The Discrete Moment Problem with Nonconvex Shape Constraints

Xi Chen (), Simai He (), Bo Jiang (), Christopher Thomas Ryan () and Teng Zhang ()
Additional contact information
Xi Chen: Stern School of Business, New York University, New York, New York 10012
Simai He: Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Yangpu District, Shanghai 200433, P.R. China
Bo Jiang: Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Yangpu District, Shanghai 200433, P.R. China
Christopher Thomas Ryan: UBC Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Teng Zhang: Department of Management Science and Engineering, Stanford University, Stanford, California 94305

Operations Research, 2021, vol. 69, issue 1, 279-296

Abstract: The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with additional shape constraints that guarantee the worst-case distribution is either log-concave (LC), has an increasing failure rate (IFR), or increasing generalized failure rate (IGFR). These classes of shape constraints have not previously been studied in the literature, in part due to their inherent nonconvexities. Nonetheless, these classes are useful in practice, with applications in revenue management, reliability, and inventory control. We characterize the structure of optimal extreme point distributions under these constraints. We show, for example, that an optimal extreme point solution to a moment problem with m moments and LC shape constraints is piecewise geometric with at most m pieces. This optimality structure allows us to design an exact algorithm for computing optimal solutions in a low-dimensional space of parameters. We also leverage this structure to study a robust newsvendor problem with shape constraints and compute optimal solutions.

Keywords: robust optimization; moment problem; shape constraints; reverse convex programming (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1287/opre.2020.1990 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:69:y:2021:i:1:p:279-296

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().