Online Facility Location: Running Stores on Wheels with Spatial Demand Learning

59 Pages Posted: 28 Sep 2021 Last revised: 8 Jan 2024

See all articles by Junyu Cao

Junyu Cao

University of Texas at Austin - Red McCombs School of Business

Wei Qi

Tsinghua University - Department of Industrial Engineering; McGill University - Desautels Faculty of Management

Yan Zhang

McGill University, Desautels Faculty of Management, Students

Date Written: September 18, 2021

Abstract

A shift toward shopping at (autonomous) wheeled vending stores is redefining urban retail. Compared with traditional brick-and-mortar stores, such mobile stores are cost-efficient to deploy and adaptive to fast-evolving business environments. However, mobile stores are confronted with unknown demand and limited capacity. Store mobility enables demand learning and profit maximization, yet an optimal dynamic store location policy remains unclear. We model this “learning-and-earning” problem by taking optimistic actions under parameter uncertainty. The joint optimization over parameter and action set is complicated by the combinatorial nature and infinite choices within the action set. We overcome these challenges by leveraging continuous approximation methods, and then propose a continuous-approximation optimistic (CA-O) learning framework under some special problem structures. Nevertheless, for more general scenarios, the problem remains intricate due to the nonconvexity in unknown parameters. We alternatively propose a CA-O faster learning algorithm by utilizing first-order approximation techniques and further proving a closed-form gradient to guarantee computational efficiency. We theoretically analyze and numerically validate the regret for the proposed algorithms. In a Toronto case study, our algorithm significantly outperforms baselines. Mobile stores earn higher profits than brick-and-mortar stores through demand learning and store mobility. More broadly, this paper envisions the future landscape of urban retail enhanced by omnipresent mobile facilities.

Keywords: mobile retail, facility location, contextual bandits, continuous approximation, joint learning and optimization

Suggested Citation

Cao, Junyu and Qi, Wei and Zhang, Yan, Online Facility Location: Running Stores on Wheels with Spatial Demand Learning (September 18, 2021). Available at SSRN: https://ssrn.com/abstract=3930617 or http://dx.doi.org/10.2139/ssrn.3930617

Junyu Cao (Contact Author)

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX
United States

Wei Qi

Tsinghua University - Department of Industrial Engineering ( email )

Beijing
China

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke Street West
Montreal, Quebec H3A 1G5
Canada

Yan Zhang

McGill University, Desautels Faculty of Management, Students ( email )

1001 Sherbrooke Street West
Montreal, Quebec H3A 1G5
Canada

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