Multi-Stage and Multi-Customer Assortment Optimization With Inventory Constraints

62 Pages Posted: 30 Aug 2019 Last revised: 27 Jul 2020

See all articles by Elaheh Fata

Elaheh Fata

Queen's University - Smith School of Business

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: August 26, 2019

Abstract

We consider an assortment optimization problem where a customer chooses a single item from a sequence of sets shown to her, while limited inventories constrain the items offered to customers over time. In the special case where all of the assortments have size one, our problem captures the online stochastic matching with timeouts problem. For this problem, we derive a polynomial-time approximation algorithm which earns at least 1-ln(2-1/e), or 0.51, of the optimum. This improves upon the previous-best approximation ratio of 0.46, and furthermore, we show that it is tight. For the general assortment problem, we establish the first constant-factor approximation ratio of 0.09 for the case that different types of customers value items differently, and an approximation ratio of 0.15 for the case that different customers value each item the same. Our algorithms are based on rounding an LP relaxation for multi-stage assortment optimization, and improve upon previous randomized rounding schemes to derive the tight ratio of 1-ln(2-1/e).

Keywords: Assortment Optimization, Online Matching, Online Marketplaces, Online Advertising

Suggested Citation

Fata, Elaheh and Ma, Will and Simchi-Levi, David, Multi-Stage and Multi-Customer Assortment Optimization With Inventory Constraints (August 26, 2019). Available at SSRN: https://ssrn.com/abstract=3443109 or http://dx.doi.org/10.2139/ssrn.3443109

Elaheh Fata (Contact Author)

Queen's University - Smith School of Business ( email )

Smith School of Business - Queen's University
143 Union Street
Kingston, Ontario K7L 3N6
Canada

Will Ma

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

New York, NY
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

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