(Rescaled) Multi-Attempt Approximation of Choice Model and Its Application to Assortment Optimization

2018 ◽  
Vol 28 (2) ◽  
pp. 341-353 ◽  
Author(s):  
Hakjin Chung ◽  
Hyun-Soo Ahn ◽  
Stefanus Jasin
Keyword(s):  
Choice Model ◽  
Assortment Optimization

Assortment Optimization under the Multi-Purchase Multinomial Logit Choice Model

2021 ◽  
Author(s):  
Jacob Feldman ◽  
Danny Segev ◽  
Huseyin Topaloglu ◽  
Laura Wagner ◽  
Yicheng Bai
Keyword(s):  
Choice Model ◽  
Multinomial Logit ◽  
Assortment Optimization

Constrained Assortment Optimization Under the Paired Combinatorial Logit Model

2021 ◽  
Author(s):  
Rohan Ghuge ◽  
Joseph Kwon ◽  
Viswanath Nagarajan ◽  
Adetee Sharma
Keyword(s):  
Logit Model ◽  
Choice Model ◽  
Customer Behavior ◽  
Multidimensional Space ◽  
Customer Choice ◽  
Assortment Optimization ◽  
Selected Subset ◽  
Unconstrained Problem ◽  
Key Aspects ◽  
Customer Choice Model

Assortment optimization involves selecting a subset of products to offer to customers in order to maximize revenue. Often, the selected subset must also satisfy some constraints, such as capacity or space usage. Two key aspects in assortment optimization are (1) modeling customer behavior and (2) computing optimal or near-optimal assortments efficiently. The paired combinatorial logit (PCL) model is a generic customer choice model that allows for arbitrary correlations in the utilities of different products. The PCL model has greater modeling power than other choice models, such as multinomial-logit and nested-logit. In “Constrained Assortment Optimization Under the Paired Combinatorial Logit Model,” Ghuge, Kwon, Nagarajan, and and Sharma provide efficient algorithms that find provably near-optimal solutions for PCL assortment optimization under several types of constraints. These include the basic unconstrained problem (which is already intractable to solve exactly), multidimensional space constraints, and partition constraints. The authors also demonstrate via extensive experiments that their algorithms typically achieve over 95% of the optimal revenues.

Constrained Assortment Optimization Under the Markov Chain–based Choice Model

2020 ◽  
Vol 66 (2) ◽  
pp. 698-721 ◽  
Author(s):  
Antoine Désir ◽  
Vineet Goyal ◽  
Danny Segev ◽  
Chun Ye
Keyword(s):  
Markov Chain ◽  
Choice Model ◽  
Assortment Optimization

Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection

2021 ◽  
Author(s):  
Pin Gao ◽  
Yuhang Ma ◽  
Ningyuan Chen ◽  
Guillermo Gallego ◽  
Anran Li ◽  
...  
Keyword(s):  
Logit Model ◽  
Choice Model ◽  
Multinomial Logit Model ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Multinomial Logit ◽  
Impatient Customers ◽  
Purchasing Decisions ◽  
Assortment Optimization ◽  
Decision Variables

Sequential Recommendation Under the Multinomial Logit Model with Impatient Customers In many applications, customers incrementally view a subset of offered products and make purchasing decisions before observing all the offered products. In this case, the decision faced by a firm is not only what assortment of products to offer, but also in what sequence to offer the products. In “Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection”, Gao, Ma, Chen, Gallego, Li, Rusmevichientong, and Topaloglu propose a choice model where each customer incrementally view the assortment of products in multiple stages, and their patience level determines the maximum number of stages. Under this choice model, the authors develop a polynomial-time algorithm that finds a revenue-maximizing sequence of assortments. If the sequence of assortments is fixed, the problem of finding revenue-maximizing prices can be transformed to a convex program. They combine these results to develop an effective approximation algorithm when both the sequence of assortments and prices are decision variables.

Assortment Optimization and Pricing Under a Nonparametric Tree Choice Model

2018 ◽  
Vol 20 (3) ◽  
pp. 550-565 ◽  
Author(s):  
Alice Paul ◽  
Jacob Feldman ◽  
James Mario Davis
Keyword(s):  
Choice Model ◽  
Assortment Optimization

scholarly journals A regret lower bound for assortment optimization under the capacitated MNL model with arbitrary revenue parameters

2021 ◽  
pp. 1-9
Author(s):  
Yannik Peeters ◽  
Arnoud V. den Boer
Keyword(s):  
Lower Bound ◽  
Incomplete Information ◽  
Positive Constant ◽  
Time Horizon ◽  
Choice Model ◽  
Multinomial Logit ◽  
Asymptotically Optimal ◽  
Assortment Optimization ◽  
Mnl Model ◽  
Expected Revenue

Abstract In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT}$ , where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $\sqrt {N T}$ . Our result implies that policies that achieve ${{\mathcal {O}}}(\sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.

scholarly journals Combinatorial Assortment Optimization

2021 ◽  
Vol 9 (1) ◽  
pp. 1-34
Author(s):  
Nicole Immorlica ◽  
Brendan Lucier ◽  
Jieming Mao ◽  
Vasilis Syrgkanis ◽  
Christos Tzamos
Keyword(s):  
Choice Function ◽  
Optimization Problem ◽  
Choice Model ◽  
Exact Algorithm ◽  
Convenience Store ◽  
Valuation Function ◽  
Probabilistic Choice ◽  
Assortment Optimization ◽  
Relative Value ◽  
Potential Customers

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a choice model in which each consumer selects a utility-maximizing bundle subject to a private valuation function, and study the complexity of the resulting optimization problem. Our main result is an exact algorithm for additive k -demand valuations, under a model of vertical differentiation in which customers agree on the relative value of each pair of items but differ in their absolute willingness to pay. For valuations that are vertically differentiated but not necessarily additive k -demand, we show how to obtain constant approximations under a “well-priced” condition, where each product’s price is sufficiently high. We further show that even for a single customer with known valuation, any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS and that no FPTAS exists even when the valuation is succinctly representable.

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