Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints

2020 ◽  
Author(s):  
Mika Sumida ◽  
Guillermo Gallego ◽  
Paat Rusmevichientong ◽  
Huseyin Topaloglu ◽  
James Davis
Keyword(s):  
Expected Utility ◽  
Logit Model ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Solution Quality ◽  
Assortment Optimization ◽  
Unimodular Matrix ◽  
Expected Revenue

We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, we discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue. This paper was accepted by Omar Besbes, revenue management and market analytics.

Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings

2020 ◽  
Vol 32 (3) ◽  
pp. 835-853 ◽  
Author(s):  
Nan Liu ◽  
Yuhang Ma ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Optimization Problem ◽  
Approximation Scheme ◽  
Optimization Problems ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Polynomial Time Approximation Scheme ◽  
Assortment Optimization ◽  
Last Stage ◽  
Expected Revenue

We consider assortment optimization problems, where the choice process of a customer takes place in multiple stages. There is a finite number of stages. In each stage, we offer an assortment of products that does not overlap with the assortments offered in the earlier stages. If the customer makes a purchase within the offered assortment, then the customer leaves the system with the purchase. Otherwise, the customer proceeds to the next stage, where we offer another assortment. If the customer reaches the end of the last stage without a purchase, then the customer leaves the system without a purchase. The choice of the customer in each stage is governed by a multinomial logit model. The goal is to find an assortment to offer in each stage to maximize the expected revenue obtained from a customer. For this assortment optimization problem, it turns out that the union of the optimal assortments to offer in each stage is nested by revenue in the sense that this union includes a certain number of products with the largest revenues. However, it is still difficult to figure out the stage in which a certain product should be offered. In particular, the problem of finding an assortment to offer in each stage to maximize the expected revenue obtained from a customer is NP hard. We give a fully polynomial time approximation scheme for the problem when the number of stages is fixed.

Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters

2014 ◽  
Vol 23 (11) ◽  
pp. 2023-2039 ◽  
Author(s):  
Paat Rusmevichientong ◽  
David Shmoys ◽  
Chaoxu Tong ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Random Choice ◽  
Assortment Optimization

scholarly journals Assortment optimization under a multinomial logit model with position bias and social influence

4OR ◽  
2015 ◽  
Vol 14 (1) ◽  
pp. 57-75 ◽  
Author(s):  
Andrés Abeliuk ◽  
Gerardo Berbeglia ◽  
Manuel Cebrian ◽  
Pascal Van Hentenryck
Keyword(s):  
Social Influence ◽  
Logit Model ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Position Bias ◽  
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.

Capacitated Assortment Optimization: Hardness and Approximation

2021 ◽  
Author(s):  
Antoine Désir ◽  
Vineet Goyal ◽  
Jiawei Zhang
Keyword(s):  
Large Class ◽  
Logit Model ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Choice Models ◽  
Capacity Constraint ◽  
Linear Functions ◽  
Nested Logit ◽  
Assortment Optimization ◽  
Unconstrained Problem

Assortment optimization is an important problem arising in various applications. In many practical settings, the assortment is subject to a capacity constraint. In “Capacitated Assortment Optimization: Hardness and Approximation,” Désir, Goyal, and Zhang study the capacitated assortment optimization problem. The authors first show that adding a general capacity constraint makes the problem NP-hard even for the simple multinomial logit model. They also show that under the mixture of multinomial logit model, even the unconstrained problem is hard to approximate within any reasonable factor when the number of mixtures is not constant. In view of these hardness results, the authors present near-optimal algorithms for a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit, and d-level nested logit choice models. In fact, their approach extends to a large class of objective functions that depend only on a small number of linear functions.

Omnichannel Assortment Optimization Under the Multinomial Logit Model with a Features Tree

2021 ◽  
Author(s):  
Venus Lo ◽  
Huseyin Topaloglu
Keyword(s):  
Polynomial Time ◽  
Logit Model ◽  
Approximation Scheme ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Polynomial Time Approximation Scheme ◽  
Online Store ◽  
Time Approximation ◽  
Assortment Optimization ◽  
Polynomial Time Approximation

Problem definition: We consider the assortment optimization problem of a retailer that operates a physical store and an online store. The products that can be offered are described by their features. Customers purchase among the products that are offered in their preferred store. However, customers who purchase from the online store can first test out products offered in the physical store. These customers revise their preferences for online products based on the features that are shared with the in-store products. The full assortment is offered online, and the goal is to select an assortment for the physical store to maximize the retailer’s total expected revenue. Academic/practical relevance: The physical store’s assortment affects preferences for online products. Unlike traditional assortment optimization, the physical store’s assortment influences revenue from both stores. Methodology: We introduce a features tree to organize products by features. The nonleaf vertices on the tree correspond to features, and the leaf vertices correspond to products. The ancestors of a leaf correspond to features of the product. Customers choose among the products within their store’s assortment according to the multinomial logit model. We consider two settings; either all customers purchase online after viewing products in the physical store, or we have a mix of customers purchasing from each store. Results: When all customers purchase online, we give an efficient algorithm to find the optimal assortment to display in the physical store. With a mix of customers, the problem becomes NP-hard, and we give a fully polynomial-time approximation scheme. We numerically demonstrate that we can closely approximate the case where products have arbitrary combinations of features without a tree structure and that our fully polynomial-time approximation scheme performs remarkably well. Managerial implications: We characterize conditions under which it is optimal to display expensive products with underrated features and expose inexpensive products with overrated features.

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