-related parameter assumptions and allow customer in- and out-degrees to be arbitrarily distributed whilemaintaining most of our conclusions robust.
