A branch-and-cut algorithm for the latent-class logit assortment problem

Méndez-Díaz, Isabel; Miranda-Bront, Juan José; Vulcano, Gustavo; Zabala, Paula

doi:10.1016/j.dam.2012.03.003

Cited by 112 publications

(72 citation statements)

References 16 publications

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“…They show that the assortment optimization problem is NP-hard in the weak sense even with two customer types and provide a performance guarantee for nested-by-revenue assortments. Bront et al (2009) show that the same problem is NP-hard in the strong sense and Mendez-Diaz et al (2010) focus on developing branch-and-cut algorithm to find the optimal assortment. Rusmevichientong and Topaloglu (2011) study the robust assortment problem under the multinomial logit model when some of the parameters of the choice model are not known.…”

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confidence: 99%

Assortment Optimization Under Variants of the Nested Logit Model

Davis

Gallego

Topaloğlu

2014

Operations Research

285

158

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We study a class of assortment optimization problems where customers choose among the offered products according to the nested logit model. There is a fixed revenue associated with each product. The objective is to find an assortment of products to offer so as to maximize the expected revenue per customer. We show that the problem is polynomially solvable when the nest dissimilarity parameters of the choice model are less than one and the customers always make a purchase within the selected nest. Relaxing either of these assumptions renders the problem NP-hard. To deal with the NP-hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. We also formulate a convex program whose optimal objective value is an upper bound on the optimal expected revenue. Thus, we can compare the expected revenue provided by an assortment with the upper bound on the optimal expected revenue to get a feel for the optimality gap of the assortment. By using this approach, our computational experiments test the performance of the parsimonious collections of candidate assortments that we develop.

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confidence: 99%

Assortment Optimization Under Variants of the Nested Logit Model

Davis

Gallego

Topaloğlu

2014

Operations Research

285

158

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“…The nested MNL model is used by Kök and Xu (2011), Gallego and Topaloglu (2014), and Lee and Eun (2016). The latent-class MNL model is used by Méndez-Díaz, Miranda-Bront, Vulcano, and Zabala (2014) and Rusmevichientong, Shmoys, Tong, and Topaloglu (2014). It is challenging to identify the right choice model.…”

Section: Literature Reviewmentioning

confidence: 99%

Callable products with dependent demands

Gallego

Lee

2020

Naval Research Logistics

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Capacity providers such as airlines often sell the same capacity to different market segments at different prices to improve their expected revenues. The absence of a secondary market, due to the nontransferability of airline tickets, gives rise to an opportunity for airlines to broker capacity between consumers with different willingness to pay. One way to broker capacity is by the introduction of callable products. The idea is similar to callable bonds where the issuer has the right, but not the obligation, to buy back the bonds at a certain price by a certain date. The idea of callable products was introduced before under the assumption that the fare‐class demands are all independent. The independent assumption becomes untenable when there is significant demand recovery (respectively, demand cannibalization) when lower fares are closed (respectively, opened). In this case, consumer choice behavior should be modeled explicitly to make meaningful decisions. In this paper, we consider a general consumer choice model and develop the optimal strategy for callable products. Our numerical study illustrates how callable products are win‐win‐win, for the capacity provider and for both high and low fare consumers. Our studies also identify conditions for callable products to result in significant improvements in expected revenues.

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“…The MMNL model, introduced by Boyd and Mellman (1980) and Cardell and Dunbar (1980), has another important characteristic -as observed by McFadden and Train (2000): "any discrete choice model derived from random utility maximization... can be approximated as closely as one pleases by a MMNL model." Assortment planning under the MMNL model, also known as the mixtures of MNL model (Feldman and Topaloglu, 2015), MNL with random choice parameters (Rusmevichientong et al, 2014), and latent-class MNL (Méndez-Díaz et al, 2014), has received considerable interest in the OR/MS community. The problem also arises as a subproblem in a new approach in revenue management called choice-based deterministic linear optimization that attempts to model customer choice behavior more realistically (Liu and van Ryzin, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the computational complexity and the ineffectiveness of standard MILP formulations of the problem, Bront et al (2009) propose a greedy heuristic. Méndez-Díaz et al (2014) design and test a branch-and-cut algorithm that generates good but often not provably optimal solutions for both capacitated and uncapacitated versions. Rusmevichientong et al (2014) identify special cases of the (uncapacitated) problem that are polynomially solvable, and characterize the performance of heuristics for other cases.…”

Section: Introductionmentioning

confidence: 99%

Technical Note—A Conic Integer Optimization Approach to the Constrained Assortment Problem Under the Mixed Multinomial Logit Model

Şen

Atamtürk

Kaminsky

2018

Operations Research

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We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.

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A branch-and-cut algorithm for the latent-class logit assortment problem

Cited by 112 publications

References 16 publications

Assortment Optimization Under Variants of the Nested Logit Model

Assortment Optimization Under Variants of the Nested Logit Model

Callable products with dependent demands

Technical Note—A Conic Integer Optimization Approach to the Constrained Assortment Problem Under the Mixed Multinomial Logit Model

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