Parameterized Approximations for the Two-sided Assortment Optimization

A. Ahmed, M. G. Sohoni, and C. Bandi. “Parameterized approximations for the two-sided assortment optimization”. In: Operations Research Letters 50.4 (2022), pp. 399–406

Posted: 4 Oct 2022 Last revised: 7 Oct 2022

Date Written: September 15, 2022

Abstract

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.

Keywords: Assortment Optimization, Online Platforms, Two-sided \sep Parametric Bounds

Suggested Citation

Ahmed, Asrar and Sohoni, Milind G. and Bandi, Chaitanya, Parameterized Approximations for the Two-sided Assortment Optimization (September 15, 2022). A. Ahmed, M. G. Sohoni, and C. Bandi. “Parameterized approximations for the two-sided assortment optimization”. In: Operations Research Letters 50.4 (2022), pp. 399–406, Available at SSRN: https://ssrn.com/abstract=4219424

Asrar Ahmed

Independent

Milind G. Sohoni (Contact Author)

Indian School of Business ( email )

Hyderabad, Gachibowli 500 032
India

HOME PAGE: http://www.isb.edu/faculty/milind_sohoni

Chaitanya Bandi

Operations Department, Kellogg School of Management, Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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