Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models

2017 ◽  
Author(s):  
Wang Chi Cheung ◽  
David Simchi-Levi
Keyword(s):  
Optimization Problems ◽  
Multinomial Logit ◽  
Choice Models ◽  
Thompson Sampling ◽  
Assortment Optimization

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.

scholarly journals Assortment Optimization Under Consider-Then-Choose Choice Models

2020 ◽  
Author(s):  
Ali Aouad ◽  
Vivek Farias ◽  
Retsef Levi
Keyword(s):  
Predictive Power ◽  
Optimization Problems ◽  
Choice Models ◽  
Empirical Literature ◽  
Data Sets ◽  
Prediction Errors ◽  
Programming Framework ◽  
Assortment Optimization ◽  
Computational Aspects ◽  
Two Phases

Consider-then-choose models, borne out by empirical literature in marketing and psychology, explain that customers choose among alternatives in two phases, by first screening products to decide which alternatives to consider and then ranking them. In this paper, we develop a dynamic programming framework to study the computational aspects of assortment optimization under consider-then-choose premises. Although nonparametric choice models generally lead to computationally intractable assortment optimization problems, we are able to show that for many empirically vetted assumptions on how customers consider and choose, our resulting dynamic program is efficient. Our approach unifies and subsumes several specialized settings analyzed in previous literature. Empirically, we demonstrate the predictive power of our modeling approach on a combination of synthetic and real industry data sets, where prediction errors are significantly reduced against common parametric choice models. In synthetic experiments, our algorithms lead to practical computation schemes that outperform a state-of-the-art integer programming solver in terms of running time, in several parameter regimes of interest. This paper was accepted by Yinyu Ye, optimization.

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.

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 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

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

Development of disaggregate mode choice models of intercity travel in Canada

1992 ◽  
Vol 19 (6) ◽  
pp. 965-974 ◽  
Author(s):  
Walid M. Abdelwahab ◽  
J. David Innes ◽  
Albert M. Stevens
Keyword(s):  
Travel Behavior ◽  
Mode Choice ◽  
Geographical Location ◽  
Predictive Ability ◽  
Multinomial Logit ◽  
Choice Models ◽  
Trip Purpose ◽  
Market Shares ◽  
Intercity Travel ◽  
Statistics Canada

This paper reports and discusses the results of an effort to develop disaggregate behavioral mode choice models of intercity travel in Canada. Currently available data bases of intercity travel in Canada are reviewed. The feasibility of using data from national travel surveys to develop statistically reliable intercity mode choice models is examined, and directions for future disaggregate data collection efforts are offered. The models developed are of the multinomial logit (MNL) type which included all intercity passenger travel modes: auto, air, bus, and rail. For purposes of estimation, the travel market was segmented by trip length (short, long); trip purpose (business, recreational); and geographical location of the trip (east, west). Then, a separate model was estimated in each sector. The models were estimated using the data collected by Statistics Canada as a part of the Labor Force Survey (The Canadian Travel Survey, CTS). The quality of the calibrated models varied from one region to another and from one travel sector to another. Overall, the models were reasonably accurate in predicting modal shares of the most frequently used modes (auto and air). The underrepresentation of the bus and rail modes in the data sets led to a deterioration in the performance of the models in predicting market shares of these two modes. More specifically, the predictive ability of the models measured by the likelihood ratio index varied from a low of 0.58 in the short travel sector to a high of 0.94 in the long travel sector. The transferability of the models described in this study was recently examined by Abdelwahab (1991). Key words: mode choice, disaggregate, travel behavior, multinomial logit, intercity, data base.

Transferability of intercity disaggregate mode choice models in Canada

1991 ◽  
Vol 18 (1) ◽  
pp. 20-26 ◽  
Author(s):  
Walid M. Abdelwahab
Keyword(s):  
Travel Behavior ◽  
Travel Demand ◽  
Mode Choice ◽  
Model Development ◽  
Predictive Ability ◽  
Multinomial Logit ◽  
Choice Models ◽  
Data Sets ◽  
Policy Analysts ◽  
Transportation Studies

In many transportation studies, the time span of data collection, model development, and analysis is often too long to be responsive to the needs of policy analysts and decision makers. This problem is often exacerbated in situations with severely constrained analysis resources. Therefore, it is often useful to transfer a model from one area to another. Model transfer is defined as the application of a model developed in one area to describe the corresponding behavior in another area. This paper examines the transferability of a class of models used in intercity travel demand analysis. Specifically, disaggregate mode choice models of the multinomial logit type are developed for two regions in Canada, and some established measures of transferability are applied to assess the potential of calibrating these models in one region and applying them in the other. Comparison of mode choice models estimated on data sets from the two regions yielded inconclusive results regarding model transferability. In general, transferred models were found to be 18–23% less accurate than local models in predicting modal shares. Adjusting models' parameters to reflect observed modal shares in the application context improved the predictive ability of the models by about 10%. Key words: transferability, mode choice, disaggregate, travel behavior, multinomial logit, intercity.

Sign in / Sign up

Export Citation Format

Share Document