MNL-Bandit: A Dynamic Learning Approach to Assortment Selection

Agrawal, Shipra; Avadhanula, Vashist; Goyal, Vineet; Zeevi, Assaf

doi:10.1287/opre.2018.1832

Cited by 117 publications

(127 citation statements)

References 26 publications

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“…The first boundedness assumption on revenue parameters is standard in the literature (see e.g., Theorem 1 in Agrawal et al. (2019)). It is also worthwhile noting that assumption (A2) is weaker than the common assumption that no purchase (with

V_{0} = 1

) is the most frequent outcome.…”

Section: Model Specifications and Assortment Space Reductionsmentioning

confidence: 99%

“…Instead, we directly estimate “nested‐level utility”

V_{i} {(\cdot)}^{γ_{i}}

(see Equation ) and the discussions above Equation ). UCB policy: We propose an upper confidence bound (UCB) algorithm using an epoch‐based strategy from Agrawal et al. (2019), which leads to a worst‐case expected regret of

\overset{false~}{O} false(\sqrt{MNT} false)

. Although the UCB has been a well‐known technique for bandit problems, adopting this high‐level idea to solve a problem with specific structures certainly requires technical innovations (e.g., how to build a confidence bound on a carefully designed parameter, see Lemma 4).…”

Section: Introductionmentioning

confidence: 99%

“…We further note that our UCB policy generalizes the one in Agrawal et al. (2019) because in our model the “level sets” are constructed within each nest, and therefore both their revenue and utility parameters are unknown (see Equation ) in section 2.2) This contrasts the setting in Agrawal et al. (2019) in which the revenue parameters of each single item are known. Discretization technique: When N is large, we introduce a discretization technique to reduce the size of the action space to

O ({(1 / δ)}^{M})

, where δ is discretization granularity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Assortment Planning Under Nested Logit Models

Chen

Shi²,

Wang

et al. 2021

Production and Operations Management

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We study a stylized dynamic assortment planning problem during a selling season of finite length T. At each time period, the seller offers an arriving customer an assortment of substitutable products and the customer makes the purchase among offered products according to a discrete choice model. The goal of the seller is to maximize the expected revenue, or equivalently, to minimize the worst‐case expected regret. One key challenge is that utilities of products are unknown to the seller and need to be learned. Although the dynamic assortment planning problem has received increasing attention in revenue management, most existing work is based on the multinomial logit choice models (MNL). In this paper, we study the problem of dynamic assortment planning under a more general choice model—the nested logit model, which models hierarchical choice behavior and is “the most widely used member of the GEV (generalized extreme value) family” (Train 2009). By leveraging the revenue‐ordered structure of the optimal assortment within each nest, we develop a novel upper confidence bound (UCB) policy with an aggregated estimation scheme. Our policy simultaneously learns customers’ choice behavior and makes dynamic decisions on assortments based on the current knowledge. It achieves the accumulated regret at the order of Ofalse~false(MNTfalse), where M is the number of nests and N is the number of products in each nest. We further provide a lower bound result of Ω(italicMT), which shows the near optimality of the upper bound when T is much larger than M and N. When the number of items per nest N is large, we further provide a discretization heuristic for better performance of our algorithm. Numerical results are presented to demonstrate the empirical performance of our proposed algorithms.

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V_{0} = 1

) is the most frequent outcome.…”

Section: Model Specifications and Assortment Space Reductionsmentioning

confidence: 99%

“…Instead, we directly estimate “nested‐level utility”

V_{i} {(\cdot)}^{γ_{i}}

\overset{false~}{O} false(\sqrt{MNT} false)

Section: Introductionmentioning

confidence: 99%

O ({(1 / δ)}^{M})

, where δ is discretization granularity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Assortment Planning Under Nested Logit Models

Chen

Shi²,

Wang

et al. 2021

Production and Operations Management

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show abstract

“…Also, in the field of dynamic assortment with discrete choice models. Most of the underlying choice model is usually the multinomial logit model [1,2,5]. Recently, Chen et al [12] study the dynamic assortment problem under the nested logit model.…”

Section: Literature Reviewmentioning

confidence: 99%

Capacitated assortment and price optimization under the nested logit model

Chen

Jiang

2020

J Glob Optim

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We study the capacitated assortment and price optimization problem, where a retailer sells categories of substitutable products subject to a capacity constraint. The goal of the retailer is to determine the subset of products as well as their selling prices so as to maximize the expected revenue. We model the customer purchase behavior using the nested logit model and formulate this problem as a non-linear binary integer program. For this NP-complete problem, we show that there exists a pseudo polynomial time approximation scheme that finds its-approximate solution. We first convert the original problem into an equivalent fixed point problem. We then show that finding an-approximate solution to the fixed point problem can be achieved by binary search, where a non-linear auxiliary problem is repeatedly approximated by a dynamic programing based algorithm involving an approximation to a series of multiple-choice parametric knapsack problems. For the special case when the capacity constraints are cardinal and nest-specific, we develop an algorithm that finds the optimal solution in strongly polynomial time. Moreover, our algorithm can be directly applied to find an-approximate solution to the capacitated assortment optimization problem under the nested logit model, which is the first approximate algorithm that is polynomial with respect to the number of nests in the literature. Keywords Assortment optimization • Nested logit model • Approximate algorithm • Combinatorial optimization 1 Introduction Consider a retailer that sells several categories of products, where products within each category are substitutable of each other to certain extent. For example, a home appliance store sells several categories of products such as televisions, refrigerators, and dish washers.

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“…is the distance sensitivity of consumer i. Then, the multinomial logit (MNL) model [19] was introduced to represent the random selection of consumers. The probabilities for consumer i to choose "buy in store" and "buy online, in-store pickup" 0 can be respectively expressed as:…”

Section: Scene-based Demand Analysis For Cssmentioning

confidence: 99%

Multi-objective Decision-Making of New Retailing Terminals Based on Particle Swarm Optimization and Genetic Algorithm

Wu¹

2019

JESA

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This paper aims to solve the multi-objective decision-making for the optimal configuration of multi-type new retailing terminals. First, the distribution of consumer demand for convenience stores (CSs) and unmanned retail terminals (URTs) was investigated in different scenes. Then, the author set up an optimization model for the configuration of multi-type terminals, aiming to maximize the daily mean profit of the retailer, maximize consumer satisfaction in multiple dimensions, and minimize the number of terminals. To solve the model, the genetic algorithm (GA) and particle swarm optimization (PSO) were combined into a hybrid algorithm, based on elite recombination and directed optimization (directed elite search). The proposed model and algorithm were proved valid through empirical analysis. The results show that the retailer can achieve better profit and consumer satisfaction by deploying multiple types of retail terminals, and arranging different terminals at different scenes; moreover, the three optimization objectives can be achieved by improving the attraction of terminals, cautiously analyzing consumer rationality and properly setting the courier fee. The research findings lay theoretical basis for terminal configuration in new retailing and provide an important guide for new retailing operations.

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MNL-Bandit: A Dynamic Learning Approach to Assortment Selection

Cited by 117 publications

References 26 publications

Dynamic Assortment Planning Under Nested Logit Models

Dynamic Assortment Planning Under Nested Logit Models

Capacitated assortment and price optimization under the nested logit model

Multi-objective Decision-Making of New Retailing Terminals Based on Particle Swarm Optimization and Genetic Algorithm

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