Discrete choice models based on random walks

Berbeglia, Gerardo

doi:10.1016/j.orl.2016.01.009

Cited by 15 publications

(4 citation statements)

References 14 publications

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“…Recently, Berbeglia [9] showed that every choice model based on Markov chains models belongs to the class of choice models based on random utility. Jagabathula [25] introduced a local search heuristic for the assortment problem under an arbitrary discrete choice model.…”

Section: Introductionmentioning

confidence: 99%

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Berbeglia

Joret

2015

SSRN Journal

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The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue π and then choosing all products with revenue at least π. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. [42]. An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition.We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.(

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Section: Introductionmentioning

confidence: 99%

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Berbeglia

Joret

2015

SSRN Journal

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“…The temporal model is a generalization of the Markov chain model discussed in this subsection and the random walk model discussed by Berbeglia (2016).…”

Section: Temporal Modelmentioning

confidence: 99%

“…We can think of

T_{i}

as the time to some random event that triggers the choice of option

i

. When given the choice set

S

, the consumer's choice would be the option whose associated event occurs first, that is,

i^{*} = \{i : T_{i} < min_{j \in S \cup false{0 false} true\ false{i false}} T_{j}, i \in S \cup {0}\} .

The temporal model is a generalization of the Markov chain model discussed in this subsection and the random walk model discussed by Berbeglia (2016).…”

Section: Models Of Consumer Choicementioning

confidence: 99%

Consumer Choice Models and Estimation: A Review and Extension

Feng

Shanthikumar

Xue

2022

Production and Operations Management

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C hoice models are widely applied in psychology, economics, transportation, marketing, and operations studies. We review the existing developments on the modeling of consumers' choices, including the attraction model, the utilitybased model, the temporal model, and the rank-based model. The relationships among different classes of structural models are established and analyzed. Moreover, an operational data analytics (ODA) framework is presented to estimate the general consumer choice model using data. This framework, generalizing the existing estimation methods for specific structural models, strikes a delicate balance between the (likely imprecise) structural knowledge and the data. This is achieved by articulating the domain of validation through extending the structural knowledge and by formulating the data-integration model based on the associated structural properties. We demonstrate the implementation of the ODA framework to identify the appropriate consumer choice models. The ODA estimate outperforms the existing parametric and nonparametric methods, particularly over the choice sets that are not covered in the data. We also discuss potential future research of developing ODA approaches to study the related aspects of consumer choice models.

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“…In their model, the customer's choice process is represented by a Markov chain. Berbeglia (2016) indicates that the Markov Chain model belongs to the class of discrete choice models based on random utility. Other papers that have considered this customer choice model are Feldman and Topaloglu (2017), Désir et al (2020), and Simsek and Topaloglu (2018).…”

Section: Introductionmentioning

confidence: 99%

An extended ε$\varepsilon $‐constraint method for a bi‐objective assortment optimization problem

Eskandari,

Ziarati,

Nikseresht

2023

Int Trans Operational Res

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The paper deals with assortment optimization when customers purchase products using a nonparametric choice model. Each customer is presented with a preference list and will buy an available highest‐ranked offered product on the preference list. The paper presents a novel bi‐objective integer programming model for assortment optimization following a ranking‐based consumer choice model. The objectives are maximizing the expected revenue and maximizing customer satisfaction. This problem is recognized as an NP‐hard problem. After developing the bi‐objective model, an improved version of the augmented ε‐constraint method is proposed to solve the problem and retrieve the Pareto‐optimal solutions. In each iteration, this algorithm solves a single‐objective linear integer programming sub‐problem. Our approach aims to obtain a complete set of Pareto‐optimal solutions. Finally, we present computational experiments on synthetic data. Several numerical illustrations are provided at the end to demonstrate the application of the proposed methodology. The computational results provide the decision‐makers with valuable information regarding the factors that mainly affect the solutions.

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Discrete choice models based on random walks

Cited by 15 publications

References 14 publications

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Consumer Choice Models and Estimation: A Review and Extension

An extended ε$\varepsilon $‐constraint method for a bi‐objective assortment optimization problem

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