Online Assortment Optimization with Reusable Resources

20 Pages Posted: 7 Mar 2019

See all articles by Xiao-Yue Gong

Xiao-Yue Gong

Massachusetts Institute of Technology (MIT)

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Rajan Udwani

Columbia University

Shuangyu Wang

Columbia University

Date Written: February 25, 2019

Abstract

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities c1,...,cn. In each period t, a user with some preferences (potentially adversarially chosen) arrives to the seller's platform who offers a subset of products St, from the set of available products. The user selects product j ∈ St with probability given by the preference model and uses it for a random number of periods, ˜ tj that is distributed i.i.d. according to some distribution that depends only on j generating a revenue rj(˜ tj) for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative over a finite horizon T. Our main contribution in this paper 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, i.e., the expected cumulative revenue of the myopic policy is at least 1/2 times the expected revenue of an optimal policy that has 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.

Keywords: Online Algorithms, Assortment Optimization, Resource Allocation, Competitive Ratio

Suggested Citation

Gong, Xiao-Yue and Goyal, Vineet and Iyengar, Garud and Simchi-Levi, David and Udwani, Rajan and Wang, Shuangyu, Online Assortment Optimization with Reusable Resources (February 25, 2019). Available at SSRN: https://ssrn.com/abstract=3334789 or http://dx.doi.org/10.2139/ssrn.3334789

Xiao-Yue Gong

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Vineet Goyal

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States
+1 212-854-4594 (Phone)
+1 212-854-8103 (Fax)

David Simchi-Levi

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

MA
United States

Rajan Udwani (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Shuangyu Wang

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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