Author
Listed:
- Omar Besbes
(Graduate School of Business, Columbia University, New York, New York 10027)
- Yash Kanoria
(Graduate School of Business, Columbia University, New York, New York 10027)
- Akshit Kumar
(Graduate School of Business, Columbia University, New York, New York 10027)
Abstract
Dynamic resource allocation problems are ubiquitous, arising in inventory management, order fulfillment, online advertising, and other applications. We initially focus on one of the simplest models of online resource allocation: the multisecretary problem. In the multisecretary problem, a decision maker sequentially hires up to B out of T candidates, and candidate ability values are independently and identically distributed from a distribution F on [ 0 , 1 ] . First, we investigate fundamental limits on performance as a function of the value distribution under consideration. We quantify performance in terms of regret , defined as the additive loss relative to the best performance achievable in hindsight. We present a novel fundamental regret lower bound scaling of Ω ( T 1 2 − 1 2 ( 1 + β ) ) for distributions with gaps in their support, with β quantifying the mass accumulation of types (values) around these gaps. This lower bound contrasts with the constant and logarithmic regret guarantees shown to be achievable in prior work, under specific assumptions on the value distribution. Second, we introduce a novel algorithmic principle, conservativeness with respect to gaps (CwG), which yields near-optimal performance with regret scaling of O ˜ ( T 1 2 − 1 2 ( 1 + β ) ) for any distribution in a class parameterized by the mass accumulation parameter β . We then turn to operationalizing the CwG principle across dynamic resource allocation problems. We study a general and practical algorithm, repeatedly act using multiple simulations, which simulates possible futures to estimate a hindsight-based approximation of the value-to-go function. We establish that this algorithm inherits theoretical performance guarantees of algorithms tailored to the distribution of resource requests, including our CwG-based algorithm, and find that it outperforms them in numerical experiments.
Suggested Citation
Omar Besbes & Yash Kanoria & Akshit Kumar, 2025.
"Dynamic Resource Allocation: Algorithmic Design Principles and Spectrum of Achievable Performances,"
Operations Research, INFORMS, vol. 73(3), pages 1273-1288, May.
Handle:
RePEc:inm:oropre:v:73:y:2025:i:3:p:1273-1288
DOI: 10.1287/opre.2022.0504
Download full text from publisher
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1273-1288. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.