Online Assortment Optimization for Two-sided Matching Platforms

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.

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MODEL OF ASSORTMENT OPTIMIZATION AND INVENTORY MANAGEMENT IN ENTERPRISE

Economics and Finance ◽

10.51586/2311-3413.2021.9.1.31.46 ◽

2021 ◽

Vol 9 (1) ◽

pp. 31-46

Author(s):

Ibrokhim Xabibullayev ◽

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Ruslana Zhovnovach ◽

Mariia Petrova ◽

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...

Keyword(s):

Inventory Management ◽

Coefficient Of Variation ◽

Methodological Approach ◽

Integrated Approach ◽

Optimization Criterion ◽

Commercial Activity ◽

Commercial Activities ◽

Individual Product ◽

Assortment Optimization

The actual problems of work in the sphere of organization of supply and sale are considered, the existing developments in the sphere of modeling and optimization of commercial activity of the wholesale trading enterprises are analyzed. The necessity of a comprehensive approach to improving the commercial activities of wholesalers is substantiated. The composition of the solutions included in the integrated approach is determined by the sole purpose, practical possibilities of its implementation and implementation at the wholesale enterprises and is based on the analysis of actual problems of the industry as a whole, interdependence in the work of departments, development of a single optimization criterion. The effectiveness of the integrated approach is based on the fact that for the sake of maximum result it is important not to isolate the development of individual operations, but to improve the entire purchasing system of the wholesale enterprise as a whole. The scientific and methodological approach of carrying out the integrated ABC-XYZ analysis of a range of a trading enterprise by its combination with R/S analysis, which acts as a criterion for the effectiveness of the XYZ analysis and an indicator of the possibility of forecasting the dynamics of sales of individual product groups, has been improved. XYZ analysis, based on the calculation of the coefficient of variation, when there are deterministic factors such as seasonality, cyclicality or trend in a series of determinants, shows erroneous results. Therefore, it is suggested to use R/S analysis to evaluate the quality of the XYZ analysis and to pre-process the data. This will allow us to draw more adequate conclusions about the possibility of forecasting the dynamics of sales of certain product groups in the future.

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Constrained Assortment Optimization Under the Paired Combinatorial Logit Model

Operations Research ◽

10.1287/opre.2021.2188 ◽

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.

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Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings

INFORMS Journal on Computing ◽

10.1287/ijoc.2019.0910 ◽

2020 ◽

Vol 32 (3) ◽

pp. 835-853 ◽

Cited By ~ 3

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.

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