Inventory Balancing with Online Learning
Name
SSRN-id3236533.pdf
Description
Submitted version
Size
1.44 MB
Format
Adobe PDF
Checksum (MD5)
6d65ecb0337300a7d858b9ab2d591b32
Author(s)
Cheung, Wang Chi
Ma, Will
Simchi-Levi, David
Wang, Xinshang
Date Issued
2022
Journal
Management Science
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Cheung, Wang Chi, Ma, Will, Simchi-Levi, David and Wang, Xinshang. 2022. "Inventory Balancing with Online Learning." Management Science, 68 (3).
Version
Original manuscript
Abstract
We study a general problem of allocating limited resources to heterogeneous customers over time under model uncertainty. Each type of customer can be serviced using different actions, each of which stochastically consumes some combination of resources and returns different rewards for the resources consumed. We consider a general model in which the resource consumption distribution associated with each customer type–action combination is not known but is consistent and can be learned over time. In addition, the sequence of customer types to arrive over time is arbitrary and completely unknown. We overcome both the challenges of model uncertainty and customer heterogeneity by judiciously synthesizing two algorithmic frameworks from the literature: inventory balancing, which “reserves” a portion of each resource for high-reward customer types that could later arrive based on competitive ratio analysis, and online learning, which “explores” the resource consumption distributions for each customer type under different actions based on regret analysis. We define an auxiliary problem, which allows for existing competitive ratio and regret bounds to be seamlessly integrated. Furthermore, we propose a new variant of upper confidence bound (UCB), dubbed lazyUCB, which conducts less exploration in a bid to focus on “exploitation” in view of the resource scarcity. Finally, we construct an information-theoretic family of counterexamples to show that our integrated framework achieves the best possible performance guarantee. We demonstrate the efficacy of our algorithms on both synthetic instances generated for the online matching with stochastic rewards problem under unknown probabilities and a publicly available hotel data set. Our framework is highly practical in that it requires no historical data (no fitted customer choice models or forecasting of customer arrival patterns) and can be used to initialize allocation strategies in fast-changing environments. This paper was accepted by J. George Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MNSC.2021.4216
