Approximation Algorithms for Product Framing and Pricing

Gallego, Guillermo; Li, Anran; Truong, Van-Anh; Wang, Xinshang

doi:10.2139/ssrn.3260279

Cited by 30 publications

(43 citation statements)

References 39 publications

(12 reference statements)

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“…It is worth mentioning that our performance guarantees are essentially best-possible. As explained in Section 1.2, under Multinomial Logit preferences, the display optimization problem captures as a special case the product framing model of Gallego et al (2016), who proved that the latter problem is NP-hard. As an interesting side note, simple counter-examples demonstrate that natural heuristics to address the display optimization problem -such as local-search or greedy procedures -have arbitrarily large optimality gaps, generating only an O( 1 n ) fraction of the optimal expected revenue in the worst case.…”

Section: Our Resultsmentioning

confidence: 99%

“…Furthermore, what makes the former significantly easier to approximate is that retailers are allowed to leave certain positions vacant, while still garnering an expected revenue from these positions, as well as to avoid displaying certain items. Subsequent to our work, Gallego et al (2016) studied the product framing model, which generalizes the assortment over time problem by allowing products to be introduced in limited-size batches, and by considering non-uniform customer arrival rates.…”

Section: Modeling Approachmentioning

confidence: 99%

“…It is worth mentioning that we are not aware of any way to employ the algorithmic ideas of Davis et al (2015) and Gallego et al (2016) in order to obtain any non-trivial performance guarantee for the display optimization problem.…”

Section: Modeling Approachmentioning

confidence: 99%

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Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Aouad

Segev

2021

Management Science

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We introduce a new optimization model, dubbed the display optimization problem, that captures a common aspect of choice behavior, known as the framing bias. In this setting, the objective is to optimize how distinct items (corresponding to products, web links, ads, etc.) are being displayed to a heterogeneous audience, whose choice preferences are influenced by the relative locations of items. Once items are assigned to vertically differentiated locations, customers consider a subset of the items displayed in the most favorable locations before picking an alternative through multinomial logit choice probabilities. The main contribution of this paper is to derive a polynomial-time approximation scheme for the display optimization problem. Our algorithm is based on an approximate dynamic programming formulation that exploits various structural properties to derive a compact state space representation of provably near-optimal item-to-position assignment decisions. As a byproduct, our results improve on existing constant-factor approximations for closely related models and apply to general distributions over consideration sets. We develop the notion of approximate assortments that may be of independent interest and applicable in additional revenue management settings. Lastly, we conduct extensive numerical studies to validate the proposed modeling approach and algorithm. Experiments on a public hotel booking data set demonstrate the superior predictive accuracy of our choice model vis-à-vis the multinomial logit choice model with location bias, proposed in earlier literature. In synthetic computational experiments, our approximation scheme dominates various benchmarks, including natural heuristics—greedy methods, local search, priority rules—and state-of-the-art algorithms developed for closely related models. This paper was accepted by Yinyu Ye, optimization.

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Section: Our Resultsmentioning

confidence: 99%

Section: Modeling Approachmentioning

confidence: 99%

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Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Aouad

Segev

2021

Management Science

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“…In contrast to this paper, their approach focuses on deriving bounds on the value function of the underlying MDP and using them to construct heuristics. A few recent studies on assortment optimization are particularly relevant to our paper: Golrezaei et al (2014), Bernstein et al (2015), Gallego et al (2016a), and Gallego et al (2016b). Bernstein et al (2015) study a dynamic assortment customization problem, which is mathematically similar to our nonsequential appointment offering problem, assuming multiple types of customers, each of which has a multinomial logit choice behavior over all product types.…”

Section: Literature Reviewmentioning

confidence: 96%

“…Gallego et al (2016b) extend the work by Golrezaei et al (2014) to allow rewards that depend on both the customer type and the product type. In addition, Gallego et al (2016a) study assortment optimization in an online retail setting, where each customer picks the number of pages to view according to a fixed distribution and then chooses among all of the products offered on those pages following some choice model. The last three studies also assume that the customer type is known to the seller, and their focus is on developing control policies competitive with respect to an offline optimum, a different type of research question from ours.…”

Section: Literature Reviewmentioning

confidence: 99%

Managing Appointment Booking Under Customer Choices

Liu

Ven²,

Zhang

2017

SSRN Journal

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Please scroll down for article-it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

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Assortment optimization under the Sequential Multinomial Logit Model

Flores

Berbeglia

Hentenryck

2019

European Journal of Operational Research

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We study the assortment optimization problem under the Sequential Multinomial Logit (SML), a discrete choice model that generalizes the multinomial logit (MNL). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products in the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique, Saito, and Tserenjigmid (2018). It can explain many behavioral phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the MNL model or any discrete choice model based on random utility. In particular, the SML model allows violations to regularity which states that the probability of choosing a product cannot increase if the offer set is enlarged.This paper shows that the seminal concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, the paper proves that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomialtime solvable. This result is particularly interesting given that the SML model does not satisfy the regularity condition and, therefore, it can explain choice behaviours that cannot be explained by any choice model based on random utility.

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Approximation Algorithms for Product Framing and Pricing

Cited by 30 publications

References 39 publications

Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Managing Appointment Booking Under Customer Choices

Assortment optimization under the Sequential Multinomial Logit Model

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