scholarly journals Combinatorial Assortment Optimization

2021 ◽  
Vol 9 (1) ◽  
pp. 1-34
Author(s):  
Nicole Immorlica ◽  
Brendan Lucier ◽  
Jieming Mao ◽  
Vasilis Syrgkanis ◽  
Christos Tzamos
Keyword(s):  
Choice Function ◽  
Optimization Problem ◽  
Choice Model ◽  
Exact Algorithm ◽  
Convenience Store ◽  
Valuation Function ◽  
Probabilistic Choice ◽  
Assortment Optimization ◽  
Relative Value ◽  
Potential Customers

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a choice model in which each consumer selects a utility-maximizing bundle subject to a private valuation function, and study the complexity of the resulting optimization problem. Our main result is an exact algorithm for additive k -demand valuations, under a model of vertical differentiation in which customers agree on the relative value of each pair of items but differ in their absolute willingness to pay. For valuations that are vertically differentiated but not necessarily additive k -demand, we show how to obtain constant approximations under a “well-priced” condition, where each product’s price is sufficiently high. We further show that even for a single customer with known valuation, any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS and that no FPTAS exists even when the valuation is succinctly representable.

Assortment Optimization Under the Paired Combinatorial Logit Model

2020 ◽  
Vol 68 (3) ◽  
pp. 741-761
Author(s):  
Heng Zhang ◽  
Paat Rusmevichientong ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Choice Model ◽  
Correlation Structure ◽  
Choice Process ◽  
General Correlation ◽  
Performance Guarantees ◽  
Assortment Optimization

When retailers decide which assortment of products to offer, they can make use of a choice model that describes how customers choose and substitute among the products. The key is to use a choice model that faithfully captures the choice process of customers, while making sure that the corresponding problem of finding the revenue-maximizing assortment remains tractable. In “Assortment Optimization Under the Paired Combinatorial Logit Model,” Zhang, Rusmevichientong, and Topaloglu consider the paired combinatorial logit model to capture the choice process of customers. This choice model uses a utility maximization framework to capture the customer choices, and the utilities of the products can have a rather general correlation structure. The authors demonstrate that one can construct algorithms with performance guarantees to solve the assortment optimization problem under this choice model.

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

scholarly journals Mice tune out not in: Violation of prediction drives auditory saliency

2019 ◽  
Author(s):  
Meike M. Rogalla ◽  
Inga Rauser ◽  
Karsten Schulze ◽  
Lasse Osterhagen ◽  
K Jannis Hildebrandt
Keyword(s):  
Auditory Processing ◽  
Choice Model ◽  
Short Term ◽  
Probabilistic Choice ◽  
Auditory Detection ◽  
Irrelevant Distractors ◽  
Serial Correlations ◽  
Low Probability ◽  
Psychophysical Studies

SummarySuccessful navigation in complex acoustic scenes requires focusing on relevant sounds while ignoring irrelevant distractors. It has been argued that the ability to track stimulus statistics and generate predictions supports the choice what to attend and what to ignore. However, the role of these predictions about future auditory events in drafting decisions remains elusive. While most psychophysical studies in humans indicate that expected stimuli serve as implicit cues attracting attention, most work studying physiological auditory processing in animals highlights the detection of unexpected, surprising stimuli. Here, we tested whether in the mouse, target probability is used as an implicit cue attracting attention or whether detection is biased towards low-probability deviants using an auditory detection task. We implemented a probabilistic choice model to investigate whether a possible dependence on stimulus statistics arises from short term serial correlations or from integration over longer periods. Our results demonstrate that target detectability in mice decreases with increasing probability, contrary to humans. We suggest that mice indeed track probability over a time scale of at least several minutes but do not use this information in the same way as humans do: instead of maximizing reward by focusing on high-probability targets, the saliency of a target is determined by surprise.

Online Assortment Optimization with Reusable Resources

2021 ◽  
Author(s):  
Xiao-Yue Gong ◽  
Vineet Goyal ◽  
Garud N. Iyengar ◽  
David Simchi-Levi ◽  
Rajan Udwani ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Online Algorithm ◽  
Random Number ◽  
Optimal Algorithm ◽  
User Preference ◽  
Substitutable Products ◽  
Assortment Optimization ◽  
Myopic Policy ◽  
Expected Revenue ◽  
And Performance

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities [Formula: see text]. In each period t, a user with some preferences (potentially adversarially chosen) who offers a subset of products, St, from the set of available products arrives at the seller’s platform. The user selects product [Formula: see text] with probability given by the preference model and uses it for a random number of periods, [Formula: see text], that is distributed i.i.d. according to some distribution that depends only on j generating a revenue [Formula: see text] for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative revenue over a finite horizon T. Our main contribution is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, that is, the expected cumulative revenue of the myopic policy is at least half the expected revenue of the optimal policy with full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a nontrivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies. This paper was accepted by Gabriel Weintraub, revenue management and analytics.

Constrained Assortment Optimization Under the Paired Combinatorial Logit Model

2021 ◽  
Author(s):  
Rohan Ghuge ◽  
Joseph Kwon ◽  
Viswanath Nagarajan ◽  
Adetee Sharma
Keyword(s):  
Logit Model ◽  
Choice Model ◽  
Customer Behavior ◽  
Multidimensional Space ◽  
Customer Choice ◽  
Assortment Optimization ◽  
Selected Subset ◽  
Unconstrained Problem ◽  
Key Aspects ◽  
Customer Choice Model

Assortment optimization involves selecting a subset of products to offer to customers in order to maximize revenue. Often, the selected subset must also satisfy some constraints, such as capacity or space usage. Two key aspects in assortment optimization are (1) modeling customer behavior and (2) computing optimal or near-optimal assortments efficiently. The paired combinatorial logit (PCL) model is a generic customer choice model that allows for arbitrary correlations in the utilities of different products. The PCL model has greater modeling power than other choice models, such as multinomial-logit and nested-logit. In “Constrained Assortment Optimization Under the Paired Combinatorial Logit Model,” Ghuge, Kwon, Nagarajan, and and Sharma provide efficient algorithms that find provably near-optimal solutions for PCL assortment optimization under several types of constraints. These include the basic unconstrained problem (which is already intractable to solve exactly), multidimensional space constraints, and partition constraints. The authors also demonstrate via extensive experiments that their algorithms typically achieve over 95% of the optimal revenues.

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.

Constrained Assortment Optimization Under the Markov Chain–based Choice Model

2020 ◽  
Vol 66 (2) ◽  
pp. 698-721 ◽  
Author(s):  
Antoine Désir ◽  
Vineet Goyal ◽  
Danny Segev ◽  
Chun Ye
Keyword(s):  
Markov Chain ◽  
Choice Model ◽  
Assortment Optimization
Sign in / Sign up

Export Citation Format

Share Document