A greedy algorithm for the two-level nested logit model

Li, Guang; Rusmevichientong, Paat

doi:10.1016/j.orl.2014.05.006

Cited by 53 publications

(23 citation statements)

References 7 publications

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“…We also classify those papers based on the integration of pricing decisions in AOP. For example, Li and Rusmevichientong [19] developed a greedy algorithm to solve the AOP in polynomial time. They assume that the nest dissimilarity parameter is less than or equal to one for all nests.…”

Section: Related Literaturementioning

confidence: 99%

An Exact Method for Assortment Optimization Under the Nested Logit Model

2020

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We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we provide a general exact method that embeds a tailored Branch-and-Bound algorithm into a fractional programming framework. Contrary to the existing literature, in which assumptions are imposed on either the structure of nests or the combination and characteristics of products, no assumptions on the input data are imposed, and hence our approach can solve the most general problem setting. We show that the parameterized subproblem of the fractional programming scheme, which is a binary highly non-linear optimization problem, is decomposable by nests, which is a main advantage of the approach. To solve the subproblem for each nest, we propose a two-stage approach. In the first stage, we identify those products that are undoubtedly beneficial to offer, or not, which can significantly reduce the problem size. In the second stage, we design a tailored Branch-and-Bound algorithm with problem-specific upper bounds. Numerical results show that the approach is able to solve assortment instances with up to 5,000 products per nest. The most challenging instances for our approach are those in which the dissimilarity parameters of nests can be either less or greater than one.

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Section: Related Literaturementioning

confidence: 99%

An Exact Method for Assortment Optimization Under the Nested Logit Model

2020

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“…Rusmevichientong et al (2010), Wang (2012), Davis et al (2013) and Wang (2013) (2014) focus on assortment problems when customer choices are governed by a mixture of multinomial logit models. Li et al (2015), Davis et al (2014), and Li and Rusmevichientong (2014) develop efficient methods for the unconstrained assortment problem when customers choose under the nested logit model. Gallego and Topaloglu (2014) and Feldman and Topaloglu (2015) consider the space and cardinality constrained versions of the assortment problem when customers choose according to the nested logit model.…”

Section: Related Literaturementioning

confidence: 99%

Assortment Optimization and Pricing Under a Nonparametric Tree Choice Model

Paul

Feldman

Davis

2018

M&SOM

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We consider assortment and pricing problems when customers purchase products according to a nonparametric choice model. Each customer arrives with a preference list and will purchase the highest-ranking offered product in her preference list. We assume the set of customer classes is derived from paths in a tree, where the order of nodes visited along each path gives the corresponding preference list. First, we study assortment problems, where the goal is to find which products to offer to maximize expected revenue. We give a dynamic programming solution, which can be extended to versions of the assortment problem where there are fixed costs for offering a product, shelf constraints, or substitution costs. Second, we study the joint assortment and pricing problem, where the goal is to simultaneously select the set of offered products as well as their prices. We solve the pricing problem optimally when the products are vertically differentiated, and hence the tree takes the form of a single path. We also solve the problem optimally on the general tree when the prices are restricted to be quality consistent; higher quality products must be priced above lower quality products. Lastly, we present computational experiments on both synthetic data and real hotel purchase data. These experiments show that the choice model yields efficient and accurate estimates. Our estimation procedure shows both how to build the tree of products and how to estimate the underlying arrival probabilities of each customer type from historical sales data.

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“…Feldman and Topaloglu [44] study the assortment problem under cardinality and space constraints in each nests similar to Gallego and Topaloglu [43]. They Li and Rusmevichientong [45] provide an efficient greedy heuristic for the twolevel nested assortment optimization problem, which has the fastest known running time. They, for the first time, provide a necessary and sufficient condition for an optimal assortment.…”

Section: Logit Modelmentioning

confidence: 99%

Multi-Location Assortment Optimization Under Capacity Constraints

2018

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We study the assortment optimization problem in an online setting where a retailer determines the set of products to carry in each of its distribution centers under a capacity constraint so as to maximize its expected profit (revenue minus the shipping costs). It is assumed that each distribution center is primarily responsible for a geographical location whose customers' choice is governed by a separate multinomial logit model. A distribution center can satisfy a demand of a region that it is not primarily responsible for, but this incurs an additional shipping cost for the retail company. We consider two variants of this problem. In the first variant, customers have access to the entire assortment in all locations but in the second variant, the online retail company can select which product to show to each region. Under each variant, we first assume that there is a constant shipping cost for all products between any two location. In the second case, we allow the shipping costs to differ based on the origin and destination. We develop conic quadratic mixed integer programming formulations and suggest a family of valid inequalities to strengthen these formulations. Numerical experiments show that our conic approach, combined with valid inequalities over-perform the mixed integer linear programming formulation and enables us to solve large instances optimally. Finally, we study the effect of various factors such as no-purchase preference, capacity constraint and shipping cost on company's profitability and assortment selection.

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A greedy algorithm for the two-level nested logit model

Cited by 53 publications

References 7 publications

An Exact Method for Assortment Optimization Under the Nested Logit Model

An Exact Method for Assortment Optimization Under the Nested Logit Model

Assortment Optimization and Pricing Under a Nonparametric Tree Choice Model

Multi-Location Assortment Optimization Under Capacity Constraints

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